Podcast appearances and mentions of mike let

Tisha Jones, Assessment as a Shared Journey: Cultivating Partnerships with Families & Caregivers ROUNDING UP: SEASON 3 | EPISODE 16 Families and caregivers play an essential role in students' success in school and in shaping their identities as learners. Therefore, establishing strong partnerships with families and caregivers is crucial for equitable teaching and learning. This episode is designed to help educators explore the importance of collaborating with families and caregivers and learn strategies for shifting to asset-based communication. BIOGRAPHY Tisha Jones is the senior manager of assessment at The Math Learning Center. Previously, Tisha taught math to elementary and middle school students as well as undergraduate and graduate math methods courses at Georgia State University. TRANSCRIPT Mike Wallus: As educators, we know that families and caregivers play an essential role in our students' success at school. With that in mind, what are some of the ways we can establish strong partnerships with caregivers and communicate about students' progress in asset-based ways? We'll explore these questions with MLC's [senior] assessment manager, Tisha Jones, on this episode of Rounding Up.  Welcome back to the podcast, Tisha. I think you are our first guest to appear three times. We're really excited to talk to you about assessment and families and caregivers.  Tisha Jones: I am always happy to talk to you, Mike, and I really love getting to share new ideas with people on your podcast.  Mike: So, we've titled this episode “Assessment as a Shared Journey with Families & Caregivers,” and I feel like that title—especially the words “shared journey”—say a lot about how you hope educators approach this part of their practice.  Tisha: Absolutely.  Mike: So, I want to start by being explicit about how we at The Math Learning Center think about the purpose of assessment because I think a lot of the ideas and the practices and the suggestions that you're about to offer flow out of that way that we think about the purpose.  Tisha: When we think about the purpose of assessment at The Math Learning Center, what sums it up best to me is that all assessment is formative, even if it's summative, which is a belief that you'll find in our Assessment Guide. And what that means is that assessment really is to drive learning. It's for the purpose of learning. So, it's not just to capture, “What did they learn?,” but it's, “What do they need?,” “How can we support kids?,” “How can we build on what they're learning?” over and over and over again. And so, there's no point where we're like, “OK, we've assessed it and now the learning of that is in the past.” We're always trying to build on what they're doing, what they've learned so far.  Mike: You know, I've also heard you talk about the importance of an asset-focused approach to assessment. So, for folks who haven't heard us talk about this in the past, what does that mean, Tisha?  Tisha: So that means starting with finding the things that the kids know how to do and what they understand instead of the alternative, which is looking for what they don't know, looking for the deficits in their thinking. We're looking at, “OK, here's the evidence for all the things that they can do,” and then we're looking to think about, “OK, what are their opportunities for growth?” Mike: That sounds subtle, but it is so profound a shift in thinking about what is happening when we're assessing and what we're seeing from students. How do you think that change in perspective shifts the work of assessing, but also the work of teaching?  Tisha: When I think about approaching assessment from an asset-based perspective—finding the things that kids know how to do, the things that kids understand—one, I am now on a mission to find their brilliance. I am just this brilliance detective. I'm always looking for, “What is that thing that this kid can shine at?” That's one, and a different way of thinking about it just to start with.  And then I think the other thing, too, is, I feel like when you find the things that they're doing, I can think about, “OK, what do I need to know? What can I do for them next to support them in that next step of growth?”  Mike: I think that sounds fairly simple, but there's something very different about thinking about building from something versus, say, looking for what's broken.  Tisha: For sure. And it also helps build relationships, right? If you approach any relationship from a deficit perspective, you're always focusing on the things that are wrong. And so, if we're talking about building stronger relationships with kids, coming from an asset-based perspective helps in that area too.  Mike: That's a great pivot point because if we take this notion that the purpose of assessment is to inform the ways that we support student learning, it really seems like that has a major set of implications for how and what and even why we would communicate with families and caregivers.  So, while I suspect there isn't a script for the type of communication, are there some essential components that you'd want to see in an asset-focused assessment conversation that an educator would have with a family or with their child's caregivers?  Tisha: Well, before thinking about a singular conversation, I want to back it up and think about—over the course of the school year. And I think that when we start the communication, it has to start before that first assessment. It has to start before we've seen a piece of kids' work. We have to start building those relationships with families and caregivers. We need to invite them into this process. We need to give them an opportunity to understand what we think about assessment. How are we approaching it? When we send things home, and they haven't heard of things like “proficiency” or “meeting current expectations”—those are common words that you'll see throughout the Bridges assessment materials—if parents haven't seen that, if families and caregivers haven't heard from you on what that means for you in your classroom at your school, then they have questions. It feels unfamiliar. It feels like, “Wait, what does this mean about how my child is doing in your class?”  And so, we want to start this conversation from the very beginning of the school year and continue it on continuously. And it should be this open invitation for them to participate in this process too, for them to share what they're seeing about their student at home, when they're talking about math or they're hearing how their student is talking about math. We want to know those things because that informs how we approach the instruction in class.  Mike: Let's talk about that because it really strikes me that what you're describing in terms of the meaning of proficiency or the meaning of meeting expectations—that language is likely fairly new to families and caregivers.  And I think the other thing that strikes me is, families and caregivers have their own lived experience with assessment from when they were children, perhaps with other children. And that's generally a mixed bag at best. Folks have this set of ideas about what it means when the teacher contacts them and what assessment means. So, I really hear what you're saying when you're talking about, there's work that educators need to do at the start of the year to set the stage for these conversations.  Let's try to get a little bit specific, though. What are some of the practices that you'd want teachers to consider when they're thinking about their communication?  Tisha: So, I think that starting at the very beginning of the year, most schools do some sort of a curriculum night. I would start by making sure that assessment is a part of that conversation and making sure that you're explaining what assessment means to you. Why are you assessing? What are the different ways that you're assessing? What are some things that [families and caregivers] might see coming home? Are they going to see feedback? Are they going to see scores from assessments? But how were you communicating progress? How do they know how their student is doing? And then also that invitation, right then and there, to be a part of this process, to hear from them, to hear their concerns or their ideas around feedback or the things that they've got questions about.  I would also suggest … really working hard to have that asset-based lens apply to parents and families and caregivers. I know that I have been that parent that was the last one to sign up for the parent teacher conferences, and I'm sending the apologetic email, and I'm begging for a special time slot. So, it didn't mean that I didn't care about my kids. It didn't mean that I didn't care about what they were doing. I was swamped. And so, I think we want to keep finding that asset-based lens for parents and caregivers in the same way that we do for the students.  And then making sure that you're giving them good news, not just bad news. And then making sure when you're sending any communication about how a student is doing, try to be concrete about what you're seeing, right? So, trying to say, “These are the things where I see your child's strengths. These are the strengths that I'm seeing from your student. And these are the areas where we're working on to grow. And this is what we're doing here at school, and this is what you can do to support them at home.” Mike: I was really struck by a piece of what you said, Tisha, when you really made the case for not assuming that the picture that you have in your mind as an educator is clear for families when it comes to assessment. So, really being transparent about how you think about assessment, why you're assessing, and the cadence of when parents or families or caregivers could expect to hear from you and what they could expect as well.  I know for a fact that if my teacher called my family when I was a kid, generally there was a look that came across their face when they answered the phone. And even if it was good news, they didn't think it was good news at the front end of that conversation.  Tisha: I've been there. I had my son's fifth grade teacher call me last year, and I was like, “Oh, what is this?” [laughs] Mike: One of the things that I want to talk about before we finish this conversation is homework. I want to talk a little bit about the purpose of homework. We're having this conversation in the context of Bridges in Mathematics, which is the curriculum that The Math Learning Center publishes. So, while we can't talk about how all folks think about homework, we can talk about the stance that we take when it comes to homework: what its purpose is, how we imagine families and caregivers can engage with their students around it.  Can you talk a little bit about our perspective on homework? How we think about its value, how we think about its purpose? And then we can dig a little bit into what it might look like at home, but let's start with purpose and intent.  Tisha: So, we definitely recognize that there are lots of different ideas about homework, and I think that shows in how we've structured homework through our Bridges units. Most of the time, it's set up so that there's a homework [assignment] that goes with every other session, but it's still optional. So, there's no formal expectation in our curriculum that homework is given on a nightly basis or even on an every-other-night basis. We really have left that up to the schools to determine what is best practice for their population. And I think that is actually what's really the most important thing is, understanding the families and caregivers and the situations that are in your building, and making determinations about homework that makes sense for the students that you're serving. And so, I think we've set homework up in a way that makes it so that it's easy for schools to make those decisions.  Mike: One of the things that I'm thinking about is that—again, I'm going to be autobiographical—when I was a kid, homework went back, it was graded, and it actually counted toward my grade at the end of the semester or the quarter or what have you. And I guess I wonder if a school or a district chose to not go about that, to not have homework necessarily be graded, I wonder if some families and caregivers might wonder, “What's the purpose?” I think we know that there can be a productive and important purpose—even if educators aren't grading homework and adding it to a percentage that is somehow determining students' grades, that it can actually still have purpose. How do you think about the purpose of homework, regardless of whether it's graded or not?  Tisha: So first off, I would just like to advocate not grading homework if I can.  Mike: You certainly can, yeah.  Tisha: [laughs] Mike: Let's talk about that.  Tisha: I think that, one, if we're talking about this idea of putting this score into an average grade or this percentage grade, I think that this is something that has so many different circumstances for kids at home. You have some students who get lots and lots of help. You get some students who do not have help available to them.  Another experience that has been very common when I was teaching was that I would get messages where it was like, “We were doing homework. The kid was in tears, I was in tears. This was just really hard.” And that's just not—I don't ever want that scenario for any student, for any family, for any caregiver, for anybody trying to support a child at home. I used to tell them, “If you are getting to the point where it's that level of frustration, please just stop and send me a message, write it on the homework. Just communicate something that [says,] ‘This was too hard' because that's information now that I can use.”  And so, for me, I think about [how] homework can be an opportunity for students to practice some skills and concepts and things that they've learned at home. It's an opportunity for parents, families, caregivers to see some of the things that the kids are working on at school.  Mike: What do you think is meaningful for homework? And I have kind of two bits to that. What do you think is meaningful for the child? And then, what do you think might be meaningful for the interaction between the child and their family or caregiver? What's the best case for homework? When you imagine a successful or a productive or a meaningful experience with homework at home between child and family and caregiver, what's that look like?  Tisha: Well, one of the things that I've heard families say is, “I don't know how to help my child with blank.” So, then I think it is, “Well, how do we support families and caregivers in knowing what [to] do with homework when we don't know how to tell them what to do?”  So, to me, it's about, how can we restructure the homework experience so that it's not this, “I have to tell you how to do it so you can get the right answer so you can get the grade.” But it's like, “How can I get at more of your thinking? How can I understand then what is happening or what you do know?” So, “We can't get to the answer. OK. So tell me about what you do know, and how can we build from there? How can we build understanding?” And that way it maybe will take some of the pressure off of families and caregivers to help their child get to the right answer.  Mike: What hits me is we've really come full circle with that last statement you made because you could conceivably have a student who really clearly understands a particular problem that might be a piece of homework, [who] might have some ideas that are on the right track, but ultimately perhaps doesn't get to a fully clear answer that is perfect. And you might have a student who at a certain point in time, maybe [for them] the context or the problem itself is profoundly challenging.  And in all of those cases, the question, “Tell me what you do know” or “Tell me what you're thinking” is still an opportunity to draw out the students' ideas and to focus on the assets. Even if the work as you described it is to get them to think about, “What are the questions that are really causing me to feel stuck?” That is a productive move for a family and a caregiver and a student to engage in, to kind of wonder about, “What's going on here that's making me feel stuck?” Because then, as you said, all assessment is formative.  Tisha: Mm-hmm. Mike: That homework that comes back is functioning as a formative assessment, and it allows you to think about your next moves, how you build on what the student knows, or even how you build on the questions that the student is bringing to you.  Tisha: And that's such a great point, too, is there's really more value in them coming back with an incomplete assignment or there's, I don't know, maybe “more value” is not the right way to say it. But there is value in kids coming back with an incomplete assignment or an attempted assignment, but they weren't sure how to get through all the problems—as opposed to a parent who has told their student what to do to get to all of the right answers. And so, now they have all these right answers, but it doesn't really give you a clear picture of what that student actually does understand.  So, I'd much rather have a student attempt the homework and stop because they got too stuck, because now I know that, than having a family [member] or a caregiver—somebody working with that student—feel like if they don't have all of the right answers, then it's a problem.  Mike: I think that's really great guidance, both for teachers as they're trying to set expectations and be transparent with families. But also I think it takes that pressure off of families or caregivers who feel like their work when homework shows up, is to get to a right answer. It just feels like a much more healthy relationship with homework and a much more healthy way to think about the value that it has.  Tisha: Well, in truth, it's a healthier relationship with math overall, right? That math is a process. It's not just—the value is not in just this one right answer or this paper of right answers, but it's really in, “How do we deepen our understanding?,” “How do we help students deepen their understanding and have this more positive relationship with math?” And I think that creating these homework struggles between families and caregivers and the children does not support that end goal of having a more positive relationship with math overall.  Mike: Which is a really important part of what we're looking for in a child's elementary experience.  Tisha: Absolutely.  Mike: I think that's a great place to stop. Tisha Jones, thank you so much for joining us. We would love to have you back at some time. It has been a pleasure talking with you.  Tisha: It's been great talking to you, too, Mike.  Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org  

On this weeks episode of the Slightly Messy Show Mike and Meaghan talk about the dress his daughter wants to wear to the Daddy/ Daughter Dance, the one thing that Meaghan is trying to find from her childhood and the arguments we have replayed in our lives in the shower. 

On this weeks episode of the Slightly Messy Show Mike and Meaghan talk about the dress his daughter wants to wear to the Daddy/ Daughter Dance, the one thing that Meaghan is trying to find from her childhood and the arguments we have replayed in our lives in the shower. 

Rounding Up Season 3 | Episode 3 – Choice as a Foundation for Student Engagement Guest: Drs. Zandra de Araujo and Amber Candela Mike Wallus: As an educator, I know that offering my students choice has a big impact on their engagement, their identity, and their sense of autonomy. That said, I've not always been sure how to design choice into the activities in my classroom, especially when I'm using curriculum. Today we're talking with Drs. Zandra de Araujo and Amber Candela about some of the ways educators can design choice into their students' learning experiences.  Welcome back to the podcast, Zandra and Amber. It is really exciting to have you all with us today.  Zandra de Araujo: Glad to be back.  Amber Candela: Very excited to be here. Mike: So, I've heard you both talk at length about the importance of choice in students' learning experiences, and I wonder if we can start there. Before we talk about the ways you think teachers can design choice in a learning experience, can we just talk about the “why”? How would you describe the impact that choice has on students' learning experiences? Zandra: So, if you think about your own life, how fun would it be to never have a choice in what you get to do during a day? So, you don't get to choose what chores to do, where to go, what order to do things, who to work with, who to talk to. Schools are a very low-choice environment, and those tend to be punitive when you have a low-choice environment. And so, we don't want schools to be that way. We want them to be very free and open and empowering places. Amber: And a lot of times, especially in mathematics, students don't always enjoy being in that space. So, you can get more enjoyment, engagement, and if you have choice with how to engage with the content, you'll have more opportunity to be more curious and joyful and have hopefully better experiences in math. Zandra: And if you think about being able to choose things in your day makes you better able to make choices. And so, I think we want students to be smart consumers and users and creators of mathematics. And if you're never given choice or opportunity to kind of own it, I think that you're at a deficit. Amber: Also, if we want problem-solving people engaged in mathematics, it needs to be something that you view as something you were able to do. And so often we teach math like it's this pre-packaged thing, and it's just your role to memorize this thing that I give you. You don't feel like it's yours to play with. Choice offers more of those opportunities for kids. Zandra: Yeah, it feels like you're a consumer of something that's already made rather than somebody who's empowered to create and use and drive the mathematics that you're using, which would make it a lot more fun.  Mike: Yeah. You all are hitting on something that really clicked for me as I was listening to you talk. This idea that school, as it's designed oftentimes, is low choice. But math, in particular, where historically it has really been, “Let me show you what to do. Let me have you practice the way I showed you how to do it,” rinse and repeat. It's particularly important in math, it feels like, to break out and build a sense of choice for kids. Zandra: Absolutely. Mike: Well, one of the things that I appreciate about the work that both of you do is the way that you advocate for practices that are both really, really impactful and also eminently practical. And I'm wondering if we can dive right in and have you all share some of the ways that you think about designing choice into learning experiences.  Amber: I feel like I want “eminently practical” on a sticker for my laptop. Because I find that is a very satisfying and positive way to describe the work that I do because I do want it to be practical and doable within the constraints of schooling as it currently is, not as we wish it to be. Which, we do want it to be better and more empowering for students and teachers. But also, there are a lot of constraints that we have to work within. So, I appreciate that.  Zandra: I think that choice is meant to be a way of empowering students, but the goal for the instruction should come first. So, I'm going to talk about what I would want from my students in my classroom and then how we can build choice in. Because choice is kind of like the secondary component. So, first you have your learning goals, your aims as a teacher. And then, “How do we empower students with choice in service of that goal?” So, I'll start with number sense because that's a hot topic. I'm sure you all hear a lot about it at the MLC. Mike: We absolutely do. Zandra: So, one of the things I think about when teachers say, “Hey, can you help me think about number sense?” It's like, “Yes, I absolutely can.” So, our goal is number sense. So, let's think about what that means for students and how do we build some choice and autonomy into that. So, one of my favorite things is something like, “Give me an estimate, and we can Goldilocks it,” for example. So, it could be a word problem or just a symbolic problem and say, “OK, give me something that you know is either wildly high, wildly low, kind of close, kind of almost close but not right. So, give me an estimate, and it could be a wrong estimate or a close estimate, but you have to explain why.” So, it takes a lot of number sense to be able to do that. You have infinitely many options for an answer, but you have to avoid the one correct answer. So, you have to actually think about the one correct answer to give an estimate. Or if you're trying to give a close estimate, you're kind of using a lot of number sense to estimate the relationships between the numbers ahead of time. The choice comes in because you get to choose what kind of estimate you want. It's totally up to you. You just have to rationalize your idea. Mike: That's awesome. Amber, your turn. Amber: Yep. So related to that is a lot of math goes forward. We give kids the problem, and we want them to come up with the answer. A lot of the work that we've been doing is, “OK, if I give you the answer, can you undo the problem?” I'll go multiplication. So, we do a lot with, “What's seven times eight?” And there's one answer, and then kids are done. And you look for that answer as the teacher, and once that answer has been given, you're kind of like, “OK, here. I'm done with what I'm doing.” But instead, you could say, “Find me numbers whose product is 24.” Now you've opened up what it comes to. There's more access for students. They can come up with more than one solution, but it also gets kids to realize that math doesn't just go one way. It's not, “Here's the problem, find the answer.” It's “Here's the answer, find the problem.” And that also goes to the number sense. Because if students are able to go both ways, they have a better sense in their head around what they're doing and undoing. And you can do it with a lot of different problems. Zandra: And I'll just add in that that's not specific to us. Barb Dougherty had really nice article in, I think, Teaching Children Mathematics, about reversals at some point. And other people have shown this idea as well. So, we're really taking ideas that are really high uptake, we think, and sharing them again with teachers to make sure that they've seen ways that they can do it in their own classroom. Mike: What strikes me about both of these is, the structure is really interesting. But I also think about what the output looks like when you offer these kinds of choices. You're going to have a lot of kids doing things like justifying or using language to help make sense of the “why.” “Why is this one totally wrong, and why is this one kind of right?” And “Why is this close, but maybe not exact?” And to go to the piece where you're like, “Give me some numbers that I can multiply together to get to 24.” There's more of a conversation that comes out of that. There's a back and forth that starts to develop, and you can imagine that back and forth bouncing around with different kids rather than just kind of kid says, teacher validates, and then you're done. Zandra: Yeah, I think one of the cool things about choice is giving kids choice means that there's more variety and diversity of ideas coming in. And that's way more interesting to talk about and rationalize and justify and make sense of than a single correct answer or everybody's doing the same thing. So, I think, not only does it give kids more ownership, it has more access. But also, it just gives you way more interesting math to think and talk about. Mike: Let's keep going. Zandra: Awesome. So, I think another one, a lot of my work is with multilingual students. I really want them to talk. I want everybody to talk about math. So, this goes right to what you were just saying. So, one of the ways that we can easily say, “OK, we want more talk.” So how do we build that in through choice is to say, “Let's open up what you choose to share with the class.” So, there have been lots of studies done on the types of questions that teachers ask: tend to be closed, answer-focused, like single-calculation kind of questions. So, “What is the answer? Who got this?” You know, that kind of thing? Instead, you can give students choices, and I think a lot of teachers have done something akin to this with sentence starters or things. But you can also just say, instead of a sentence starter to say what your answer is, “I agree with X because of Y.” You can also say, “You can share an incorrect answer that you know is wrong because you did it, and it did not work out. You can also share where you got stuck because that's valuable information for the class to have.” You could also say, “I don't want to really share my thinking, my solution because it's not done, but I'll show you my diagram.” And so, “Let me show you a visual.” And just plop it up on the screen. So, there are a lot of different things you could share a question that you have because you're not sure, and it's just a related question. Instead of always sharing answers, let kids open up what they may choose to share, and you'll get more kids sharing. Because answers are kind of scary because you're expecting a correct answer often. And so, when you share and open up, then it's not as scary. And everybody has something to offer because they have a choice that speaks to them. Amber: And kids don't want to be wrong. People don't want to be wrong. “I don't want to give you a wrong answer.” And we went to the University of Georgia together, but Les Steffe always would say, “No child is ever wrong. They're giving you an answer with a purpose behind what that answer is. They don't actually believe that's a wrong answer that they're giving you.” And so, if you open up the space … And teachers say, “We want spaces to be safe, we want kids to want to come in and share.” But are we actually structuring spaces in that way? And so, some of the ideas that we're trying to come up with, we're saying that “We actually do value what you're saying when you choose to give us this. It's your choice of offering it up and you can say whatever it is you want to say around that,” but it's not as evaluative or as high stakes as trying to get the right answer and just like, “Am I right? Did I get it right?” And then what the teacher might say after that. Zandra: I would add on that kids do like to give wrong answers if that's what you're asking for. They don't like to give wrong answers if you're asking for a right one and they're accidentally wrong. So, I think back to my first suggestion: If you ask for a wrong answer and they know it's wrong, they're likely to chime right in because the right answer is the wrong answer, and there are multiple, infinite numbers of them. Mike: You know, it makes me think there's this set of ideas that we need to normalize mistakes as being productive things. And I absolutely agree with that. I also think that when you're asking for the right answer, it's really hard to kind of be like, “Oh, my mistake was so productive.” On the other hand, if you ask for an error or a place where someone's stuck, that just feels different. It feels like an invitation to say, “I've actually been thinking about this. I'm not there. I may be partly there. I'm still engaged. This is where I'm struggling.” That just feels different than providing an answer where you're just like, “Ugh.” I'm really struck by that. Zandra: Yeah, and I think it's a culture thing. So, a lot of teachers say to me that “it's hard to have kids work in groups because they kind of just tell each other the answers.” But they're modeling what they experience as learners in the classroom. “I often get told the answers,” that's the discourse that we have in the classroom. So, if you open up the discourse to include these things like, “Oh, I'm stuck here. I'm not sure where to go here.” They get practice saying, “Oh, I don't know what this is. I don't know how to go from here.” Instead of just going to the answer. And I think it'll spread to the group work as well. Mike: It feels like there's value for every other student in articulating, “I'm certain that this one is wrong, and here's why I know that.” There's information in there that is important for other kids. And even the idea of “I'm stuck here,” right? That's really a great formative assessment opportunity for the teacher. And it also might validate some of the other places where kids are like, “Yeah. Me, too.” Zandra: Uh-hm. Amber: Right, absolutely. Mike: What's next, my friend? Amber: I remember very clearly listening to Zandra present about choice, her idea of choice of feedback. And this was very powerful to me. I had never thought about asking my students how they wanted to receive the feedback I'd be giving them on the problems that they solved. And this idea of students being able to turn something in and then say, “This is how I'd like to receive feedback” or “This is the feedback I'd like to receive,” becomes very powerful because now they're the ones in charge of their own learning. And so much of what we do, kids should get to say, “This is how I think that I will grow better, is if you provide this to me.” And so, having that opportunity for students to say, “This is how I'll be a better learner if you give it to me in this way. And I think if you helped me with this part that would help the whole rest of it.” Or “I don't actually want you to tell me the answer. I am stuck here. I just need a little something to get me through. But please don't tell me what the answer is because I still want to figure it out for myself.” And so, allowing kids to advocate for themselves and teaching them how to advocate for themselves to be better learners; how to advocate for themselves to learn and think about “What I need to learn this material and be a student or be a learner in society” will just ultimately help students. Zandra: Yeah, I think as a student, I don't like to be told the answers. I like to figure things out, and I will puzzle through something for a long time. But sometimes I just want a model or a hint that'll get me on the right path, and that's all I need. But I don't want you to do the problem for me or take over my thinking. If somebody asked me, “What do you want?” I might say like, “Oh, a model problem or something like that.” But I don't think we ask kids a lot. We just do whatever we think as an adult. Which is different, because we're not learning it for the first time. We already know what it is. Mike: You're making me think about the range of possibilities in a situation like that. One is I could notice a student who is working through something and just jump in and take over and do the problem for them essentially and say, “Here, this is how you do it.” Or I guess just let them go, let them continue to work through it. But potentially there could be some struggle, and there might be some frustration. I am really kind of struck by the fact that I wonder how many of us as teachers have really thought about the kinds of options that exist between those two far ends of the continuum. What are the things that we could offer to students rather than just “Let me take over” or productive struggle, but perhaps it's starting to feel unproductive? Does that make sense? Zandra: Yeah, I think it does. I mean, there are so many different ways. I would ask teachers to re-center themselves as the learner that's getting feedback. So, if you have a principal or a coach coming into your room, they've watched a lesson, sometimes you're like, “Oh, that didn't go well. I don't need feedback on that. I know it didn't go well, and I could do better.” But I wonder if you have other things that you notice just being able to take away a part that you know didn't go well. And you're like, “Yep, I know that didn't go well. I have ideas for improving it. I don't really want to focus on that. I want to focus on this other thing.” Or “I've been working really hard on discourse. I really want feedback on the student discourse when you come in.” That's really valuable to be able to steer it—not taking away the other things that you might notice, but really focusing in on something that you've been working on is pretty valuable. And I think kids often have these things that maybe they haven't really thought about a lot, but when you ask them, they might think about it. And they might grow this repertoire of things that they're kind of working on personally. Amber: Yeah, and I just think it's getting at, again, we want students to come out of situations where they can say, “This is how I learn” or “This is how I can grow,” or “This is how I can appreciate math better.” And by allowing them to say, “It'd be really helpful if you just gave me some feedback right here” or “I'm trying to make this argument, and I'm not sure it's coming across clear enough,” or “I'm trying to make this generalization, does it generalize?” We're also maybe talking about some upper-level kids, but I still think we can teach elementary students to advocate for themselves also. Like, “Hey, I try this method all the time. I really want to try this other method. How am I doing with this? I tried it. It didn't really seem to work, but where did I make a mistake? Could you help me out with that? Because I think I want to try this method instead.” And so, I think there are different ways that students can allow for that. And they can say: “I know this answer is wrong. I'm not sure how this answer is wrong. Could you please help me understand my thinking or how could I go back and think about my thinking?” Zandra: Yeah. And I think when you said upper level, you meant upper grades. Amber: Yes. Zandra: I assume.  Amber: Yes.  Zandra: OK, yeah. So, for the lower-grade-level students, too, you can still use this. They still have ideas about how they learn and what you might want to follow up on with them. “Was there an easier way to do this? I did all these hand calculations and stuff. Was there an easier way?” That's a good question to ask. Maybe they've thought about that, and they were like, “That was a lot of work. Maybe there was an easier way that I just didn't see?” That'd be pretty cool if a kid asked you that. Mike: Or even just hearing a kid say something like, “I feel really OK. I feel like I had a strategy. And then I got to this point, and I was like, ‘Something's not working.'” Just being able to say, “This particular place, can you help me think about this?” That's the kind of problem-solving behavior that we ultimately are trying to build in kids, whether it's math or just life. Amber: Right, exactly. And I need, if I want kids to be able … because people say, “I sometimes just want a kid to ask a question.” Well, we do need to give them choice of the question they ask. And that's where a lot of this comes from is, what is your goal as a teacher? What do you want kids to have choice in? If I want you to have choice of feedback, I'm going to give you ideas for what that feedback could be, so then you have something to choose from. Mike: OK, so we've unpacked quite a few ideas in the last bit. I wonder if there are any caveats or any guidance that you would offer to someone who's listening who is maybe thinking about taking up some of these practices in their classroom? Zandra: Oh, yeah. I have a lot. Kids are not necessarily used to having a lot of choice and autonomy. So, you might have to be gentle building it in because it's overwhelming. And they actually might just say, “Just tell me what to do,” because they're not used to it. It's like when you're get a new teacher and they're really into explaining your thinking, and you've never had to do that. Well, you've had 10 years of schooling or however many years of schooling that didn't involve explaining your thinking, and now, all of a sudden, “I'm supposed to explain my thinking. I don't even know what that means. What does that look like? We never had to do that before.”  So maybe start small and think about some things like, “Oh, you can choose a tool or two that helps you with this problem. So, you can use a multiplication table, or you can use a calculator or something to use. You can choose. There are all these things out. You can choose a couple of tools that might help you.” But start small. And you can give too many choices. There's like choice overload. It's like when I go on Amazon, and there are way too many reviews that I have to read for a product, and I never end up buying anything because I've read so many reviews. It's kind of like that. It could get overwhelming. So purposeful, manageable numbers of choices to start out with is a good suggestion. Amber: And also, just going back to what Zandra said in the beginning, is making sure you have a purpose for the choice. And so, if you just are like, “Oh, I'm having choice for choice's sake.” Well, what is that doing? Is that supporting the learning, the mathematics, the number sense, the conceptual understanding, and all of that? And so, have that purpose going in and making sure that the choices backtrack to that purpose. Zandra: Yeah. And you could do a little choice inventory. You could be like, “Huh, if I was a student of my own class today, what would I have gotten to choose? If anything? Did I get to choose where I sat, what utensil I used? What type of paper did I use? Which problems that I did?” Because that's a good one. All these things. And if there's no choice in there, maybe start with one. Mike: I really love that idea of a “choice inventory.” Because I think there's something about really kind of walking through a particular day or a particular lesson that you're planning or that you've enacted, and really thinking about it from that perspective. That's intriguing. Zandra: Yeah, because really, I think once you're aware of how little choice kids get in a day … As an adult learner, who has presumably a longer attention span and more tolerance and really likes math, I've spent my whole life studying it. If I got so little choice and options in what I did, I would not be a well-behaved, engaged student. And I think we need to remember that when we're talking about little children. Mike: So, last question, is there research in the field or researchers who have done work that has informed the kind of thinking that you have about choice? Zandra: Yeah, I think we're always inspired by people who come before us, so it's probably an amalgamation of different things. I listen to a lot of podcasts, and I read a lot of books on behavioral economics and all kinds of different things. So, I think a lot of those ideas bleed into the work in math education. In terms of math education, in particular, there have been a lot of people who have really influenced me, like Marian Small's work with parallel tasks and things like that. I think that's a beautiful example of choice. You give multiple options for choice of challenge and see which ones the students feel like is appropriate instead of assigning them competence ahead of time. So, that kind of work has really influenced me. Amber: And then just, our team really coming together; Sam Otten and Zandra and their ideas and collaborating together. And like you mentioned earlier, that Barb Dougherty article on the different types of questions has really been impactful. More about opening up questions, but it does help you think about choice a little bit better. Mike: I think this is a great place to stop. Zandra, Amber, thank you so much for a really eye-opening conversation. Zandra: Thank you for having us.  Amber: Thanks for having us. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2024 The Math Learning Center | www.mathlearningcenter.org

Rounding Up Season 3 | Episode 2 – Responsive Curriculum Guest: Dr. Corey Drake Mike Wallus: When it comes to curriculum, educators are often told to implement with “fidelity.” But what does fidelity mean? And where does that leave educators who want to be responsive to students in their classrooms? Today we're talking with Dr. Corey Drake about principles for responsive curriculum use that invite educators to respond to the students in their classrooms while still implementing curriculum with integrity. Mike: One of the age-old questions that educators grapple with is how to implement a curriculum in ways that are responsive to the students in their classroom. It's a question I thought a lot about during my years as a classroom teacher, and it's one that I continue to discuss with my colleague at MLC, Dr. Corey Drake. As a former classroom teacher and a former teacher educator who only recently began working for an organization that publishes curriculum, Corey and I have been trying to carve out a set of recommendations that we hope will help teachers navigate this question. Today on the podcast, we'll talk about this question of responsive curriculum use and offer some recommendations to support teachers in the field. Mike: Welcome back to the podcast, Corey. I'm excited to have you with us again. Corey Drake: It's great to be with you again. Mike: So, I've been excited about this conversation for a while because this question of, “What does it mean to be responsive to students and use a curriculum?” is something that teachers have been grappling with for so long, and you and I often hear phrases like “implementation with fidelity” used when folks are trying to describe their expectations when a curriculum's adopted. Corey: Yeah, I mean, I think this is a question teachers grapple with. It's a question I've been grappling with for my whole career, from different points of view from when I was a classroom teacher and a teacher educator and now working at The Math Learning Center. But I think this is the fundamental tension: “How do you use a set of published curriculum materials while also being responsive to your students?” And I think ideas like implementation with fidelity didn't really account for the responsive-to-your-students piece. Fidelity has often been taken up as meaning following curriculum materials, page by page, word for word, task for task. We know that's not actually possible. You have to make decisions, you have to make adaptations as you move from a written page to an enacted curriculum. But still the idea of fidelity was to be as close as possible to the written page. Whereas ideas like implementation with integrity or responsive curriculum use are starting with what's written on the page, staying consistent with the key ideas of what's on the page, but doing it in a way that's responsive to the students who are sitting in front of you. And that's really kind of the art and science of curriculum use. Mike: Yeah, I think one of the things that I used to think was that it was really a binary choice between something like fidelity, where you were following things in what I would've described as a lockstep fashion. Or the alternative, which would be, “I'm going to make everything up.” And you've helped me think, first of all, about what might be some baseline expectations from a large-scale curriculum. What are we actually expecting from curriculum around design, around the audience that it's written for? I wonder if you could share with the audience some of the things that we've talked about when it comes to the assets and also the limitations of a large-scale curriculum. Corey: Yeah, absolutely. And I will say, when you and I were first teachers probably, and definitely when we were students, the conversation was very different. We had different curriculum materials available. There was a very common idea that good teachers were teachers who made up their own curriculum materials, who developed all of their own materials. But there weren't the kinds of materials out there that we have now. And now we have materials that do provide a lot of assets, can be rich tools for teachers, particularly if we release this expectation of fidelity and instead think about integrity. So, some of the assets that a high-quality curriculum can bring are the progression of ideas, the sequence of ideas and tasks that underlies almost any set of curriculum materials; that really looks at, “How does student thinking develop across the course of a school year?” And what kinds of tasks, in what order, can support that development of that thinking. Corey: That's a really important thing that individual teachers or even teams of teachers working on their own, that would be very hard for them to put together in that kind of coherent, sequential way. So, that's really important. A lot of curriculum materials also bring in many ideas that we've learned over the last decades about how children learn mathematics: the kinds of strategies children use, the different ways of thinking that children bring. And so, there's a lot that both teachers and students can learn from using curriculum materials. At the same time, any published set of large-scale curriculum materials are, by definition, designed for a generic group of students, a generic teacher in a generic classroom, in a generic community. That's what it means to be large scale. That's what it means to be published ahead of time. So, those materials are not written for any specific student or teacher or classroom or community. Corey: And so, that's the real limitation. It doesn't mean that the materials are bad. The materials are very good. But they can't be written for those specific children in that specific classroom and community. That's where this idea that responsive curriculum use and equitable instruction always have to happen in the interactions between materials, teachers, and students. Materials by themselves cannot be responsive. Teachers by themselves cannot responsibly develop the kinds of ideas in the ways that curriculum can, the ways they can when using curriculum as a tool. And, of course, students are a key part of that interaction. And so, it's really thinking about those interactions among teachers, students, and materials and thinking about, “What are the strengths the materials bring? What are the strengths the teacher brings?” The teacher brings their knowledge of the students. The teacher brings their knowledge of the context. And the students bring, of course, their engagement and their interaction with those materials. And so, it's thinking about the strengths they each bring to that interaction, and it's in those interactions that equitable and responsive curriculum use happens. Mike: One of the things that jumps out from what you said is this notion that we're not actually attempting to fix “bad curriculum.” We're taking the position that curriculum has a set of assets, but it also has a set of limitations, and that's true regardless of the curriculum materials that you're using. Corey: Absolutely. This is not at all about curriculum being bad or not doing what it's supposed to do. This assumes that you're using a high-quality curriculum that does the things we just talked about that has that progression of learning, those sequences of tasks that brings ideas about how children learn and how we learn and teach mathematics. And then, to use that well and responsibly, the teacher then needs to work in ways, make decisions to enact that responsibly. It's not about fixing the curriculum. It's about using the curriculum in the most productive and responsive ways possible. Mike: I think that's good context, and I also think it's a good segue to talk about the three recommendations that we want educators to consider when they're thinking about, “What does it mean to be responsive when you're using curriculum?” So, just to begin with, why don't we just lay them out? Could you unpack them, Corey? Corey: Yeah, absolutely. But I will say that this is work you and I have developed together and looking at the work of others in the field. And we've really come up with, I think, three key criteria for thinking about responsive curriculum use. One is that it maintains the goals of the curriculum. So again, recognizing that one of the strengths of curriculum is that it's built on this progression of ideas and that it moves in a sequential way from the beginning of the year to the end of the year. We want teachers to be aware of, to understand what the goals are of any particular session or unit or year, and to stay true to those goals, to stay aligned with those goals. But at the same time, doing that in ways that open up opportunities for voice and choice and sensemaking for the specific students who are in front of them in that classroom. And then the last is, we're really concerned with and interested in supporting equitable practice. And so, we think about responsive curriculum use as curriculum use that reflects the equity-based practices that were developed by Julia Aguirre and her colleagues. Mike: I think for me, one of the things that hit home was thinking about this idea that there's a mathematical goal and that goal is actually part of a larger trajectory that the curriculum's designed around. And when I've thought about differentiation in the past, what I was really thinking about was replacement that fundamentally altered the instructional goal. And I think the challenge in this work is to say, “Am I clear on the instructional goal? And do the things that I'm considering actually maintain that for kids or are they really replacing them or changing them in a way that will alter or impact the trajectory?” Corey: I think that's such a critical point. And it's not easy work. It's not always clear even in materials that have a stated learning goal or learning target for a session. There's still work to do for the teacher to say, “What is the mathematical goal? Not the activity, not the task, but what is the goal? What is the understanding I'm trying to support for my students as they engage in this activity?” And so, you're right. I think the first thing is, teachers have to be super clear about that because all the rest of the decisions flow from understanding, “What is the goal of this activity, what are the understandings that I am trying to develop and support with this session? And then I can make decisions that are enhancing and providing access to that goal, but not replacing it. I'm not changing the goal for any of my students. I'm not changing the goal for my whole group of students. Instead, I'm recognizing that students will need different ways into that mathematics. Students will need different kinds of supports along the way. But all of them are reaching toward or moving toward that mathematical goal.” Mike: Yeah. When I think about some of the options, like potentially, number choice; if I'm going to try to provide different options in terms of number choice, is that actually maintaining a connection to the mathematical goal, or have I done something that altered it? Another thing that occurs to me is the resources that we share with kids for representation, be it manipulatives or paper, pencil, even having them talk about it—any of those kinds of choices. To what extent do they support the mathematical goal, or do they veer away from it? Corey: Yeah, absolutely. And there are times when different numbers or different tools or different models will alter the mathematical goal because part of the mathematical goal is to learn about a particular tool or a particular representation. And there are other times when having a different set of numbers or a different set of tools or models will only enhance students' access to that mathematical goal because maybe the goal is understanding something like two-digit addition and developing strategies for two-digit addition. Well then, students could reach that goal in a lot of different ways. And some students will be working just with decade numbers, and some students will be working with decades and ones, and some students will need number pieces, and others will do it mentally. But if the goal is developing strategies, developing your understanding of two-digit addition, then all of those choices make sense, all of those choices stay aligned with the goal. Corey: But if the goal is to understand how base ten pieces work, then providing a different model or telling students they don't need to use that model would, of course, fundamentally alter the goal. So, this is why it's so critically important that we support teachers in understanding, making sense of the goal, figuring out how do they figure that out. How do you open a set of curriculum materials, look at a particular lesson, and understand what the mathematical goal of that lesson is? And it's not as simple as just looking for the statement of the learning goal and the learning target. But it's really about, “What are the understandings that I think will develop or are intended to develop through this session?” Mike: I feel like we should talk a little bit about context, because context is such a powerful tool, right? If you alter the context, it might help kids surface some prior knowledge that they have. What I'm thinking about is this task that exists in Bridges where we're having kids look at a pet store where there are arrays of different sorts and kinds of dog foods or dog toys or cat toys. And I remember an educator saying to me, “I wonder if I could shift the context.” And the question that I asked her is, “If you look at this image that we're using to launch the task, what are the particular parts of that image that are critical to maintain if you're going to replace it with something that's more connected to your students?” Corey: Connecting to your students, using context to help students access the mathematics, is so important and such an empowering thing for teachers and students. But you're asking exactly the right question. And of course, that all relates to, “What's the mathematical goal?” Again. Because if I know that, then I can look for the features of the context that's in the textbook and see the ways in which that context was designed to support students in reaching that mathematical goal. But I can also look at a different context that might be more relevant to my students, that might provide them better access to the mathematics. And I can look at that context through the lens of that mathematical goal and see, “Does this context also present the kinds of features that will help my students understand and make sense of the mathematical goal?” And if the answer is yes, and if that context is also then more relevant to my students or more connected to their lives, then great. That's a wonderful adaptation. That's a great example of responsive curriculum use. If now I'm in a context that's distracting or leading me away from the mathematical goal, that's where we run into adaptations that are less responsive and less productive. Mike: Well, and to finish the example, the conversation that this led to with this educator was she was talking about looking for bodegas in her neighborhood that her children were familiar with, and we end up talking quite a bit about the extent to which she could find images from the local bodega that had different kinds of arrays. She was really excited. She actually did end up finding an image, and she came back, and she shared that this really had an impact on her kids. They felt connected to it, and the mathematical goal was still preserved. Corey: I love that. I think that's a great example. And I think the other thing that comes up sometimes when we present these ideas, is maybe you want to find a different context that is more relevant to your students that they know more about. Sometimes you might look at a context that's presented in the textbook and say, “I really love the mathematical features here. I really see how knowing something about this context could help my students reach the mathematical goal, but I'm going to have to do some work ahead of time to help my students understand the context, to provide them some access to that, to provide them some entry points.” So, in your example, maybe we're going to go visit a pet store. Maybe we're going to look at images from different kinds of stores and notice how things are arranged on shelves, and in arrays, and in different combinations. So, I think there are always a couple of choices. One is to change the context. One is to do some work upfront to help your students access the context so that they can then use that context to access the mathematics. But I think in both cases, it's about understanding the goal of the lesson and then understanding how the features of the context relate to that goal. Mike: Let's shift and just talk about the second notion, this idea of opening up space for students' voice or for sensemaking when you're using curriculum. For me at least, I often try to project ideas for practice into a mental movie of myself in a classroom. And I wonder if we could work to help people imagine what this idea of opening space for voice or sensemaking might look like. Corey: I think a lot of times those opportunities for opening up voice and choice and sensemaking are not in the direct, action steps or the direct instructions to teachers within the lesson, but they're kind of in the in-between. So, “I know I need to introduce this idea to my students, but how am I going to do that? What is that going to look like? What is that going to sound like? What are students going to be experiencing?” And so, asking yourself that question as the lesson plays out is, I think, where you find those opportunities to open up that space for student voice and choice. It's often about looking at that and saying, “Am I going to tell students this idea? Or am I going to ask them? Are students going to develop their strategy and share it with me or turn it in on a piece of paper? Or are they going to turn and talk to a partner? Are they going to share those ideas with a small group, with a whole group? What are they going to listen for in each other's strategies? How am I going to ask them to make connections across those strategies? What kinds of tools am I going to make available to them? What kinds of choices are they going to have throughout that process?” Corey: And so, I think it's having that mental movie play through as you read through the lesson and thinking about those questions all the way through. “Where are my students going to have voice? How are they going to have choice? How are students going to be sensemaking?” And often thinking about, “Where can I step back, as the teacher, to open up that space for student voice or student choice?” Mike: You're making me think about a couple things. The first one that really jumped out was this idea that part of voice is not necessarily always having the conversation flow from teacher to student, but having a turn and talk, or having kids listen to and engage with the ideas that their partners are sharing is a part of that idea that we're creating space for kids to share their ideas, to share their voice, to build their own confidence around the mathematics. Corey: Absolutely. I think that, to me, is the biggest difference I see when I go into different classrooms. “Whose voice am I hearing most often? And who's thinking do I know about when I've spent 20 minutes in a classroom?” And there are some classrooms where I know a lot about what the teacher's thinking. I don't know a lot about what the students are thinking. And there are other classrooms where I can tell you something about the thinking of every one of the students in that room after 10 minutes in that classroom because they're constantly turning and talking and sharing their ideas. Student voice isn't always out loud either, right? Students might be sharing their ideas in writing, they might be sharing their ideas through gestures or through manipulating models, but the ideas are communicating their mathematical thinking. Really, student communication might be an even better way to talk about that because there are so many different ways in which students can express their ideas. Mike: Part of what jumped out is this notion of, “What do you notice? What do you wonder?” Every student can notice, every student can wonder. So, if you share a context before you dive right into telling kids what's going to happen, give them some space to actually notice and wonder about what's going on, generate questions, that really feels like something that's actionable for folks. Corey: I think you could start every activity you did with a, “What do you notice? What do you wonder?” Students always have ideas. Students are always bringing resources and experiences and ideas to any context, to any task, to any situation. And so, we can always begin by accessing those ideas and then figuring out as teachers how we might build on those ideas, where we might go from there. I think even more fundamentally is just this idea that all students are sensemakers. All students bring brilliance to the classroom. And so ,what we need to do is just give them the opportunities to use those ideas to share those ideas, and then we as teachers can build on those ideas. Mike: Before we close this conversation, I want to spend time talking about responsive curriculum use being a vehicle for opening up space for equity-based practice. Personally, this is something that you've helped me find words for. There were some ideas that I had an intuitive understanding of. But I think helping people name what we mean when we're talking about opening space for equity-based practice is something that we might be able to share with folks right now. Can you share how a teacher might take up this idea of creating space for equity-based practice as they're looking at lessons or even a series of lessons? Corey: Yeah, absolutely. And I think student voice and choice are maybe outcomes of equity-based practices. And so, in a similar way, I think teachers can begin by looking at a lesson or a series of lessons and thinking about those spaces and those decisions in between the action steps. And again, asking a series of questions. The equity-based practices aren't a series of steps or rules, but really like a lens or a series of questions that as a teacher, you might ask yourself as you prepare for a lesson. So, “Who is being positioned as mathematically capable? Who's being positioned as having mathematically important ideas? Are all of my students being positioned in that way? Are some of my students being marginalized? And if some of my students are being marginalized, then what can I do about that? How could I physically move students around so that they're not marginalized? How can I call attention to or highlight a certain student's ideas without saying that those ideas are the best or only ideas? But saying, ‘Look, this student, who we might not have recognized before as mathematically capable and brilliant, has a really cool idea right now.'” Corey: You and I have both seen video from classrooms where that's done brilliantly by these small moves that teachers can make to position students as mathematically brilliant, as having important or cool or worthwhile ideas, valuable ideas to contribute. So, I think it's those kinds of decisions that make such a difference. Those decisions to affirm learners' identities. Those aren't big changes in how you teach. Those are how you approach each of those interactions minute by minute in the classroom. How do you help students recognize that they are mathematicians, that they each bring valuable ideas to the classroom? And so, it's more about those in-between moments and those moments of interaction with students where these equity-based practices come to life. Mike: You said a couple things that I'm glad that you brought out, Corey. One of them is this notion of positioning. And the other one that I think is deeply connected is this idea of challenging places where kids might be marginalized. And I think one of the things that I've been grappling with lately is that there's a set of stories or ideas and labels that often follow kids. There are labels that we affix to kids within the school system. There are stories that exist around the communities that kids come from, their families. And then there are also the stories that kids make up about one another, the ideas that carry about, “Who's good at math? Who's not? Who has ideas to share? Who might I listen to, and who might I not?” And positioning, to me, has so much opportunity as a practice to help press back against those stories that might be marginalizing kids. Corey: I think that's such an important point. And I think, along with that is the recognition that this doesn't mean that you, as the individual teacher, created those stories or believed stories or did anything to perpetuate those stories—except if you didn't act to disrupt them. Because those stories come from all around us. We hear Pam Seda and Julia Aguirre and people like that saying, “They're the air we breathe. They're the smog we live in. Those stories are everywhere. They're in our society, they're in our schools, they're in the stories students tell and make up about each other.” And so, the key to challenging marginality is not to say, “Well, I didn't tell that story, I don't believe that story. But those stories exist, and they affect the children in my classroom, so what am I going to do to disrupt them? What am I going to do? Because I know the stories that are told about certain students, even if I'm not the one telling them, I know what those stories are. So how am I going to disrupt them to show that the student who the story or the labels about that student are, that they are not as capable, or they are behind or struggling or ‘low students.' What am I going to do to disrupt that and help everyone in our classroom community see the brilliance of that child, understand that that child has as much to contribute as anybody else in the math classroom?” And that's what it means to enact equity-based practices. Mike: You're making me think about an interview we did earlier this year with Peter Liljedahl, and he talked about this idea. He was talking about it in the context of grouping, but essentially what he was saying is that kids recognize the stories that are being told in a classroom about who's competent and who's not. And so, positioning, in my mind, is really thinking about—and I've heard Julia Aguirre say it this way—“Who needs to shine? Whose ideas can we bring to the center?” Because what I've come to really have a better understanding of, is that the way I feel about myself as a mathematician and the opportunities that exist within a classroom for me to make sense of math, those are really deeply intertwined. Corey: Yes, yes, absolutely. We are not focusing on marginality or identity just because it makes people feel good, or even just because it's the right thing to do. But actually in the math classroom, your identity and the expectations and the way you're positioned in that classroom fundamentally affect what you have opportunities to learn and the kinds of math you have access to. And so, we will do this because it's the right thing to do and because it supports math learning for all students. And understanding the role of identity and marginality and positioning in student learning is critically important. Mike: You're making me think about a classroom that we visited earlier this year, and it was a really dynamic math discussion. There was a young man, I'll call him David, and he was in a multilingual classroom. And I'm thinking back on what you said. At one point you said, “I can go into a classroom, and I can have a really clear idea of what the teacher understands, and perhaps less so with the kids.” In this case, I remember leaving thinking, “I really clearly understand that David has a deep conceptual understanding of the mathematics.” And the reason for that was, he generally volunteered to answer every single question. And it was interesting. It's not because the educator in the classroom was directing all of the questions to him, but I really got the sense that the kids, when the question was answered, were to almost turn their bodies because they knew he was going to say something. And it makes me think David is a kid who, over time, not necessarily through intention, but through the way that status works in classrooms, he was positioned as someone who really had some ideas to share, and the kids were listening. The challenge was, not many of them were talking. And so, the question is, “How do we change that? Not because anyone has any ill intent toward those other children, but because we want them to see themselves as mathematicians as well.” Corey: Yeah, absolutely. And that is part of what's tricky about this is that that's so important is that I think for many years we've talked about opening up the classroom for student talk and student discourse. And we do turn and talks, and we do think pair shares. And we've seen a lot of progress, I think, in seeing those kinds of things in math classrooms. And I think the next step to that is to do those with the kind of intentionality and awareness that you were just demonstrating there; which is to say, “Well, who's talking and how often are they talking? And what sense are people making of the fact that David is talking so much? What sense are they making? What stories are they telling about who David is as a mathematician? But also who they are as mathematicians. And what does it mean to them that even though there are lots of opportunity for students talk in that classroom, it's dominated by one or maybe two students. And so, we have opened it up for student discourse, but we have more work to do. We have more work to say, “Who's talking, and what sense are they making, and what does that look like over time? And how is mathematical authority distributed? How is participation distributed across the class? And, in particular, with intentionality toward disrupting some of those narratives that have become entrenched in classrooms and schools.” Mike: I think that's a great place for us to stop. I want to thank you again for joining us, Corey. It was lovely to have you back on the podcast. Corey: Thanks. It was great to be with you. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2024 The Math Learning Center | www.mathlearningcenter.org 

(10 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) by Jason Newland

(10 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) Deep Relaxation by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License creativecommons.org/licenses/by/3.0/ Music promoted by freemusicbg.com and www.chosic.com

(5 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) Deep Relaxation Kevin MacLeod (incompetech.com)Licensed under Creative Commons: By Attribution 3.0 Licensehttp://creativecommons.org/licenses/by/3.0/Music promoted by https://freemusicbg.comand https://www.chosic.com

(10 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) Deep Relaxation by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/ Music promoted by https://freemusicbg.com and https://www.chosic.com

(5 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) Deep Relaxation by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License creativecommons.org/licenses/by/3.0/ Music promoted by freemusicbg.com and www.chosic.com

(5 Hours) #949 ASMR Mike - Let Me Bore You To Sleep (Jason Newland) (6th January 2023) Deep Relaxation by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/ Music promoted by https://freemusicbg.com and https://www.chosic.com

Rounding Up Season 2 | Episode 8 – It's a Story, Not a Checklist! Guest: Dr. John Staley Mike Wallus: There's something magical about getting lost in a great story. Whether you're reading a book, watching a movie, or listening to a friend, stories impart meaning, and they capture our imagination. Dr. John Staley thinks a lot about stories. On this episode of Rounding Up, we'll talk with John about the ways that he thinks that the concept of story can impact our approach to the content we teach and the practices we engage in to support our students.  Well, John, welcome to the podcast. We're really excited to talk with you today. John Staley: I'm glad to be here. Thank you for the invitation, and thank you for having me. Mike: So when we spoke earlier this year, you were sharing a story with me that I think really sets up the whole interview. And it was the story of how you and your kids had engaged with the themes and the ideas that lived in the Harry Potter universe. And I'm wondering if you could just start by sharing that story again, this time with the audience. John: OK. When I was preparing to present for a set of students over at Towson University and talking to them about the importance of teaching and it being a story. So the story of Harry Potter really began for me with our family—my wife, Karen, and our three children—back in '97 when the first book came out. Our son Jonathan was nine at that time and being a reader and us being a reading family, we came together. He would read some, myself and my wife would read some, and our daughter Alexis was five, our daughter Mariah was three. So we began reading Harry Potter. And so that really began our journey into Harry Potter. Then when the movies came out, of course we went to see the movies and watch some of those on TV, and then sometimes we listened to the audio books. And then as our children grew, because Harry Potter took, what, 10 years to develop the actual book series itself, he's 19 now, finally reading the final book. By then our three-year-old has picked them up and she's begun reading them and we're reading. So we're through the cycle of reading with them.  But what they actually did with Harry Potter, when you think about it, is really branch it out from just books to more than books. And that right there had me thinking. I was going in to talk to teachers about the importance of the story in the mathematics classroom and what you do there. So that's how Harry Potter came into the math world for me, [chuckles] I guess you can say. Mike: There's a ton about this that I think is going to become clear as we talk a little bit more.  One of the things that really struck me was how this experience shaped your thinking about the ways that educators can understand their role when it comes to math content and also instructional practice and then creating equitable systems and structures. I'm wondering if we can start with the way that you think this experience can inform an educator's understanding for content. So in this case, the concepts and ideas in mathematics. Can you talk about that, John? John: Yeah, let's really talk about the idea of what happens in a math classroom being a story. The teaching and learning of mathematics is a story that, what we want to do is connect lesson to lesson and chapter to chapter and year to year.  So when you think about students' stories, and let's start pre-K. When students start coming in pre-K and learning pre-K math, and they're engaging in the work they do in math with counting and cardinality initially, and as they grow across the years, especially in elementary, and they're getting the foundation, it's still about a story. And so how do we help the topics that we're taught, the grade level content become a story? And so that's the connection to Harry Potter for me, and that's what helped me elevate and think about Harry Potter because when you think about what Harry Potter and the whole series did, they've got the written books. So that's one mode of learning for people for engaging in Harry Potter.  Then they went from written books to audiobooks, and then they went from audiobooks to movies. And so some of them start to overlap, right? So you got written books, you got audiobooks, you got movies—three modes of input for a learner or for an audience or for me, the individual interested in Harry Potter, that could be interested in it. And then they went to additional podcasts, Harry Potter and the Sacred Text and things like that. And then they went to this one big place called Universal Studios where they have Harry Potter World. That's immersive. That I can step in; I can put on the robes; I can put the wand in my hand. I can ride on, I can taste, so my senses can really come to play because I'm interactive and engaged in this story. When you take that into the math classroom, how do we help that story come to life for our students? Let's talk one grade. So it feels like the content that I'm learning in a grade, especially around number, around algebraic thinking, around geometry, and around measurement and data. Those topics are connected within the grade, how they connect across the grade and how it grows. So the parallel to Harry Potter's story—there's, what, seven books there? And so you have seven books, and they start off with this little young guy called Harry, and he's age 11. By the time the story ends, he's seven years later, 18 years old. So just think about what he has learned across the years and how what they did there at Hogwarts and the educators and all that kind of stuff has some consistency to it. Common courses across grade levels, thinking, in my mind, common sets of core ideas in math: number, algebra, thinking, geometry, measurement of data. They grow across each year. We just keep adding on.  So think about number. You're thinking with base ten. You then think about how fractions show up as numbers, and you're thinking about operations with whole numbers, base ten, and fractions. You think about decimals and then in some cases going into, depending if you're K–8 or K–5, you might even think about how this plays into integers. But you think about how that's all connected going across and the idea of, “What's the story that I need to tell you so that you understand how math is a story that's connected?” It's not these individual little pieces that don't connect to each other, but they connect somehow in some manner and build off of each other. Mike: So there are a couple of things I want to pick up on here that are interesting. When you first started talking about this, one of the things that jumped out for me is this idea that there's a story, but we're not necessarily constrained to a particular medium. The story was first articulated via book, but there are all of these ways that you can engage with the story. And you talked about the immersive experience that led to a level of engagement. John: Mm-hmm. Mike: And I think that is helping me make sense of this analogy—that there's not necessarily one mode of building students' understanding. We actually need to think about multiple modes. Am I picking up on that right? John: That's exactly right. So what do I put in my tool kit as an educator that allows me to help tap into my students' strengths, to help them understand the content that they need to understand that I'm presenting that day, that week, that month, that I'm helping build their learning around? And in the sense of thinking about the different ways Harry Potter can come at you—with movies, with audio, with video—I think about that from the math perspective. What do I need to have in my tool kit when it comes to my instructional practices, the types of routines I establish in the classroom?  Just think about the idea of the mathematical tools you might use. How do the tools that you use play themselves out across the years? So students working with the different manipulatives that they might be using, the different mathematical tools, a tool that they use in first grade, where does that tool go in second grade, third grade, fourth grade, as they continue to work with whole numbers, especially with doing operations, with whatever the tool might be? Then what do you use with fractions? What tools do you use with decimals? We need to think about what we bring into the classroom to help our students understand the story of the mathematics that they're learning and see it as a story. Is my student in a more concrete stage? Do they need to touch it, feel it, move it around? Are they okay visually? They need to see it now, they're at that stage. They're more representational so they can work with it in a different manner or they're more abstract. Hmm. Oh, OK. And so how do we help put all of that into the setting? And how are we prepared as classroom teachers to have the instructional practices to meet a diverse set of students that are sitting in our classrooms? Mike: You know, the other thing you're making me think about, John, is this idea of concepts and content as a story. And what I'm struck by is how different that is than the way I was taught to think about what I was doing in my classroom, where it felt more like a checklist or a list of things that I was tracking. And oftentimes those things felt disconnected even within the span of a year.  But I have to admit, I didn't find myself thinking a lot about what was happening to grade levels beyond mine or really thinking about how what I was doing around building kindergartners' understanding of the structure of number or ten-ness. John: Mm-hmm. Mike: How that was going to play out in, say, fifth grade or high school or what have you. You're really causing me to think how different it is to think about this work we're doing as story rather than a discrete set of things that are kind of within a grade level. John: When you say that, it also gets me thinking of how we quite often see our content as being this mile-wide set of content that we have to teach for a grade level. And what I would offer in the space is that when you think about the big ideas of what you really need to teach this year, let's just work with number. Number base ten, or, if you're in the upper elementary, number base ten and fractions. If you think about the big ideas that you want students to walk away with that year, those big ideas continue to cycle around, and those are the ones that you're going to spend a chunk of your time on. Those are the ones you're going to keep bringing back. Those are the ones you're going to keep exposing students to in multiple ways to have them make sense of what they're doing. And the key part of all of that is the understanding, the importance of the vertical nature as to what is it I want all of my students sitting in my classroom to know and be able to do, have confidence in, have their sense of agency. Like, “Man, I can show you. I can do it, I can do it.” What do we want them to walk away with that year? So that idea of the vertical nature of it, and understanding your learning progressions, and understanding how number grows for students across the years is important. Why do I build student understanding with a number line early? So that when we get the fractions, they can see fractions as numbers. So later on when we get the decimals, they can see decimals as numbers, and I can work with it. So the vertical nature of where the math is going, the learning progression that sits behind it, helps us tell the story so that students, when they begin and you are thinking about their prior knowledge, activate that prior knowledge and build it, but build it as part of the story.  The story piece also helps us think about how we elevate and value our students in the classroom themselves. So that idea of seeing our students as little beings, little people, really, versus just us teaching content. When you think about the story of Harry Potter, I believe he survived across his time at Hogwarts because of relationships. Our students make it through the math journey from year to year to year to year because of relationships. And where they have strong relationships from year to year to year to year, their journey is a whole lot better. Mike: Let's make a small shift in our conversation and talk a little bit about this idea of instructional practice. John: OK.  Mike: I'm wondering how this lived experience with your family around the Harry Potter universe, how you think that would inform the way that an educator would think about their own practice? John: I think about it in this way. As I think about myself being in the classroom—and I taught middle school, then high school—I'm always thinking about what's in my tool kit. I think about the tools that I use and the various manipulatives, the various visual representations that I need to have at my fingertips. So part of what my question would be, and I think about it, is what are those instructional strategies that I will be using and how do I fine-tune those? What are my practices I'm using in my routines to help it feel like, “OK, I'm entering into a story”?  Harry Potter, when you look at those books, across the books, they had some instructional routines happening, some things that happen every single year. You knew there was going to be a quidditch match. You knew they were going to have some kind of holiday type of gathering or party or something like that. You knew there was going to be some kind of competition that happened within each book that really, that competition required them to apply the knowledge and skills from their various courses that they learned. They had a set of core courses that they took, and so it wasn't like in each individual course that they really got to apply. They did in some cases, they would try it out, they'd mess up and somebody's nose would get big, ears would get big, you know, change a different color. But really, when they went into some of those competitions, that's when the collection of what they were learning from their different courses, that's when the collection of the content. So how do we think about providing space for students to show what they know in new settings, new types of problems? Especially in elementary, maybe it's science application type problems, maybe they're doing something with their social studies and they're learning a little bit about that. As an educator, I'm also thinking about, “Where am I when it comes to my procedural, the conceptual development, and the ability to think through and apply the applications?” And so I say that part because I have to think about students coming in, and how do I really build this? How do I strike this balance of conceptual and procedural? When do I go conceptual? When do I go procedural? How do I value both of them? How do I elevate that? And how do I come to understand it myself? Because quite often the default becomes procedural when my confidence as a teacher is not real deep with building it conceptually. I'm not comfortable, maybe, or I don't have the set of questions that go around the lesson and everything. So I've got to really think through how I go about building that out. Mike: That is interesting, John, because I think you put your finger on something. I know there have been points in time during my career when I was teaching even young children where we'd get to a particular idea or concept, and my perception was, “Something's going on here and the kids aren't getting it.” But what you're causing me to think is often in those moments, the thing that had changed is that I didn't have a depth of understanding of what I was trying to do. Not to say that I didn't understand the concept myself or the mathematics, but I didn't have the right questions to draw out the big ideas, or I didn't have a sense of, “How might students initially think about this and how might their thinking progress over time?” So you're making me think about this idea that if I'm having that moment where I'm feeling frustrated, kids aren't understanding, it might be a point in time where I need to think to myself, “OK, where am I in this? How much of this is me wanting to think back and say, what are the big ideas that I'm trying to accomplish? What are the questions that I might need to ask?” And those might be things that I can discover through reflection or trying to make more sense of the mathematics or the concept. But it also might be an opportunity for me to say, “What do my colleagues know? Are there ways that my colleagues are thinking about this that I can draw on rather than feeling like I'm on an island by myself?” John: You just said the key point there. I would encourage you to get connected to someone somehow. As you go through this journey together, there are other teachers out there that are walking through what they're walking through, teaching the grade level content. And that's when you are able to talk deeply about math. Mike: The other thing you're making me think about is that you're suggesting that educators just step back from whether kids are succeeding or partially succeeding or struggling with a task and really step back and saying, like, “OK, what's the larger set of mathematics that we're trying to build here? What are the big ideas?” And then analyzing what's happening through that lens rather than trying to think about, “How do I get kids to success on this particular thing?” Does that make sense? Tell me more about what you're thinking. John: So when I think about that one little thing, I have to step back and ask myself the question, “How and where does that one thing fit in the whole story of the unit?" The whole story of the grade level. And when I say the grade level, I'm thinking about those big ideas that sit into the big content domains, the big idea number. How does this one thing fit into that content domain? Mike: That was lovely. And it really does help me have a clearer picture of the way in which concepts and ideas mirror the structures of stories in that, like, there are threads and connections that I can draw on from my previous experience to understand what's happening now. You're starting to go there.  So let's just talk about where you see parallels to equitable systems and structures in the experience that you had with Harry Potter when you were in that world with your family. John: First, let's think about this idea of grouping structures. And so when you think about the idea of groups and the way groups are used within the classroom, and you think about the equitable nature of homogeneous, heterogeneous, random groupings, truly really thinking about that collectively. And I say collectively in this sense, when you think about the parallel to the Harry Potter story, they had a grouping structure in place. They had a random sorting. Now who knows how random it was sometimes, right? But they had a random sorting the minute the students stepped into the school. And they got put into one of the four houses. But even though they had that random sorting then, and they had the houses structured, those groups, those students still had opportunities as they did a variety of things—other than the quidditch tournaments and some other tournaments—they had the opportunity where as a collection of students coming from the various houses, if they didn't come together, they might not have survived that challenge, that competition, whatever it was. So the idea of grouping and grouping structures and how we as educators need to think about, “What is it really doing for our students when we put them in fixed groups? And how is that not of a benefit to our students? And how can we really go about using the more random grouping?”  One of the books that I'm reading is Building Thinking Classrooms [in Mathematics: Grades K–12: 14 Teaching Practices for Enhancing Learning]. And so I'm reading Peter [Liljedahl]'s book and I'm thinking through it in the chapter when he talks about grouping. I think I read that chapter and highlighted and tapped every single page in it multiple times because it really made me think about what's really happening for our students when we think about grouping. So one structure and one part to think about is, “What's happening when we think we're doing our grouping that's not really getting students engaged in the lesson, keeping them engaged, and benefiting them from learning?” Another part, and I don't know if this is a part of equitable systems and structures or just when I think about equity work: One of the courses that they had to take at Hogwarts was about the history of wizarding. I bring that up in this space because they learned about the history of what went on with wizards and what went on with people. And to me, in my mindset, that's setting up and showing the importance of us sharing the history and bringing the history of our students—their culture, their backgrounds, in some cases their lived experiences—into the classroom. So that's us connecting with our students' culture and being culturally responsive and bringing that into the classroom. So as far as an equitable structure, the question I would ask you to think about is, “Do my students see themselves in my mathematics classroom?”  And I say it that way versus “in the mathematics,” because some people will look at the problems in the math book and say, “Oh, I don't see them there. I don't see, oh, their names, their culture, their type of foods.” Some of those things aren't in the written work in front of you. But what I would offer is the ability for me as the educator to use visuals in my classroom, the ability for me to connect with the families in my classroom and learn some of their stories, learn some of their backgrounds—not necessarily learn their stories, but learn about them and bring that in to the space—that's for me to do. I don't need a textbook series that will do that for me. And as a matter of fact, I'm not sure if a textbook series can do that for you, for all the students that you have in your classroom or for the variety of students that you have in your classroom, when we think about their backgrounds, their culture, where they might come from. So thinking about that idea of cultural responsiveness, and really, if you think about the parallel in the Harry Potter series, the history of wizarding and the interaction, when you think about the interaction piece between wizards and what they call Muggles, right? That's the interactions between our students, learning about other students, learning about other cultures, learning about diverse voices. That's teaching students how to engage with and understand others and learn about others and come to value that others have voice also. Mike: I was just thinking, John, if I were to critique Hogwarts, I do wonder about the houses. Because in my head, there is a single story that the reader comes to think about anyone who is in Harry's house versus, say, like Slytherin house. John: Yes. Mike: And it flattens anyone who's in Slytherin house into bad guys, right? John: Mm-hmm. Mike: And so it makes me think there's that element of grouping where as an educator, I might tell a single story about a particular group, especially if that group is fixed and it doesn't change. But there's also, like, what does that do internally to the student who's in that group? What does that signal to them about their own identity? Does that make sense? John: That does make sense. And so when you think about the idea of grouping there at Hogwarts, and you think about these four fixed groups, because they were living in these houses, and once you got in that house, I don't think anybody moved houses. Think about the impact on students. If you put them in a group and they stay in that group and they never change groups, you will have students who realize that the way you did your groups and the way you named your groups and the way they see others in other groups getting more, doing different, and things like that. That's a nice caution to say the labels we put on our groups. Our kids come to internalize them and they come to, in some cases, live up to the level of expectations that we set for “just that group.” So if you're using fixed groups or thinking about fixed groups, really I'd offer that you really get into some of the research around groups and think, “What does it do for students?” And not only what does it do for students in your grade, but how does that play out for students across grades? If that student was in the group that you identified as the “low group” in grade 2, [exhales] what group did they show up in grade 3? How did that play with their mindset? Because you might not have said those words in front of students, but our students pick up on being in a fixed group and watching and seeing what their peers can do and what their peers can't do, what their group members can do and what their group can't do. As our students grow from grades 2 to 3, 4, 5, that really has an impact. There's somewhere between grade 3 and 5 where students' confidence starts to really shake. And I wonder how much of it is because of the grouping and types of grouping that is being used in the classroom that has me in a group of, “Oh, I am a strong doer [of mathematics]” or, “Oh, I'm not a good doer of mathematics.” And that, how much of that just starts to resonate with students, and they start to pick that up and carry that with them, an unexpected consequence because we thought we were doing a good thing when we put 'em in this group. Because I can pull them together, small group them, this and that. I can target what I need to do with them in that moment. Yeah, target what you need to do in that moment, but mix them up in groups. Mike: Just to go back and touch on the point that you started with. Building Thinking Classrooms has a lot to say about that particular topic among others, and it's definitely a book that, for my money, has really caused me to think about a lot of the practices that I used to engage in because I believed that they were the right thing to do. It's a powerful read. For anyone who hasn't read that yet, I would absolutely recommend it. John: And one last structure that I think we can speak to. I've already spoken to supports for students, but the idea of a coherent curriculum is I think an equitable structure that systems put in place that we need to put in place that you need to have in place for your students. And when I say a coherent curriculum, I'm thinking not just your one grade, but how does that grow across the grades? It's something for me, the teacher, to say, “I need to do it my way, this way…”. But it's more to say, “Here's the role I play in their pre-K to 12 journey.” Here's the chapter I'm going to read to them this year to help them get their deep understanding of whichever chapter it was, whichever book it happened to be of.  In the case of the parallel of Harry Potter, here's the chapter I'm doing. I'm the third grade chapter, I'm the fourth grade chapter, I'm the fifth grade chapter. And the idea of that coherent curriculum allows the handoff to the next and the entry from the prior to be smoother. Many of the curriculums, when you look at them, a K–5 curriculum series will have those coherent pieces designed in it—similar types of tools, similar types of manipulatives, similar types of question prompts, similar types of routines—and that helps students build their confidence as they grow from year to year. And so to that point, it's about this idea of really thinking about how a coherent curriculum helps support equity because you know your students are getting the benefit of a teacher who is building from their prior knowledge because they've paid attention to what came before in this curriculum series and preparing them for where they're going. And that's quite often what the power of a coherent curriculum will do.  The parallel in the Harry Potter series, they had about five to seven core courses they had to take. I think about the development of those courses. Boom. If I think about those courses as a strand of becoming a wizard, [laughs] how did I grow from year to year to year to year in those strands that I was moving across? Mike: Okay, I have two thoughts. One, I fully expect that when this podcast comes out, there's going to be a large bump in whoever is tracking the sale of the Harry Potter series on Amazon or wherever it is.  John: [laughs] Mike: But the other question I wanted to ask you is what are some books outside of the Harry Potter universe that you feel like you'd recommend to an educator who's wanting to think about their practice in terms of content or instructional practices or the ways that they build equitable structure? John: When I think about the works around equitable structure, I think about The Impact of Identity and K–8 Mathematics: Rethinking Equity-Based Practices by Julia Aguirre, Karen Mayfield-Ingram, and Danny Martin as being one to help step back and think about how am I thinking about what I do and how it shows up in the classroom with my students.  Another book that I just finished reading: Humanizing Disability in Mathematics Education[: Forging New Paths]. And my reason for reading it was I continue to think about what else can we do to help our students who are identified, who receive special education services? Why do we see so many of our students who sit in an inclusive environment—they're in the classroom on a regular basis; they don't have an IEP that has a math disability listed or anything along those lines—but they significantly underperform or they don't perform as well as their peers that don't receive special education services. So that's a book that got me just thinking and reading in that space.  Another book that I'm reading now, or rereading, and I'll probably reread this one at least once a year, is Motivated[: Designing Mathematics Classrooms Where Students Want to Join In] by Ilana [Seidel] Horn. And the reason for this one is the book itself, when you read it, is written with middle schools' case stories. Part of what this book is tackling is what happens to students as they transition into middle school. And the reason why I mentioned this, especially if you're elementary, is somewhere between third grade and fifth grade, that process of students' self-confidence decreasing their beliefs in themselves as doers of math starts to fall apart. They start to take the chips in the armor. And so this book, Motivated itself, really does not speak to this idea of intrinsic motivation. “Oh, my students are motivated.” It speaks to this idea of by the time the students get to a certain age, that upper fifth grade, sixth grade timeframe, what shifts is their K, 1, 2, 3, “I'm doing everything to please my teacher.” By [grades] 4 or 5, I'm realizing, “I need to be able to show up for my peers. I need to be able to look like I can do for my peers.” And so if I can't, I'm backing out. I'm not sharing, I'm not volunteering, I'm not “engaging.”  So that's why I bring it into this elementary space because it talks about five pieces of a motivational framework that you can really push in on, and not that you push in on all five at one time. [chuckles] But you pick one, like meaningfulness, and you push in on that one, and you really go at, “How do I make the mathematics more meaningful for my students, and what does it look like? How do I create that safe space for them?” That's what you got to think about. Mike: Thanks. That's a great place to stop. John Staley, thank you so much for joining us. It's really been a pleasure. John: Thank you for having me. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. ©2023 The Math Learning Center - www.mathlearningcenter.org

Rounding Up Season 2 | Episode 7 – Making Fractions More Meaningful Guest: Dr. Susan Empson Mike Wallus: For quite a few adults, fractions were a stumbling block in their education that caused many to lose their footing and begin to doubt their ability to make sense of math. But this doesn't have to be the case for our students. Today on the podcast, we're talking with Dr. Susan Empson about big ideas and fractions and how we can make them more meaningful for our students. Welcome to the podcast. Susan. Thanks for joining us. Susan Empson: Oh, it's so great to be here. Thank you for having me. Mike: So, your book was a real turning point for me as an educator, and one of the things that it did for me at least, it exposed how little that I actually understood about the meaning of fractions. And I say this because I don't think that I'm alone in saying that my own elementary school experience was mostly procedural. So rather than attempting to move kids quickly to procedures, what types of experiences can help children build a more meaningful understanding of fractions? Susan: Great question. Before I get started, I just want to acknowledge my collaborators because I've had many people that I've worked with. There's Linda Levi, co-author of the book, and then my current research partner, Vicki Jacobs. And of course, we wouldn't know anything without many classroom teachers we've worked with in the current and past graduate students. In terms of the types of experiences that can help children build more meaningful experiences of fractions, the main thing we would say is to offer opportunities that allow children to use what they already understand about fractions to solve and discuss story problems. Children's understandings are often informal and early on, for example, may consist mainly partitioning things in half. What I mean by informal is that understandings emerge in situations out of school. So, for example, many children have siblings and have experienced situations where they have had to share, let's say three cookies or slices of pizza between two children. In these kinds of situations, children appreciate the need for equal shares, and they also develop strategies for creating them. So, as children solve and discuss story problems in school, their understandings grow. The important point is that story problems can provide a bridge between children's existing understandings and new understandings of fractions by allowing children to draw on these informal experiences. Generally, we recommend lots of experiences with story problems before moving on to symbolic work to give children plenty of opportunity to develop meaningful fractions. And we also recommend using story problems throughout fraction instruction. Teachers can use different types of story problems and adjust the numbers in those problems to address a range of fraction content. There are also ideas that we think are foundational to understanding fractions, and they're all ideas that can be elicited and developed as children engage in solving and discussing story problems.  Susan: So, one idea is that the size of a piece is determined by its relationship to the whole. What I mean is that it's not necessarily the number of pieces into which a whole is partitioned that determines the size of a piece. Instead, it's how many times the piece fits into the whole. So, in their problem-solving, children create these amounts and eventually name them and symbolize them as unit fractions. That's any fraction with 1 in the numerator. Mike: You know, one of the things that stands out for me in that initial description that you offered, is this idea of kids don't just make meaning of fractions at school, that their informal lived experiences are really an asset that we can draw on to help make sense of what a fraction is or how to think about it. Susan: That's a wonderful way to say it. And absolutely, the more teachers get to know the children in their classrooms and the kinds of experiences those children might have outside of school, the more of that can be incorporated into experiences like solving story problems in school. Mike: Well, let's dig into this a little bit. Let's talk a little bit about the kinds of story problems or the structure that actually provides an entry point and can build understanding of fractions for students. Can you talk a bit about that, Susan? Susan: Yes. So, I'll describe a couple types of story problems that we have found especially useful to elicit and develop children's fraction understandings. So first, equal sharing story problems are a powerful type of story problem that can be used at the beginning of and even throughout instruction. These problems involve sharing multiple things among multiple sharers. So, for example, four friends equally sharing 10 oranges. How much orange would each friend get? Problems like this one allow children to create fractional amounts by drawing things, partitioning those things, and then attaching fraction names and symbols. So, let's [talk] a little bit about how a child might solve the oranges problem. A child might begin by drawing four friends and then distributing whole oranges one by one until each friend has two whole oranges. Now, there are two oranges left and not enough to give each friend another whole orange. So, they have to think about how to partition the remaining oranges. Susan: They might partition each orange in half and give one more piece to each friend, or they might partition each of the remaining oranges into fourths and give two pieces to each friend. Finally, they have to think about how to describe how much each friend gets in terms of the wholes and the pieces. They might simply draw the amount, they might shade it in, or they might attach number names to it. I also want to point out that a problem about four friends equally sharing 10 oranges can be solved by children with no formal understanding of fraction names and symbols because there are no fractions in the story problem. The fractions emerge in children's strategies and are represented by the pieces in the answer. The important thing here is that children are engaged in creating pieces and considering how the pieces are related to the wholes or other pieces. The names and symbols can be attached gradually. Mike: So, the question that I wanted to ask is how to deal with this idea of how you name those fractional amounts, because the process that you described to me, what's powerful about it is that I can directly model the situation. I can make sense of partitioning. I think one of the things that I've always wondered about is, do you have a recommendation for how to navigate that naming process? I've got one of something, but it's not really one whole orange. So how do I name that? Susan: That's a great question. Children often know some of the informal names for fractions, and they might understand halves or even fourths. Initially, they may call everything a half or everything a piece or just count everything as one. And so, what teachers can do is have conversations with children about the pieces they've created and how the pieces relate to the whole. A question that we've found to be very helpful is, how many of those pieces fit into the whole? Mike: Got it. Susan: Not a question about how many pieces are there in the whole, but how many of the one piece fit into the whole. Because it then focuses children on thinking about the relationship between the piece and the whole rather than simply counting pieces. Mike: Let's talk about the other problem type that was kind of front and center in your thinking. Susan: Yes. So, another type of story problem that can be used early in fraction instruction involves what we think of as special multiplication and division story problems that have a whole number of groups and a unit fraction amount in each group. So, what do I mean by that? For example, let's say there are six friends and they each will get one-third of a sub sandwich for lunch. So, there's a whole number of groups—that's the six friends—and there's a unit fraction amount in each group that's the one-third of a sandwich that they each get. And then the question is how many sandwiches will be needed for the friends? So, a problem like this one essentially engages children in reasoning about six groups of one-third. And again, as with the equal sharing problem about oranges, they can solve it by drawing out things. They might draw each one-third of a sandwich, and then they have to consider how to combine those to make whole sandwiches. An important idea that children work on with this problem then is that three groups of one-third of a sandwich can be combined to make one whole sandwich. There are other interesting types of story problems, but teachers have found these two types, in particular, effective in developing children's understandings of some of the big ideas and fractions. Mike: I wonder if you have educators who hear you talk about the second type of problem and are a little bit surprised because they perceive it to be multiplication. Susan: Yes, it is surprising. And the key is not that you teach all of multiplying and dividing fractions before adding and subtracting fractions, but that you use these problem types with special number combinations. So, a whole number of groups, for example, the six groups unit fractions in each group—because those are the earliest fractions children understand. And I think maybe one way to think about it is that fractions come out of multiplying and dividing, kind of in the way that whole numbers come out of adding and counting. And the key is to provide situations story problems that have number combinations in them that children are able to work with. Mike: That totally makes sense. Can you say more about the importance of attending to the number combinations? Susan: Yes. Well, I think that the number combinations that you might choose would be the ones that are able to connect with the fraction understandings that children already have. So, for example, if you're working with kindergartners, they might have a sense of what one half is. So, you might choose equal sharing problems that are about sharing things among two children. So, for example, three cookies among two children. You could even, once children are able to name the halves, they create in a problem like that, you can even pose problems that are about five children who each get half of a sandwich, how many sandwiches is that? But those are all numbers that are chosen to allow children to use what they understand about fractions. And then as their understandings grow and their repertoire of fractions also grows, you can increase the difficulty of the numbers. So, at the other end, let's think about fifth grade and posing equal sharing problems. If we take that problem about four friends sharing 10 oranges, we could change the number just a little bit to make it a lot harder to, four friends sharing 10 and a half oranges, and then fifth-graders would be solving a problem that's about finding a fraction of a fraction, sharing the half orange among the four children. Mike: Let me take what you've shared and ask a follow-up question that came to me as you were talking. It strikes me that the design, the number choices that we use in problems matter, but so does the space that the teacher provides for students to develop strategies and also the way that the teacher engages with students around their strategy. Could you talk a little bit about that, Susan? Susan: Yes. We think it's important for children to have space to solve problems, fraction story problems, in ways that make sense to them and also space to share their thinking. So, just as teachers might do with whole number problem-solving in terms of teacher questioning in these spaces, the important thing is for the teacher to be aware of and to appreciate the details of children's thinking. The idea is not to fix children's thinking with questioning, but to understand it or explore it. So, one space that we have found to be rich for this kind of questioning is circulating. So, that's the time when as children solve problems, the teacher circulates and has conversations with individual children about their strategies. So, follow-up questions that focus on the details of children's strategies help children to both articulate their strategies and to reflect on them and help teachers to understand what children's strategies are. We've also found that obvious questions are sometimes underappreciated. So, for example, questions about what this child understands about what's happening in a story problem, what the child has done so far in a partial strategy, even questions about marks on a child's paper; shapes or tallies that you as a teacher may not be quite sure about, asking what they mean to the child. “What are those? Why did you make those? How did they connect with the problem?” So, in some it benefits children to have the time to articulate the details of what they've done, and it benefits the teacher because they learn about children's understandings. Mike: You're making me think about something that I don't know that I had words for before, which is I wonder if, as a field, we have made some progress about giving kids the space that you're talking about with whole number operations, especially with addition and subtraction. And you're also making me wonder if we still have a ways to go about not trying to simply funnel kids to, even if it's not algorithms, answer-getting strategies with rational numbers. I'm wondering if that strikes a chord for you or if that feels off base. Susan: It feels totally on base to me. I think that it is as beneficial, perhaps even more beneficial for children to engage in solving story problems and teachers to have these conversations with them about their strategies. I actually think that fractions provide certain challenges that whole numbers may not, and the kinds of questioning that I'm talking about really depend on the details of what children have done. And so, teachers need to be comfortable with and familiar with children's strategies and how they think about fractions as they solve these problems. And then that understanding, that familiarity, lays the groundwork for teachers to have these conversations. The questions that I'm talking about can't really be planned in advance. Teachers need to be responsive to what the child is doing and saying in the moment. And so that also just adds to the challenge. Mike: I'm wondering if you think that there are ways that educators can draw on the work that students have done composing and decomposing whole numbers to support their understanding of fractions? Susan: Yes. We see lots of parallels just as children's understandings of whole numbers develop. They're able to use these understandings to solve multi-digit operations problems by composing and decomposing numbers. So, for example, to take an easy addition, to add 37 plus eight, a child might say, “I don't know what that is, but I do know how to get from 37 to 40 with three.” So, they take three from the eight, add it to the 37 get to 40, and then once at 40 they might say, “I know that 40 plus five more is 45.” So, in other words, they decompose the eight in a way that helps them use what they understand about decade numbers. Operations with fractions work similarly, but children often do not think about the similarities because they don't understand fractions or numbers to, versus two numbers one on top of the other. Susan: If children understand that fractions can be composed and decomposed just as whole numbers can be composed and decomposed, then they can use these understandings to add, subtract, multiply, and divide fractions. For example, to add one and four-fifths plus three-fifths, a child might say, “I know how to get up to two from one in four-fifths. I need one more fifth, and then I have two more fifths still to add from the three-fifths. So, it's two and two-fifths.” So, in other words, just as they decompose the eight into three and five to add eight to 37, they decompose the three-fifths into one-fifth and two-fifths to add it to one and four-fifths. Mike: I could imagine a problem like one and a half plus five-eighths. I could say, “Well, I know I need to get a half up. Five-eighths is really four-eighths and one-eighths, and four-eighths is a half.” Susan: Yep. Mike: “So, I'm actually going from one and a half plus four-eighths. OK. That gets me to two, and then I've got one more eighth left. So, it's two and an eighth.” Susan: Nice. Yeah, that's exactly the kind of reasoning this approach can encourage. Mike: Well, I have a final question for you, Susan. “Extending Children's Mathematics” came out in 2011, and I'm wondering what you've learned since the book came out. So, are there ideas that you feel like have really been affirmed or refined, and what are some of the questions about the ways that students make meaning of fractions that you're exploring right now? Susan: Well, I think, for one, I have a continued appreciation for the power of equal sharing problems. You can use them to elicit children's informal understandings of fractions early in instruction. You can use them to address a range of fraction understandings, and they can be adapted for a variety of fraction content. So, for example, building meaning for fractions, operating with fractions, concepts of equivalence. Vicki and I are currently writing up results from a big research project focused on teachers' responsiveness to children's fraction thinking during instruction. And right now, we're in the process of analyzing data on third-, fourth-, and fifth-grade children's strategies for equal sharing problems. We specifically focused on over 1,500 drawing-based strategies used by children in a written assessment at the end of the school year. We've been surprised both by the variety of details in these strategies—so, for example, how children represent items, how they decide to distribute pieces to people—and also by the percentages of children using these drawing-based strategies. For each of grades three, four, and five, over 50 percent of children use the drawing-based strategy. There are also, of course, other kinds of strategies that don't depend on drawings that children use, but by far the majority of children were using these strategies. Mike: That's interesting because I think it implies that we perhaps need to recognize that children actually benefit from time using those strategies as a starting point for making sense of the problems that they're solving. Susan: I think it speaks to the length of time and the number of experiences that children need to really build meaning for fractions that they can then use in more symbolic work. I'll mention two other things that we've learned for which we actually have articles in the NCTM publication MTLT, which is “Mathematics Teacher: Learning and Teaching in PK–I2.” So first, we've renewed appreciation for the importance of unit fractions and story problems to elicit and develop big ideas. Another idea is that unit fractions are building blocks of other fractions. So, for example, if children solve the oranges problem by partitioning both of the extra oranges into fourths, then they have to combine the pieces in their answer. One-fourth from each of two oranges makes two-fourths of an orange. Another idea is that one whole can be seen as the same amount as a grouping of same-sized unit fractions. So, those unit fractions can all come from the same hole or different wholes, for example, to solve the problem about six friends who will each get one-third of a sub sandwich. A child has to group the one-third sandwiches to make whole sandwiches. Understanding that the same sandwich can be seen in these two ways, both as three one-third sandwiches or as one whole sandwich, provides a foundation for flexibility and reasoning. For those in the audience who are familiar with CGI, this idea is just like the IDM base ten, that 1 ten is the same amount as ten 1s, or what we describe in shorthand as 10 as a unit. And we also have an article in MTLT. It's about the use of follow-up equations to capture and focus on fraction ideas in children's thinking for their story problems. So basically, teachers listen carefully as children solve problems and explain their thinking to identify ideas that can be represented with the equations. Susan: So, for example, a child solving the sub-sandwiches problem might draw a sandwich partitioned into thirds and say they know that one sandwich can serve three friends because there are three one-thirds in the sandwich. That idea for the child might be drawn, it might be verbally stated. A follow-up equation to capture this idea might be something like one equals one-third plus one-third plus blank, with the question for the child, “Could you finish this equation or make it a true equation?” So, follow-up equation[s] often make ideas about unit fractions explicit and put them into symbolic form for children. And then at the same time, the fractions in the equations are meaningful to children because they are linked to their own meaning-making for a story problem. And so, while follow-up equations are not exactly a question, they are something that teachers can engage children with in the moment as a way to kind of put some symbols onto what they are saying, help children to reflect on what they're saying or what they've drawn, in ways that point towards the use of symbols. Mike: That really makes sense. Susan: So, they could be encouraged to shade in the piece and count the total number of pieces into which an orange is cut. However, we have found that a better question is, how many of this size piece fit into the whole? Because it focuses children on the relationship between the piece and the whole, and not on only counting pieces. Mike: Oh, that was wonderful. Thank you so much for joining us, Susan. It's really been a pleasure talking with you. Susan: Thank you. It's been my pleasure. I've really enjoyed this conversation. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. © 2023 The Math Learning Center | www.mathlearningcenter.org

The Nightly Rant: Examining Society from a Sarcastic Point of ViewWelcome to The Nightly Rant with your hosts, Mike and Torya. In this show, we take a sarcastic look at society and dive into various topics that provoke thought and conversation. Today, we want to discuss the importance of being prepared to answer questions and engage in meaningful dialogue when expressing opinions publicly. We believe that adults should act like adults and handle disagreements in a mature manner. Let's dive into the details.The Importance of Being Prepared to Answer QuestionsMike: "People in general should not ask questions unless they're prepared to hear any answer."Torya: "I'll take what you just said a step further to also include stating your opinion publicly."Mike: "If you state your opinion publicly on something, then you need to be prepared to answer questions. Some people are going to be confused. You put your opinion out there that that is influential. It means something. I don't care who you are. Be prepared to answer questions. That's all."Torya: "Influences at least one other person in the universe."Mike: "Be prepared to answer questions. That's all I ask. Is that bad?"Torya: "Well, why are you asking the questions? What is your goal with asking people questions about their opinion?"Mike: "To understand their viewpoint on that issue."Torya: "Because to tell them how wrong they are, that they're dumb or that their opinion is factually incorrect. No."Mike: "In fact, usually these days especially, I will say your opinion is completely valid, but it isn't one that I completely connect with because I don't understand this aspect."Torya: "Can you explain?"Mike: "And I blah out whatever the question is and then they attempt to answer. And most times they don't even attempt to answer because they don't care. They just growl back at you and it's like, no, I was truly trying to understand where you were coming from."Torya: "Well, then if your intention is to just understand, then no, right, you're not doing it."Mike: "Exactly. There's nothing wrong. Then if your intention is to drag them into a trap and then pounce on them and beat them to death, yeah, that'd be pretty wrong."Torya: "Or at least mean and nasty. Sure."Mike: "Which is wrong sometimes."Torya: "It's fun."Mike: "Well, it can be. I won't lie. It can be."Torya: "Especially when somebody has a really obscure and ridiculous and factually incorrect opinion. But I digress. We don't need to go there."Mike: "Well, yeah, and why can't somebody disagree about that and not make it be such a big deal? I mean, come on, there's a specific incident in my head. And the minuteness of the topic, if you think about it, it was like less than a grain of sand in the grand scheme of everything. Right?"Torya: "We've had disagreements about things way bigger than that and laughing together about something else five minutes later."Mike: "Nothing. That's like nothing. That's what I'm trying to say. It's like fart dust is a bigger deal than that."Torya: "Fart dust pretty bad."Mike: "And yet people who are allegedly adults make it about them and, oh, we need to quit the friendship. And that's literally what people do these days. Grown ass adults. Yeah, grown ass adults just leave and don't talk to you anymore. They don't have even the balls to say I'm going to say it. They don't even have the balls to say, fuck you."Torya: "Wow."Mike: "They don't have the balls to say anything. Yes, I'm the reason never for the E. It's always all me now."Torya: "I feel like all the words are fair game, though."Mike: "But here's the thing. It's like they don't even have the guts to say goodbye. Like, I'm done. That's a woosy move. I mean, those are the kind of people that disappear from their family, too. No BS."Torya: "I had a great idea earlier, and I was thinking that it'd be great if society would just chew up these cocksucking assholes that you're describing. The people who don't function as part of society because they're just too fucking wrapped up in their own self."Mike: "Yeah, they're not adults."Torya: "Chew them up and shit them out into outer space using the Earth's giant rectum. Yeah, the Earth is going to grow a giant rectum and it needs to shit these people out because they're destroying."Mike: "The world in many senses of the word. Yes, they are."Torya: "They're the most hostile people yet. They're the people who will call everybody else hostile."Mike: "Well, and that's the thing. There's also this issue where adults can't be adults, they just can't. Like we're talking about ghosting. That's not an adult move ghosting people. That's a little baby's move ghosting."Torya: "Right?"Mike: "Oh, where's your friend Johnny? Oh, I don't talk to him anymore. It's what the little kid does. It's not what an adult does."Torya: "Right? And then there's poor Johnny crying in the corner because he doesn't know why nobody likes him. And also, Johnny will continue to be an asshole for the rest of Johnny's life because nobody has ever told him why they don't like him."Mike: "Which in my opinion, makes you the asshole for not pointing it out to."Torya: "Right?"Mike: "I mean, if you pointed it out to him and he continued down the pathway, you pointed it out to him, and he gets to continue down the pathway if he wants to."Torya: "You've got to tell people how you feel about things. You know, it's interesting. When I was in Canada, not this most recent time, but the time before, I was hanging out with Alicia, you know, how she has miniature humans. Well, the boy miniature human punched the girl miniature human. And she came screaming and crying to know kid stuff. And Alicia told her that she needed to go tell miniature boy human how it made her feel so that he would apologize to her."Torya: "And she did, and he apologized and then gave her a hug for a five year old. People. Yeah."Mike: "And, you know, the honest truth is there's no reason whatsoever for someone to act like everything's okay when there are obvious signals that everything's not okay. There's no reason for anyone to ever do that to anybody. That's why I think we talk about this all the time. Our relationship works because it takes you longer than me to get there, but we tell each other, well, that bothered me when that happened."Torya: "I know that I'm a little bit irrational. Okay, whatever. Don't even no commenting. Not allowed. I know that I'm a little bit irrational, and sometimes I don't know if I'm actually annoyed with you or if I'm being crazy, so I need to take some time to decipher if I am being crazy."Mike: "But see but that's fair, because that means instead of that even makes you even more reasonable, because instead of putting our relationship through a roller coaster of crap, you take the time to filter it yourself. Here's the thing, though. A lot of people would bitch at you for that, but I commend you for it because you still come forward with the issues to get them fixed. You do."Torya: "Think about it. You're doing something that's annoying the crap out of me. Okay? Not right now. This is a hypothetical you are doing something."Mike: "Well, it's a hypothetical reality. It happens."Torya: "Yeah. Anyway, I could say something right then when you're being annoying in my hyper irrational, super annoyed state sure. Which what would happen bad?"Mike: "Let's just say doom would ensue. Always."Torya: "Nobody needs that. Or I could stew quietly about it for a while and then come back to it the next day when I'm not crazy and decide if I was actually annoyed with you or not. And then if I was actually annoyed with you, I could be like, hey, Mike, you did this thing. Please don't do it again."Mike: "Yeah, you know what, though? I obviously am the same person as you, so I obviously approach that same issue the same way as you. And I, though, have one time only with you, followed the completely reasonable give her the benefit of the doubt approach. I've done it many times, but once and only once did I regret doing it. And you did something like you had a comeback of, like I can't even remember the comeback at this point, but it was really this really sassy."Mike: "You didn't deny that you were doing something and that it would have bothered me. You didn't deny that at all, but instead, you just sort of ignored it. And went like, what about this? And it's like, wow, man. That isn't how we're supposed to deal with each other. We're supposed to deal with each other face to face. We're not supposed to try to duck around one another. And that's how that felt, right?"Torya: "That's why everybody has to calm down."Mike: "Before issues should be correct. Exactly. And that's the thing. There's times when you do have to wait, and there's times when you should take time to think about things. And I think it's more adult like to wait rather than overreact. However, I'm going to say something different. One last thing. When someone does that to you, they overreact. It's best for you to quote overreact back and protect yourself. That's what I think."Torya: "Well, because then you're going to get the whole thing out of the way right there, instead of you stewing that I overreacted and making it a fight the next day and the next day and the next day. I agree with you. If one person has already gone off the deep end, well, you might as well just have the knockdown drag out fight right there. Just get it over with."Mike: "I think we agree with that. And it's healthy. That's the healthy way, and we act like adults about it. And that's the key thing, though. You have to be able to speak your mind without the other person getting offended. And honestly, I think a big thing that most adults just don't have any longer than they used to is the ability to separate things. Just because you're not the most empathetic person in the world doesn't mean you're stupid."Torya: "Yeah, that's what I was going to say before you had something else you had to say. If I didn't take the minute to calm myself or minute or hours or six days, whatever is necessary, all arguments I had with everybody would be like, my fight with the Sam's Club lady where I called them an idiot and."Mike: "They walked wasn't your that wasn't your proudest moment."Torya: "Or my slight disagreement with that soccer mom that one time that I won't repeat."Mike: "Well, what's funny about that? What's funny about that is both of those situations turned out okay in the end, but they had the potential not to be. But here's the thing. By us being reasonable people, 98.5% of the time, you can get away with a slip up like that. And the rest of the people are like, in particular the soccer incident, the rest of the parents, you were like, oh, I'm so sorry that I said that in front of you. And they're like, Are you kidding? I would have said worse to her."Mike: "She deserved what you said. And then everyone that was literally the opinion, they would be like, oh, I would have said worse. Oh, she deserved it. Blah, blah, blah, blah, blah. Not a single person sided with the other person. Not a single person. Now, here's the thing. We still set our apologies to everybody. To everybody."Torya: "Even though the person I exactly."Mike: "Even though they supported us, we still apologized."Torya: "Well, to be fair, I used the worst word Americans can possibly use in front of, like, twelve year old children."Mike: "Well, the twelve year old children were out on the soccer field, though Mitchell."Torya: "Said he heard it."Mike: "Well, it is what it is, man. You did apologize."Torya: "That's what I felt like I needed."Mike: "But you apologized. You did. To everybody. And yet the point is, they were supportive of us because we had always been reasonable people. We didn't yell and scream on the sidelines at our kid, at the referee. We didn't do that stuff. We sat there and we cheered."Torya: "Called the referee a sight."Mike: "We talked to each other."Torya: "Only when you were egged on by other groups of people, though, too."Mike: "We would just talk to each other and ignore everyone. I mean, that's just how we handled things. And so it's sort of annoying that people go down roads that they don't even bother to think about. Well, are they the type of people that would act that way?"Torya: "So can we officially shoot these hyper aggressive snowflake motherfuckers into space?"Mike: "Yeah, with the rectum. You said this already, and I fully agree with you."Torya: "Well, I need to know if other."Mike: "People."Torya: "We're not feeding the rectum Taco Bell."Mike: "Both of those are going to make a great audio club. That's the little shorty. Munch, munch, munch kapow. And we're not feeding in Taco Bell. Just wow. All right. Well, I think we have beaten this topic to death. I didn't even expect us to talk about it for this long. Here's what I want to kind of close up with tomorrow, which is the day after we record this, which will be weeks from the time you hear it."Mike: "We are getting involved in our very first official sporting event together. We are going to play fantasy hockey with the rest of our family. Yes, we are. And we suck at this for my ultimate failure. We're going to learn this quick. So with that, that is all I've got for you people."Torya: "Good night, everyone."Mike: "Hasta La Bye bye."Conclusion and Future OutlookIn this episode of The Nightly Rant, Mike and Torya discuss the importance of being prepared to answer questions and engage in meaningful dialogue when expressing opinions publicly. They emphasize the need for adults to act like adults and handle disagreements in a mature manner. The hosts share personal anecdotes and observations to highlight the negative consequences of ghosting and avoiding confrontation.The conversation delves into the significance of open communication and the ability to separate personal opinions from personal attacks. Mike and Torya stress the importance of understanding different viewpoints and seeking clarification rather than resorting to hostility. They also touch upon the need for self-reflection and taking the time to assess one's own emotions before engaging in discussions.The hosts conclude the episode by announcing their participation in a fantasy hockey league, highlighting the importance of learning new skills and embracing new experiences. They encourage listeners to approach disagreements with maturity and respect, fostering a culture of open dialogue and understanding.Moving forward, it is crucial for individuals to recognize the impact of their words and opinions on others. By being prepared to answer questions and engage in meaningful conversations, adults can foster a more inclusive and understanding society. The Nightly Rant serves as a reminder that communication is key, and it is essential to approach disagreements with empathy and respect.TimestampSummary0:00:15Introduction to the podcast and topic of the day0:01:34Importance of being prepared to answer questions when stating opinions0:03:34Adults making small disagreements a big deal0:05:02Criticism of people who ghost others without explanation0:06:34Society's inability to handle conflicts maturely0:08:25The importance of open communication in a relationship0:09:11The need to address issues face-to-face rather than avoiding them0:10:59Reacting to overreactions to protect oneself0:11:46Having a knockdown drag out fight to resolve conflicts0:12:22Lack of empathy and offense to criticism of empathy0:12:27Torya talks about needing time to calm herself before arguments0:12:55C mentions the soccer incident and how it turned out okay0:13:48They discuss apologizing to everyone involved in the incident0:14:11C talks about how they were always reasonable people0:14:54Torya suggests shooting hyper aggressive people into space0:15:55They mention their upcoming fantasy hockey event0:16:22Closing remarks0:31:54Mike thanks listeners and asks for a rating0:32:06End of transcript

#949 ASMR Mike Let Me Bore You To Sleep (Jason Newland) (6th January 2023) by Jason Newland

Rounding Up Season 2 | Episode 3 – Student Engagement Guest: Dr. Meghan Shaughnessy Mike Wallus: When we say students are engaged in a discussion or a task, what do we really mean? There are observable behaviors that we often code as engaged, but those are just the things that we can see or hear. What does engagement really mean, particularly for students who may not verbally participate on a regular basis? Today on the podcast, we're talking with Dr. Meghan Shaughnessy about the meaning of engagement and a set of strategies teachers can use to extend opportunities for participation to each and every student. Mike: Welcome to the podcast, Meghan. We are super excited to have you joining us. Meghan: I'm excited to be here. Mike: So, I want to start with a question that I think in the past I would've thought had an obvious answer. So, what does or what can participation look like? Meghan: So, I think in answering that question, I want to start with thinking about one of the ways that teachers get feedback on participation in their classroom is through administrator observation. And oftentimes those observations are focused on students making whole-group verbal contributions and discussions, particularly with a focus on students sharing their own ideas. Administrators are often looking at how quiet the space is and how engaged students appear to be, which is often determined by looking at students' body language and whether or not that language matches what is often seen as listening body language, such as having your head up, facing the speaker, et cetera. And as I say all of this, I would also say that defining participation in this way for discussions is both a limited and a problematic view of participation. I say limited in the sense that not all participation is going to be verbal, and it certainly won't always include sharing new ideas. Meghan: So, to give a concrete example, a student might participate by revoicing another student's strategy, which could be really important, providing other students a second chance to hear that strategy. A second example is that a student might create a representation of a strategy being shared verbally by a classmate. And this nonverbal move of creating a representation could be really useful for the class in developing collective understanding of the strategy. The traditional view is problematic, too, in the sense that it assumes that students are not participating when they don't display particular behaviors. To turn to a more equitable approach to conceptualizing and supporting participation, I and my colleagues would argue that this includes learning children's thinking body language, including a focus on written pair talk, and supporting contributions. In other words, moving beyond just having students share their own ideas, having students share what they learned from our classmate. Mike: Yeah. I want to dig into this a little bit more. Because this idea that my read on a child's behavior influences my understanding of what's happening, but also my practice, is really interesting to me. You've really had me thinking a lot about the way that a teacher's read on a student's engagement or participation, it has a lot to do with the cultural script for how adults and children are expected to interact, or at least what we've learned about that in our own lived experiences. I'm wondering if you could just talk a little bit about that.  Meghan: Yeah. One way to start answering that question might be to ask everyone to take a minute to think about how you participate in a discussion. Do you use the sort of listening behaviors that teachers are told matter? Are you always sharing new ideas when you participate in a discussion? You also might want to imagine sitting down with a group of your colleagues and asking them to think about when they engage in a discussion outside of class, what does it look and feel like? Are there lots of people talking at once or people talking one at a time? Is everyone that's participating in the discussion sharing new ideas, or are they participating in other sorts of ways? And further, you might imagine asking those colleagues about their discussions outside of class as a child. What did those discussions look and feel like? One of the challenges of being teachers is that we bring our own experiences and sometimes we don't reflect on what children are experiencing. Children's experiences don't necessarily match our own, and we need to be thinking about changing our expectations or explicitly teaching what it means to participate in particular sorts of ways. Yet another layer of challenge here is a tendency to make assumptions about how students from particular cultural groups engage in discussions. You only know what you know. And teachers need opportunities to learn from their students about how they engage in discussions inside and outside of math class, and to be able to think about the connections and disconnections and the opportunities to leverage. Mike: So, you really have me deconstructing some of the norms that were unspoken in my own childhood about being a learner, being a good student. And what you have me thinking is, some of those were voiced, some of those were unvoiced, but I'm really reflecting on how that showed up in the way that I read kids. So, I want to ask you to even go a little bit deeper. Can you share some examples of where our read on the meaning of behaviors might lead to an inaccurate understanding of students' cognitive engagement or the contributions that they might make to discourse? Meghan: Yeah. Some of it can be thinking about sort of traditional behavior reads in a traditional sense. Oftentimes, when children have their heads down or their eyes closed or they're not looking at the speaker, the child is seen as not engaging or participating. But if we think about it, people have lots of different thinking postures, and for some people having their heads down or closing their eyes is actually the way in which they're thinking deeply about the ideas that are being shared in the discussion. And so, engagement might look for them. They may be carefully tracking and thinking about the ideas, but the way that that gets expressed may not be the way that we traditionally think about what engagement should look like in classrooms. Mike: It feels like there's two pieces to this question about reading behavior and interpretation. One piece that you talked about there was just this idea that we need to have conversations with children. The other piece that I kept thinking about is, how might an educator interrogate their own cultural script around participation? Are there questions that educators could ask themselves or practices that they might engage in with colleagues that would help them take these things that are subconscious and unspoken and maybe raise them up? So, if you have an awareness of them, it's easy to recognize how that's influencing your read or your instructional moves. Meghan: Yeah, I think there are kind of two pieces to this. So, one goes back to the idea that I shared about the importance of recognizing our own experiences in school as a student and our experiences out of school, both as a child and as an adult in discussions and trying to think about what are we bringing to our work as a teacher that we might need to interrogate because it may be different than the experiences of children? And at the same time, we need to be having conversations with children about what it looks like to participate in discussions in different sorts of spaces so that we can learn more about what children's experiences are outside of school. The big idea is to recognize that children's experiences are often very different from our own, and we have to be careful at the same time not to make assumptions that all children from particular communities experience participation and discussion in the same way. This can be highly variable. Mike: I think what's really interesting about the work that you and your colleagues have done is, there's an element of it that's really about taking a step back and recognizing these ideas like cultural scripts that we have about participation and really trying to interrogate our own understandings that we've come to, and then how do we interact with kids. But on the other hand, you all have some really practical strategies and suggestions for educators on how they can use an expanded understanding of participation to create more opportunity for kids. So, I'm wondering if we can talk a little bit about some of those things. Meghan: Absolutely. So, I have a set of four different strategies that my colleagues and I have been working on over time. So, I'm going to start by talking about task selection. Sometimes students' cultural backgrounds and experiences in schools may be at odds, particularly around the work of critiquing the ideas of others. And this can in particular be a challenge when the critiquing is about critiquing the teacher's ideas. So, it leads to this question of, “How can we support students in learning to critique in ways that don't dismiss their own culture and experience?” So, our practical solution to working in this space is that we've used written critique tasks. So, when working with students, we'll show a fictitious person's response to a mathematics task and ask students to do three sorts of things. So, one is to describe the student's strategy in their own words. A second thing is to think about and write down the questions that they have about the student's strategy. And then the third piece is for students to think about and record what suggestions they have for the student and how they would convince the student to use those suggestions. Meghan: So, how does this support participation? Well, it can explicitly support the work of critiquing. It's written, and it allows students to think carefully rather than needing to think on the spot. And thirdly, the student is not a classmate, which can reduce the feeling of confrontation that some students feel when engaging in critique. So, one thing that I want to name with this particular strategy around task selection and using a written critique task, is that we've recognized that the way that critiquing is often worked on in mathematics classrooms may be at odds with some students' experiences with critique outside of school. And so, we're not trying to say that students shouldn't be supported in learning to critique mathematical ideas. That's an important part of mathematical work. But rather we're trying to design a structure that's going to not dismiss students' experiences outside of school, but at the same time give them experiences with the mathematical work of critiquing. Mike: Yeah, the questions themselves are powerful, but it seems like the choice to use a fictitious person is really critical to this task design. Meghan: Absolutely. And as a teacher, too, it really does give us a little bit more control in terms of what is the critique that's going to unfold in that particular classroom. Mike: It strikes me that they're able to engage in the task of critique without that feeling of conflict. Meghan: Absolutely. It really opens up space for students to engage in that critiquing work and takes a lot of that pressure off of them. Mike: Let's talk about the second idea. Meghan: Alright. So, the second strategy is to use a deliberate turn and talk. In discussions, some students are ready to share their ideas right away, but other students need a chance to practice verbalizing the ideas that they're about to share. Sometimes students' ideas are not completely formed, and they need to learn how others hear the ideas to refine their arguments. Further, in multilingual classrooms, sometimes students need opportunities to refine their thinking in their home language, and importantly, they also need opportunities to develop academic language in their home language. So, in a deliberate turn and talk, a teacher deliberately pairs students to share their thinking with a partner, and the partner asks clarifying questions. The pairs might be made based on knowledge of students' home language use, their mathematical understandings, or some other important thing the teacher is thinking about as they engage in that pairing. So how might using deliberately paired turn and talks broaden participation in a discussion? Meghan: Well, first, all students are being asked to participate and have the opportunity to refine their own mathematical argument and consider someone else's ideas. In a whole-class discussion, it's not the case that every student is likely to have that opportunity. So, turn and talks provide that opportunity. Second, turn and talks can support a broader range of students in feeling ready and willing to share their thinking in a whole group. Third, these pairs can also set up students who are not yet comfortable sharing their own ideas in whole group to be able to share someone else's idea. So, a way for them to still share ideas in whole group, even though it's not necessarily their own idea that's being shared. Mike: So, what I'm thinking about is, if you and I were engaged in a deliberate turn and talk, what might it look like if I'm a student, you're a student and we've engaged in the norms of the deliberate turn and talk as you described them? Let's just walk through that for a second. What would it look like? Meghan: So, in a pair turn and talk, it really has the structure of partner A, sharing their thinking, and then partner B being responsible for asking questions about the ideas that they just heard in order to further their own understanding of partner's ideas, but also to provide partner A with some feedback about the ways in which they've been expressing their ideas. So, that's pretty different than what often happens in classrooms where kids are invited to share in a discussion and they actually haven't tried verbalizing it yet, right? And they have no way of thinking about, or limited ways of thinking about, how other people might hear those ideas that they're about to share. Mike: I think the other thing that pops up to me is that another scenario that often occurs in turn and talk is it's really turn and tell. Because one person is essentially sharing their thinking and the norms aren't necessarily that they respond, it's just that they share in kind, right? So, this idea that you're actually engaging with someone's idea feels like an important piece of what it looks like to do a deliberate turn and talk versus some of the other iterations that we've just been describing. Meghan: Absolutely. Mike: Well, I'm excited to hear about the third strategy. Meghan: Alright. Our third strategy focuses on supporting participation through connection-making. So, when you think about a typical discussion in a classroom, opportunities for individual students to make explicit connections between ideas shared, are often pretty limited—or at least their opportunities to verbalize or to record in some other way. Often, only one or two students are able to share the connections. And so, a question for us has been how can we provide opportunities for students who are not yet ready to share those connections in whole group or might not have the opportunity? When you think about the fact that 28 students are not going to be able to share connections on a given day to be able to engage in the making of those connections. So, we have two different structures that we have been exploring. The first structure is really a pair share. Students are paired, if possible, with a student who used a different strategy, who has a different solution. Meghan: Each partner explains their strategy, and then together they look for connections between their thinking. So again, this moves beyond the traditional turn and talk because in addition to sharing your thinking, there's a task that the partners are doing about thinking about the connections between those two strategies. A second sort of structure is really using a stop and jot. In this instance, the teacher selects one strategy for students to be thinking about making a connection to, and then each student jots a connection between their strategy or solution and the strategy that the teacher has selected. And they do this in their notebook or in some other written form in the classroom. And so, these two different structures can support participation by having all students have an opportunity to share their own thinking, either verbally with a partner or by recording it in written form. And all students at the same time are having an opportunity to make connections in the classroom. Mike: I think what's interesting about that is to compare that one with the initial idea around critique. In this particular case, I'm going to make a guess that part of the reason that in this one you might actually use students from the classroom versus a fictitious student, is that connecting versus critiquing our two really different kind of social practices. Is that sensible? Meghan: That is sensible. And I would argue that if you're going to be engaging in critique work just to say it, that part of critiquing actually is recognizing, too, what is similar and different about strategies. Mike: Gotcha. Meghan: Right? So, there is that piece in addition to put that out there. Mike: Gotcha. Let's talk about the fourth one. Meghan: Alright. So, the fourth strategy really focuses on broadening participation in the conclusion of a discussion. So, as we all know in a discussion, students hear lots of different ideas, but they don't all get to share their thinking in a discussion, nor do they all get to share what they are thinking at the end of the discussion. But we also know that students need space to consolidate their own thinking and the questions that they have about the ideas that have been shared. At the same time, teachers need access to students' thinking to plan for the next day, particularly when a discussion is not finished at the end of a given math lesson. With all of this, the challenge is that time is often tight at the end of a discussion. So, one structure that we've used has been a note to self. And in a note to self, students write a note to themselves about how they are currently thinking about a particular sort of problem at the end of a discussion. And a note to self allows students to take stock of where they are with respect to particular ideas, similar to a stop and jot. It can create a record of thinking that can be accessed on a subsequent day by students. If those notes yourself are recorded in a notebook. Again, support students and tracking on their own questions and how their thinking is changing over time, and it can provide the teacher with a window into all students' thinking. Mike: Can you talk about the experience of watching the note to self and just seeing the impact that it had? Meghan: So, it was day one of our mathematics program, and we had done a discussion around an unequally partitioned rectangle task, and students were being asked to figure out what fraction of the hole was shaded. And there clearly wasn't enough time that day to really explore all the different sorts of ideas. And so, Darius Robinson, who was one of the co-teachers, invited students to share some of their initial ideas about the task. And the way that Darius then ended up deciding to conclude things that day was saying to students, “I think we're going to do this thing that I'm going to call a note to self.” And he invited the students to open up their notebooks and to record how they were thinking about the different ideas that had gotten shared thus far in the discussion. There was some modeling of what that might look like, something along the lines of, “I agree with … because,” but it really opened up that space then for students to begin to record how they were thinking about otherwise ideas in math class. So, how might using a note to self-broaden participation in a discussion? Well, first of all, students have the opportunity to participate. All students are being asked to write a note to themselves. It creates space for students to engage with others' ideas that doesn't necessarily require talk, right? So, this is an opportunity to privilege other ways of participating, and it also allows for thinking and processing time for all students. Mike: I think the other piece that jumps out for me is this idea that it's normal and to be expected that you're going to have some unfinished thinking or understanding at the end of a particular lesson or what have you, right? That partial understanding or growing understanding is a norm. That's the other thing that really jumps out about this practice is it allows kids to say, “This is where I am now,” with the understanding that they have room to grow or they have room to continue refining their thinking. I really love that about that. Meghan: I think it's so important, right? And oftentimes, we read curriculum materials, we read through a lesson for a particular day and get the sense that everything is going to be tied off with a bow at the end of the lesson, and that we're expecting everybody to have a particular sort of understanding at the end of Section 3.5. But as we all know, that's not the reality in classrooms, right? Sometimes discussions take longer because there are really rich ideas that are being shared, and it's just not feasible to get to a particular place of consensus on a particular day. So, it is for teachers to have access to where students are. But at the same time to feel empowered, to be able to say, “I'm going to pick this up the next day, and that doesn't need to be finished on Monday, but that these ideas that we're working on Monday can flow nicely into Tuesday. And as students, your responsibility is to think about, ‘How are you thinking about the task right now?' Jot some notes so when we come back to it tomorrow, we can pick that up together.” Mike: Well, I think that's the other lovely piece about it, too, is that they're engaging in that self-reflection, but they've got an artifact of sorts that they can come back to and say, “Oh yeah, that's where I was, or that's how I was thinking about it.” That allows for a smoother re-engagement with this or that idea. Meghan: Absolutely. And you can add on the pieces of notation that students might choose to do the next day as well, where they might choose to annotate their notes with notes that said, “Yesterday I was thinking this, but now I think this” as a way to further record the ideas that thinking changes over time. Mike: So, I think before we close this interview, I want to say to you that I watched you do your presentation in Los Angeles at NCTM, and it was really eye-opening for me, and I found myself stuck on this for some time. And I suspect that there are people who are going to listen to this podcast who are going to think the same thing. So, what I want to ask you is, if someone's a listener, and this is a new set of ideas for them, do you have any recommendations for where they might go to kind of deepen their understanding of these ideas we've been talking about? Meghan: Sure. I want to give three different sorts of suggestions. So, one suggestion is to look at the fabulous books that have been put together by Amy Lucenta and Grace Kelemanic, who are the authors of “Routines for Reasoning and Thinking for Teaching.” And I would argue that many of the routines that they have developed and that they share in those resources are ones that are really supportive of thinking about, “How do you broaden participation in mathematics discourse?” A second resource that someone might be interested in exploring is a research article that was written in 2017 by Cathy O'Connor, Sarah Michaels, Suzanne Chapin, and Alan (G.) Harbaugh that focuses on the silent and the vocal participation in learning in whole-class discussion, where they carefully looked at learning outcomes for students who were vocally expressing ideas and discussion as well as the silent participants in the discussion, and really found that there was no difference in the learning outcomes for those two groups of students. And so that's important, I think, for us to think about as teachers. At the same time, I want to be clear in acknowledging that all of what we do as teachers needs to be in relation to the learning goals that we have for students. So, sometimes our learning goals are that we want students to be able to share ideas and discussions. And if that's the case, then we actually do need to make sure that we build in opportunities for students to share their ideas verbally in addition to participating in other sorts of ways. Mike: I'm really glad you said that because what I hear you saying is, “This isn't a binary. We're not talking about … Meghan: Correct. Mike: … verbal participation and other forms of participation and saying you have to choose.” I think what I hear you saying is, “If you've only thought about participation from a verbal perspective, these are ways that you can broaden access and also access your students' thinking at the same time.” Meghan: Absolutely. The third thing to share, which has been a theme across this podcast, has really been the importance of learning from our students and talking with the children with whom we're working about their experiences, participating in discussions both in school and outside of school. Mike: Megan, thank you so much for joining us. It really was a pleasure. Meghan: Thank you, Mike, for the opportunity to really share all of these ideas that my colleagues and I have been working on. I want to acknowledge my colleagues, Nicole Garcia, Aileen Kennison, and Darius Robinson, who all played really important roles in developing the ideas that I shared with you today. Mike: Fabulous. Thank you so much. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. © 2023 The Math Learning Center | www.mathlearningcenter.org

Rounding Up Season 2 | Episode 2 – Empathy Interviews Guest: Dr. Kara Imm Mike Wallus: If there were a list of social skills we hope to foster in children, empathy is likely close to the top. Empathy matters. It helps us understand how others are feeling so we can respond appropriately, and it can help teachers understand the way their students are experiencing school. Today on a podcast, we talk with Dr. Kara Imm about a practice referred to as an empathy interview. We'll discuss the ways empathy interviews can help educators understand their students' lived experience with mathematics and make productive adaptations to instructional practice. Mike: Well, welcome to the podcast, Kara. We're excited to have you join us. Kara Imm: Thanks, Mike. Happy to be here. Mike: So, I have to confess that the language of an empathy interview was new to me when I started reading about this, and I'm wondering if you could just take a moment and unpack, what is an empathy interview, for folks who are new to the idea? Kara: Yeah, sure. I think I came to understand empathy interviews in my work with design thinking as a former teacher, classroom teacher, and now teacher-educator. I've always thought of myself as a designer. So, when I came to understand that there was this whole field around design thinking, I got very intrigued. And the central feature of design thinking is that designers, who are essentially thinking about creating new products, services, interactions, ways of being for someone else, have to start with empathy because we have to get out of our own minds and our own experiences and make sure we're not making assumptions about somebody else's lived experience. So, an empathy interview, as I know it now, is first and foremost a conversation. It's meant to be as natural a conversation as possible. When I do empathy interviews, I have a set of questions in mind, but I often abandon those questions and follow the child in front of me or the teacher, depending on who I'm interviewing. Kara: And the goal of an empathy interview is to elicit stories; really granular, important stories, the kind of stories that we tell ourselves that get reiterated and retold, and the kinds of stories that cumulatively make up our identities. So, I'm not trying to get a resumé, I'm not interested in the facts of the person, the biography of the person. I'm interested in the stories people tell about themselves. And in my context, the stories that kids tell themselves about their own learning and their own relationship to school, their classrooms, and to mathematics. I'm also trying to elicit emotions. So, designers are particularly listening for what they might call unmet needs, where as a designer we would then use the empathy interview to think about the unmet needs of this particular person and think about designing something uniquely and specifically for them—with the idea that if I designed something for them, it would probably have utility and purpose for other people who are experiencing that thing. So, what happened more recently is that I started to think, “Could empathy interviews change teachers' relationship to their students? Could it change leaders' relationships to the teachers?” And so far, we're learning that it's a different kind of conversation, and it's helping people move out of deficit thinking around children and really asking important questions about, what does it mean to be a kid in a math class? Mike: There's some language that you've used that really stands out for me. And I'm wondering if you could talk a little bit more about it. You said “the stories that we tell about ourselves”; or, maybe paraphrased, the stories that kids tell themselves. And then you had this other bit of language that I'd like to come back to: “the cumulative impact of those stories on our identity.” Can you unpack those terms of phrase you used and talk a little bit about them specifically, as you said, when it comes to children and how they think about their identity with relation to mathematics? Kara: Sure. I love that kind of phrase, “the story we tell ourselves.” That's been a pivotal phrase for me. I think stories kind of define and refine our existence. Stories capture this relationship between who we are and who we want to become. But when I'm thinking about stories in this way, I imagine as an interviewer that I'm trying to paint a portrait of a child, typically. And so, I'm trying to interact with this child in such a way that I can elicit these stories, painting a unique picture of this kid, not only as a learner but also as a human. What inevitably happens when you do these interviews is that I'm interested in their experience in math class. When I listen to kids, they have internalized, “I'm good at math, and here's why” or “I'm bad at math, and here's why. I just know it.” But when you dig a little bit deeper, the stories they tell are a little more nuanced, and they kind of live in the space of gray. And I'm interested in that space, not the space of testing and measurement that would land you in a particular identity as meant for math or not meant for math. Mike: I think what I was going to suggest is, why don't we listen to a few, because you shared a couple clips before we got ready for the interview, and I was fascinated by the approach that you had in chatting with these children and just how much information I could glean from even a minute or two of the interview slices that you shared. Why don't we start and get to know a few of these kiddos and see what we can learn together. Kara: Sounds great. Mike: We've got a clip that I'm going to invite you to set it up and give us as much context as you want to, and then we'll play the clip and then we can talk a little bit about it. I would love to start with our friend Leanna. Kara: Great. Leanna is a third-grader. She goes to an all-girls school. I've worked in Leanna's school over multiple years. I know her teacher well. I'm a part of that community. Leanna was kind of a new mathematician to me. Earlier in the day I had been in Leanna's classroom, and the interview starts with a moment that really struck me, which I won't say much more about. And I invited Leanna to join me after school so we could talk about this particular moment. And I really wanted to know how she made sense of what happened. So, I think we'll leave it at that and we'll listen to what happened. Mike: Alright, let's give it a listen. Leanna: Hi, I'm Leanna, and I'm 8 years old. Kara: Hi, Leanna. Today when I was in your class, something interesting happened where I think the kids said to me, and they said, “Do you know we have a math genius in our class?” Do you remember that moment? Leanna: Yeah. Kara: Tell me what happened in that moment. Leanna: Um, they said, “We have a math genius in our class.” And then they all started pointing at me. Kara: And what was that like for you? Leanna: It was … like, maybe, like, it was nice, but also it was kind of like, all the pressure was on me. Kara: Yeah, I was wondering about that. Why do you think the girls today—I mean, I'm a visitor, right?—why do you think they use the word “math genius”? And why did they choose you? What do you think they think of you? Leanna: A mathematician … Kara: Yeah. Leanna: … because I go to this thing every Wednesday. They ask me what I want to be when I grow up, and I always say a mathematician. So, they think that I am a math genius. Kara: Gotcha. Do you think all the girls in your class know that you want to be a mathematician when you grow up? But do they mean something else? They didn't say, “We have a mathematician in our class.” They said, “We have a math genius.” Leanna: Maybe. Kara: Are you a math genius? Do think, what does that even mean? Leanna: Like, I'm really good at math. Kara: Yeah. Do you think that's a true statement? Leanna: Yeah, a little bit. Kara: A little bit? Do you love math? Leanna: Yeah. Kara: Yeah. Have you always loved math? Leanna: Yeah. Kara: And so, it might be true that, like, is a math genius the same as a mathematician? Leanna: No. Kara: OK. Can you say how they're different? Leanna: Like, a mathematician is, like … Like, when you're a math genius, you don't always want to be a mathematician when you grow up. A math genius is when you just are really good at math, but, like, a mathematician is when you really, like, want to be when you grow up. Kara: Yeah. Mike: That was fascinating to listen to. So, my first inclination is to say, as you were making meaning of what Leanna was sharing, what were some of the things that were going on for you? Kara: Yeah, I was thinking about how math has this kind of unearned status, this measure of success in our culture that in this interview, Leanna is kind of pointing to. I was thinking about the mixed emotions she has being positioned as a math genius. It called into mind the model minority myth in which folks of Asian descent and Asian Americans are often positioned as stereotypically being good at math. And people say, “Well, this is such a lovely and respectful stereotype, who cares if it's not true?” But she later in the interview talks about the pressure of living up to this notion of math genius and what means. I think about her status in the classroom and how she has the agency to both take up this idea of math genius, and does she have the agency to also nuance it or reject it? And how that might play out in her classroom? So yeah, those are all the things that kind of come to mind as I listen to her. Mike: I think you're hitting on some of the themes that jumped out for me; this sense that kids who are participating in particular activities have been positioned, either by their participation or by their kids' perceptions of what participation means. And I thought the most interesting part was when she said, “Well, it's nice”—but there was a long pause there. And then she talked about this sense of pressure. What it's making me think about as a practitioner is that there are perhaps ways that as a teacher, if I'm aware of that, that might change something small, some things big about the way that I choose to engage with Leanna in the classroom; that I choose to help her navigate that space that she finds herself in. There's a lot for me there as a practitioner in that small clip that helps me really see her, understand her, and think about ways that I can support her. Kara: Yeah. And, like, from a design perspective, I huddled with her teacher later in the day, and we talked about this interview, and we thought about what would it mean to design or redesign a space where Leanna could feel really proud of who she was as a mathematician, but she didn't feel the kind of pressure that this math genius moniker is affording her. And so, ultimately, I want these interviews to be conducted by teachers so that, as you said, practitioners might show up differently for kids or think about what we might need to think more deeply about or design for kids like her. She's certainly not the only one. Mike: Yeah, absolutely. And I think part of what's hitting me in the face is that the term “empathy interview” really is taking on new meaning, even listening to this first one. Because feeling the feelings that she's sharing with us, feeling what it would be like to be in those shoes, I've had kiddos in my class who have been identified or whose folks have chosen to have them participate in programming. And I have to confess that I don't know that I thought as much about what that positioning meant to them or what it meant about how kids would perceive them. I was just struck by how, in so many subtle ways doing an interview like this, might really shift the way that I showed up for a child. Kara: Yeah, I think so. Mike: Well, let's listen to another one. Kara: OK. Maybe Matthew, should we meet Matthew? Mike: I think we should meet Matthew. Kara: Yeah. Mike: Do you want to set up Matthew and give us a sense of what we might need to know about the context? Kara: Absolutely. Matthew is a fifth-grader who describes, in my conversation with him, several years of what he calls “not good” years in math. And he doesn't enjoy mathematics. He doesn't think he's good at it. He has internalized, he's really blamed himself and taken most of the responsibility for those “bad“ years of learning. When I meet him, he's a fifth-grader, and he has written a mathography at the invitation of his classroom teacher. This is a practice that's part of this school. And in his mathography as a fifth-grader, he uses the word “evolving,” and he tells the story of how he's evolving as a mathematician. That alone is pretty profound and beautiful that he has the kind of insight to describe this kind of journey with mathematics. And he really just describes a fourth-grade teacher who fundamentally changed his relationship to mathematics, his sense of himself, and how he thinks about learning. Mike: Let's give it a listen. Kara: Maybe we'll end, Matthew, with: If people were thinking about you as—and maybe there's other Matthews in their class, right—what kinds of things would've helped you back in kindergarten, first and second grade to just feel like math was for you? It took you until fourth grade, right … Matthew: Yeah. Kara: … until you really had any positive emotions about math? I'm wondering what could we have done for younger Matthew? Matthew: Probably, I think I should have paid a lot more attention. Kara: But what if it wasn't about you? What if it's the room and the materials and the teacher and the class? Matthew: I think it was mostly just me, except for some years it was really, really confusing. Kara: OK. Matthew: And when … you didn't really want in third grade or second grade, you didn't want to be the kid that's always, like, “Hey, can you help me with this?” or something. So that would be embarrassing for some people. Kara: OK. You just made air quotes right, when you did embarrassing? Matthew: Yeah. Kara: Was it embarrassing to ask for help? Matthew: It wasn't embarrassing to ask for help, and now I know that. But I would always not ask for help, and I think that's a big reason why I wasn't that good at math. Kara: Got it. So, you knew in some of these math lessons that it was not making sense? Matthew: It made no sense. Kara: It made no sense. Matthew: And then I was, like, so I was in my head, “I think I should ask, but I also don't want to embarrass myself.” Kara: Hmm. Matthew: But also, it's really not that embarrassing. Kara: OK, but you didn't know that at the time. At the time it was like, “Ooh, we don't ask for help.” Matthew: Yeah. Kara: OK. And did that include asking another kid for help? You didn't ask anybody for help? Matthew: Um, only one of my friends that I knew for a really long time … Kara: Hmm. Matthew: He helped me. So, I kind of got past the first stage, but then if he was absent on those days or something, then I'd kind of just be sitting at my desk with a blank sheet. Kara: Wow, so it sounds like you didn't even know how to get started some days. Matthew: Yeah, some days I was kind of just, like, “I'm not even going to try.” Kara: “I'm not” … OK. Matthew: But now I'm, like, “It's not that big of a deal if I get an answer wrong.” Kara: Yeah, that's true. Right? Matthew: “I have a blank sheet. That is a big deal. That's a problem.” Kara: So having a blank sheet, nothing written down, that is a bigger problem for you than, like, “Oh, whoops, I got the answer wrong. No big deal.” Matthew: I'd rather just get the answer wrong because handing in a blank sheet would be, that would probably be more embarrassing. Mike: Oh, my goodness. There is a lot in a little bit of space of time. Kara: Yeah. These interviews, Mike, are so rich, and I offer them to this space and to teachers with such care and with such a deep sense of responsibility 'cause I feel like these stories are so personal. So, I'm really mindful of, can I use this story in the space of Matthew for a greater purpose? Here, I feel like Matthew is speaking to all the kind of socio-mathematical norms in classrooms. And I didn't know Matthew until this year, but I would guess that a kid like Matthew, who is so quiet and so polite and so respectful, might've flown under the radar for many years. He wasn't asking for help, but he was also not making trouble. It makes me wonder, “How would we redesign a class so that he could know earlier on that asking for help—and that this notion that in this class, mathematics—is meant to make sense, and when it doesn't make sense, we owe it to ourselves and each other to help it make sense?” I think it's an invitation to all of us to think about, “What does it mean to ask for help?” And how he wants deep down mathematics to make sense. And I agree with him, that should be just a norm for all of us. Mike: I go back to the language that you used at the beginning, particularly listening to Matthew talk, “the stories that we tell ourselves.” The story that he had told himself about what it meant to ask for help or what that meant about him as a person or as a mathematician. Kara: Yeah. I mean, I am trained as a kind of qualitative researcher. So as part of my dissertation work, I did all kinds of gathering data through interviews and then analyzing them. And one of the ways that is important to me is thinking about kind of narrative analysis. So, when Matthew tells us the things that were in his head, he tells you the voice that his head is saying back to him. Kids will do that. Similarly, later in the interview I said, “What would you say to those kids, those kids who might find it?” And what I was interested in is getting him to articulate in his own voice what he might say to those children. So, when I think about stories, I think about when do we speak in a first person? When do we describe the voices that are in our heads? When do we quote our teachers and our mothers and our cousins? And how that's a powerful form of storytelling, those voices. Mike: Well, I want to listen to one more, and I'm particularly excited about this one. This is Nia. I want to listen to Nia and have you set her up. And then I think what I want to do after this is talk about impact and how these empathy interviews have the potential to shift practice for educators or even school for that matter. So, let's talk about Nia and then let's talk about that. Kara: You got it. Nia is in this really giant classroom of almost 40 kids, fifth-graders, and it's co-taught. It's purposely designed as this really collaborative space, and she uses the word “collaboration,” but she also describes how that's a really noisy environment. On occasion, there's a teacher who she describes pulling her into a quieter space so that she can concentrate. And so, I think that's an important backstory for her just in terms of her as a learner. I ask her a lot of questions about how she thinks about herself as a mathematician, and I think that's the clip we're going to listen to. Mike: Alright, let's listen in. Nia: No, I haven't heard it, but … Kara: OK. I wonder what people mean by that, “I'm not a math person.” Nia: I'm guessing, “I don't do math for fun.” Kara: “I don't do math for fun.” Do you do math for fun? Nia: Yes. Kara: You do? Like, what's your for-fun math? Nia: Me and my grandma, when we were in the car, we were writing in the car. We had this pink notebook, and we get pen or a pencil, and she writes down equations for me in the backseat, and I do them and she times me, and we see how many questions I could get right in, like, 50 seconds. Kara: Oh, my gosh. What's an example of a question your grandma would give you? Nia: Like, they were just practice questions, like, three times five, five times eight. Well, I don't really do fives because I already know them. Mike: So, we only played a real tiny snippet of Nia. But I think one of the things that's really sticking out is just how dense these interviews are with information about how kids think or the stories that they've told themselves. What strikes you about what we heard or what struck you as you were having this conversation with Nia at that particular point in time? Kara: For me, these interviews are about both storytelling and about identity building. And there's that dangerous thinking about two types of people, math people and non-math people. I encounter adults and children who have heard of that phrase. And so, I sometimes offer it in the interview to find out what sense do kids make of that? Kids have told me, “That doesn't make sense.” And other kids have said, “No, no, my mom says that. My mom says she's not a math person.” So, she, I'm playing into it to see what she says. And I love her interpretation that a math person is someone who does math for fun. And truthfully, Mike, I don't know a lot of kids who describe doing math for fun. And so, what I loved about that she, A: She a described a math person's probably a person who, gosh, enjoys it, gets some joy or pleasure from doing mathematics. Kara: But then the granularity of the story she offers, which is the specific pink notebook that she and her grandmother are passing back and forth in the backseat of the car, tell you about mathematics as a thing that she shares a way of relating to her grandmother. It's been ritualized, and really all they're doing if you listen to it is, her grandmother's kind of quizzing her on multiplication facts. But it's such a different relationship to multiplication facts because she's in relationship to her grandmother. They have this beautiful ongoing ritual. And quite honestly, she's using it as an example to tell us that's the fun part for her. So, she just reminds us that mathematics is this human endeavor, and for her, this one ritual is a way in which she relates and connects to her grandmother, which is pretty cool. Mike: So, I want to shift a little bit and talk about a couple of different things: the types of questions that you ask, some of the norms that you have in mind when you're going through the process, and then what struck me about listening to these is you're not trying to convince the kids who you're interviewing of anything about their current thinking or their feelings or trying to shift their perspective on their experience. And I'm just wondering if you can think about how you would describe the role you're playing when you're conducting the interview. 'Cause it seems that that's pretty important. Kara: Yeah. I think the role I'm playing is a deep listener. And I'm trying to create space. And I'm trying to make a very, very, very safe environment for kids to feel like it's OK to tell me a variety of stories about who they are. That's my role. I am not their classroom teacher in these interviews. And so, these interviews probably look and sound differently when the relationship between the interviewer and the interviewee is about teachers and students and/or has a different kind of power differential. I get to be this frequent visitor to their classroom, and so I just get to listen deeply. The tone that I want to convey, the tone that I want teachers to take up is just this fascination with who they are and a deep curiosity about their experience. And I'm positioned in these interviews as not knowing a lot about these children. Kara: And so, I'm actually beautifully positioned to do what I want teachers to do, which is imagine you didn't know so much. Imagine you didn't have the child's cumulative file. Imagine you didn't know what they were like last year. Imagine you didn't know all that, and you had to ask. And so, when I enter these interviews, I just imagine, “I don't know.” And when I'm not sure, I ask another smaller question. So I'll say, “Can you say more about that?” or “I'm not sure if you and I share the same meaning.” The kinds of questions I ask kids—and I think because I've been doing this work for a while, I have a couple questions that I start with and after that I trust myself to follow the lead of the children in front of me—I often say to kids, “Thank you for sitting down and having a conversation with me today. I'm interested in hearing kids' stories about math and their math journey, and somebody in your life told me you have a particularly interesting story.” And then I'll say to kids sometimes, “Where do you want to start in the story?” And I'll try to give kids agency to say, “Oh, well, we have to go back to kindergarten” or “I guess we should start now in high school” or kids will direct me where they think are the salient moments in their own mathematical journey. Mike: And when they're sharing that story, what are the types of questions that you might ask along the way to try to get to clarity or to understanding? Kara: Great question. I'm trying to elicit deep emotion. I'm trying to have kids explain why they're telling me particular stories, like, what was significant about that. Kids are interesting. Some kids in these interviews just talk a lot. And other kids, I've had to really pepper them with questions and that has felt a little kind of invasive, like, this isn't actually the kind of natural conversation that I was hoping for. Sometimes I'll ask, “What is it like for you or how do you think about a particular thing?” I ask about things like math community, I ask about math partners. I ask about, “How do you know you're good at math and do you trust those ways of knowing?” I kind of create spaces where we could have alternative narratives. Although you're absolutely right, that I'm not trying to lead children to a particular point of view. I'm kind of interested in how they make sense. Mike: One of the things that, you used a line earlier where you said something about humanizing mathematics, and I think what's striking me is that statement you made: “What if you didn't have their cumulative report card?” You didn't have the data that tells one story, but not necessarily their story. And that really is hitting me, and I'm even feeling a little bit autobiographical. I was a kid who was a lot like Matthew, who, at a certain point, I just stopped raising my hand because I thought it meant something about me, and I didn't want people to see that. And I'm just struck by the impact of one, having someone ask you about that story as the learner, but also how much an educator could take from that and bring to the relationship they had with that child while they were working on mathematics together. Kara: You said a lot there, and you actually connect to how I think about empathy interviews in my practice now. I got to work with Rochelle Gutiérrez this summer, and that's where I learned deeply about her framework, rehumanizing mathematics. When I do these empathy interviews, I'm living in this part of her framework that's about the body and emotions. Sometimes kids in the empathy interview, their body will communicate one thing and their language will communicate something else. And so, that's an interesting moment for me to notice how body and motions even are associated with the doing of mathematics. And the other place where empathy interviews live for me is in the work of “Street Data,” Jamila Dugan and Shane Safir's book, that really call into question this idea that what is measurable and what is quantifiable is really all that matters, and they invite us to flip the data dashboard. Kara: In mathematics, this is so important 'cause we have all these standardized tests that tell children about who they are mathematically and who they're about to become. And they're so limiting, and they don't tell the full story. So, when they talk about “Street Data,” they actually write about empathy interviews as a way in which to be humanizing. Data can be liberatory, data can be healing. I feel that when I'm doing these interviews, I have this very tangible example of what they mean because it is often the case that at the end of the interview—and I think you might've had this experience just listening to the interview—there's something really beautiful about having a person be that interested in your story and how that might be restorative and might make you feel like, “There's still possibility for me. This isn't the last story.” Mike: Absolutely. I think you named it for me, which is, the act of telling the story to a person, particularly someone who, like a teacher, might be able to support me being seen in that moment, actually might restore my capacity to feel like, “I could do this” or “My fate as a mathematician is not sealed.” Or I think what I'm taking away from this is, empathy interviews are powerful tools for educators in the sense that we can understand our students at a much deeper level, but it's not just that. It's the experience of being seen through an empathy interview that can also have a profound impact on a child. Kara: Yes, absolutely. I'm part of a collaboration out of University of California where we have thought about the intersection of disability and mathematics, and really thinking about how using the tools of design thinking, particularly the empathy interview can be really transformative. And what the teachers in our studies have told us is that just doing these empathy interviews—and we're not talking about interviewing all the kids that you teach. We're talking about interviewing a select group of kids with real intention about, “Who's a kid who has been marginalized?” And/or “Who's a kid who I don't really know that much about and/or I don't really have a relationship with?” Or “Who's a kid who I suspect doesn't feel seen by me or doesn't feel, like, a deep sense of belonging in our work together?” Teachers report that just doing a few of these interviews starts to change their relationship to those kids. Kara: Not a huge surprise. It helped them to name some of the assumptions they made about kids, and it helped them to be in a space of not knowing around kids. I think the other thing it does for teachers that we know is that they describe to do an empathy interview well requires a lot of restraint, restraint in a couple of ways. One, I'm not fixing, I'm not offering advice. I'm also not getting feedback on my teaching. And I also think it's hard for teachers not to insert themselves into the interview with our own narratives. I really try to make sure I'm listening deeply and I'm painting a portrait of this kid, and I'm empathetic in the sense I care deeply and I'm deeply listening, which I think is a sign of respect, but the kids don't need to know about my experience in the interview. That's not the purpose. Mike: We could keep going for quite a long time. I'm going to make a guess that this podcast is going to have a pretty strong on a lot of folks who are out in the field listening. Kara: Hmm. Mike: If someone was interested in learning more about empathy interviews and wanted to explore or understand more about them, do you have any particular recommendations for where someone might go to continue learning? Kara: Yes, and I wish I had more, but I will take that as an invitation that maybe I need to do a little bit more writing about this work. I think the “Street Data” is an interesting place where the co-authors do reference empathy interviews, and I do think that they have a few videos online that you could see. I think Jamila Dugan has an empathy interview that you could watch and study. People can write me and/or follow me. I'm working on an article right now. My colleagues in California and I have a blog called “Designing4Inclusion,” “4” being the number four, and we've started to document the work of empathy and how it shows up in teachers' practice there. Mike: Well, I want to thank you so much for joining us, Kara. It has really been a pleasure talking with you. Kara: Thank you, Mike. I was really happy to be invited. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. © 2023 The Math Learning Center | www.mathlearningcenter.org

Rounding Up Season 1 | Episode 19 – Building a Broader Definition of Participation Guest: Juanita Silva Mike Wallus: Participation is an important part of learning to make sense of mathematics. But stop and ask yourself, “What counts as participation?” In this episode, we'll talk with Dr. Juanita Silva from Texas State University about an expanded definition of participation and what it might mean for how we engage with and value our students' thinking.  Mike: Welcome, Juanita. Thanks for joining us on the podcast. Juanita Silva: Hi. Thank you for inviting me. I'm excited to talk about this topic. Mike: I think I'd like to start by asking you to just talk about the meaning of participation. What is it and what forms can participation take in an elementary math classroom? Juanita: Well, there's a mixture of nonverbal and verbal communication. And you can add in there gestures [as a] form of communication, not just in an interconnected space, but also thinking about students' respect. And it's not just bidirectional, but there's a lot of things that are kind of added in that space. Mike: So, it strikes me that when I was a classroom teacher, when I look back, I probably overemphasized verbal communication when I was assessing my students' understanding of math concepts. And I have a feeling that I'm not alone in that. And I'm wondering if you could talk about the way that we've traditionally thought about participation and how that might have impacted student learning? Juanita: Yes, this is a great question. In thinking about, “What does this look like, how to participate in the classroom?” Mostly teachers think about this as whole group discussions or in small group discussions. And I emphasize the word “their” discussions, where students can share verbally how they thought about the problem. So, for example, if a student is solving a fraction word problem, the teacher may ask, “OK, so how did you solve this problem? Can you share your strategy with the class? What does that look like?” And so, the student sometimes will say, “If I'm solving a fraction word problem about four parts or four chocolate bars, then I can cut those leftovers into four parts.” So that's usually what we think of, as in our teaching and practice in elementary schooling. We think of that as verbal communication and verbal participation, but there are others. ( laughs ) Mike: Let's talk about that. I think part of what you have pushed me to think about is that a student's verbal communication of their thinking, it really only offers a partial window into their actual thinking. What I'd like to do is just talk about what it might look like to consciously value participation that's nonverbal in an elementary classroom. Like, what are the norms and the routines that a teacher could use to value nonverbal communication, maybe in a one-to-one conversation in a small group or even in a whole group discussion? Juanita: Yes. So, I can share a little bit for each one of those. For example, in a one-to-one environment, the teacher and student can more effectively actually communicate ideas if the teacher attends to that child's thinking in nonverbal ways as well. So, for instance, I've had a student before in the past where he would love to explain his thinking using unifix cubes and to share his thinking on a multiplication problem that was about three sets of cookies. And those sets were in groups of seven. So, there were seven cookies in each bag. And I asked him, “Well, how would you share? Could you explain your thinking to me?” And so, he showed me three sets of seven unifix cubes, and he pointed to each of the seven linking cubes and then wrote on his paper, the number sentence, “seven plus seven plus seven is 21.” And when I asked him if the seven represented the cookies, he simply nodded yes and pointed to his paper, saying and writing the words “21 total.” Juanita: So, I didn't ask him to further explain anything else to me verbally because I had completely understood how he thought of the problem. And in this example, I'm showing that a student's gestures and a student's explanation on a piece of paper should be valued enough. And we don't necessarily need to engage in a verbal communication of mathematical ideas because this honors his ways of thinking. But at the same time, I could clearly understand how this child thought of the problem. So, I think that's one way to think about how we can privilege a nonverbal communication in a one-to-one setting. Mike: That's really helpful. I think that part of the example that you shared that jumps out for me is attending to the ways that a child might be using manipulative tools as well, right?  Juanita: Correct.  Mike: So, it was kind of this interaction of the student's written work, their manipulative tools, the way that they gestured to indicate their thinking … that gave you a picture of how this child was thinking. And you didn't really need to go further than that. You had an understanding as an educator that would help you think about what you might do next with that child. Juanita: Absolutely. And that is one of the tools that I find to be super useful, is to not just have students explain their thinking, but also just listen to their nonverbal cues. And so, paying attention to those and also valuing those is extremely important in our practice. I can share one of my favorites, which is a small group example. And this one is kind of foundational to think of the practice when we're teaching in our elementary math classrooms. It's not just that interactions between student and teacher, but the interactions between students and students can be very powerful. So, that's why this is one of my favorite examples. I had two students at one point in my practice. And this was Marco and José, and they were in fourth grade. They were having a hard time communicating verbally with one another, and José was trying to convince Marco of his strategy to split the leftovers of an equal-sharing problem into three parts instead of halves. Juanita: But his verbal communication of these ideas were not clear to Marco. And José explains to Marco, “You have to cut it into halves.” And Marco would say, “Yes, that is what I did.” Like, frustrated, as if, like, “You have to cut this into halves.” And José would say, and Marco was like, “Yes, that's exactly what I did.” So, this exchange of verbal communication was not really helping both of them showcase how they were trying to communicate. So, then José started to insist, and he said, “No, look.” And then he showed Marco his strategy on his paper. And in his paper, he had split the bar into three parts. And then Marco looked at José and said, “Ah, OK.” Had José not shown this strategy on his paper, then Marco would have never really understood what he meant by “You have to cut it into halves.” And so, I share this example because it really showcases that sometimes what we're trying to say and communicate might come across differently verbally, but we mean something else when we showcase it nonverbally. So, in this instance, José was trying to explain that, but he couldn't figure out how to tell that to Marco. And so, in this instance, I feel like it really showcases the power of the nonverbal communication among students. Mike: I think what's fascinating about that is, conceptually the strategy was right there. It was kind of like, “I'm going to equally partition into three parts.” The issue at hand was the language choice. I'm essentially referring to this equal partition as a half, this second equal partition as a half, and this third equal partition as a half. That's a question of helping figure out what is the language that we might use to describe those partitions. But if we step back and say, “Mathematically, does the child actually understand the idea of equal partitioning?” Yes. And then it seems as though it becomes a second question about how do you work with children to actually say what we call this, or the way that we name fractions is—that's a different question, as opposed to, “Do you understand equal partitioning, conceptually?” Juanita: Yeah. So, you're pointing at something that I've found in my research in the past. Oftentimes students will use the word half. And verbally explaining, use the word to mean that they're trying to equally partition a piece of a bar. They'll say, “Well, I cut it into halves.” And then when we look at the document, they're pointing to the lines, the partition lines, that are within the bar. And that's what they're referring to. So, we know that they don't necessarily mean that the part itself is a half, but that the partition is what they're indicating. It means that it's a half. And it's this idea that it's behind … languages really attained to this development over time, where students really think about their prior experiences, as in, “I've cut items before. And those cuts before have been halves.” And so, that particular prior knowledge can transfer into new knowledge. And so, there's this disjuncture, or there's this complexity, within the language communication and those actions. And that's why it's important not just to value the verbal communication—but also nonverbals—because they might mean something else. Mike: Well, part of what you're making me think about, too, is in practice, particularly the way that you described that, Juanita, was this idea that my prior knowledge, my lived experience led me to call the partitions “half.” And the mathematical piece of that is, like, “I understand equal partitioning. The language that I use to describe partitioning is the language of half.” So, my wondering for you is, what would it look like to value the child's partitioning and value the fact that they used this idea of partitioning when they were thinking about halves—and then also build on that to help them have the language of, “We call this type of a partition a third or a fourth,” or what have you. Juanita: So, this is one of those conundrums that I've talked to and discussed with other colleagues, and we talk about how sometimes they're just not ready for it. And so, when we are trying, and that's the other thing, right? Honoring what they say and taking it as they're saying it. And sometimes it's OK not to correct that. So, because we as the teachers have that, you know, we're honoring their thinking as it is, and eventually that language will develop. It eventually will become where they're no longer calling the partitions halves, and they're calling them appropriately, and they're using the part instead. So, it takes time for the student to really understand that connection. So, if we just say it and we tell them, it doesn't necessarily mean it's going to transfer and that they're going to pick up on that. So, I often try not to tell them, and I just let them explain how they're thinking and how they're saying. Juanita: And if I honor their nonverbal ways, then I definitely can see what they mean by halves, that they're not necessarily thinking of the part, they're thinking of the partition itself. And so, that is a very important, nuanced, mathematical evolution in their knowledge. And that sometimes, we as teachers try and say, “Oh, well, we should just tell him how it is.” Or how we should develop the appropriate language. And in some instances, it might be OK. But I think most often I would defer not to do something like that because like I said, I still can access their mathematical thinking even if they don't have that language yet. ( chuckles ) Mike: That's super helpful. I think we could probably do a podcast … Juanita: On that alone? ( laughs ) Mike: The nuances of thinking about that decision. But I want to ask you before we close about whole group. Let's talk a little bit about whole group and what it looks like to value nonverbal communication in a whole group setting. Tell me your thinking. Juanita: Yeah, so this one is a fascinating one that I've recently come across in my own work. And I have to say, it takes a lot of effort on the part of the teacher to enact these things in the classroom, but it is possible. And so, I'll share an example of what I came across in my practice. So, if this was a bilingual classroom, and the teacher was asking students to participate silently and in written form to attend to each other's mathematical ideas, and they had examples. They had to solve a multiplication area problem individually, and then the teacher would post the student's solutions on a large poster paper and then ask all of the students to go around the room with a sticky note offering comments to each of their peer solutions. And so, what we found was just fascinating because the students were able to really dive deep into the students' solutions. Juanita: So, they were more deeply involved in those mathematical ideas with … when you took out the verbal communication. We had an instance where a student was like, “Well, you solved it this way, and I noticed that you had these little pencil marks on each of those squares.” And the student was saying, “Did you count 25 or did you count 26? I think you missed one.” And so, the gestures and the marks, the pencil marks on the piece of paper, that's how detailed the students were kind of attending to each other's thinking. So, they were students that were offering ideas to other students' solutions. So, they were saying, “Well, what if you thought about it this way?” And they would write their explanation of that strategy of how they would solve it instead of how the student actually did it. And so, it was just fantastical. We were just amazed by how much richness there was to their explanations. Had the teacher done this particular activity verbally, then I wonder how many students would have actually participated. Right? So that was one of our bigger or larger questions, was noticing how many students participated in the level and the depth of their justifications for each other, versus had the teacher done this verbally with the students and had them communicate in a whole group discussion. How many students would've been able to do this? So, it is just fascinating. ( chuckles ) Mike: You touched on some of the things that were coming to mind as I heard you describe this practice, and I'd love your take on it. One of the things that strikes me about this strategy of posting solutions and then asking kids to use Post-it Notes to capture the comments or capture the noticings: Does it have the potential to break down some of the status dynamics that might show up in a classroom if you're having this conversation verbally? What I mean by that is, kids recognize that when someone speaks who they've perceived as, like, “Well, that person understands it, so I'm going to privilege their ideas.” That kind of goes away, or at least it's minimized, in the structure that you described. Juanita: That is correct. So, I do a lot of writing on also thinking about culturally sustaining pedagogies in our teaching of practice of math. And some of the things that we find, is that a lot of the students that do participate verbally tend to be white monolinguals. And that oftentimes the teacher or other students privilege their knowledge over the student of color. And so being able to participate in nonverbal ways in this manner really showcases that everybody's knowledge can be privileged. And so, those kind of dynamics within the classroom go away. And so, it really highlights that everybody is valued equally, and that everybody can contribute to these ideas, and that everybody has a voice. That's one of the reasons why this particular piece is just dear to my heart, is because it really showcases to teachers that this can be done in the classroom. Mike: Yeah, I've said this oftentimes on the podcast. I find myself wanting to step back into my classroom role and try this protocol out. It just feels really powerful. Let me go back to something that I wanted to clarify. So, as we've talked about practices that value nonverbal communication, a question that I've been forming and that I suspect other people might be wondering about is, I don't think you're saying that teachers have to either choose to value verbal or nonverbal communication. Juanita: Yes, that is correct. So, I often do both. ( laughs ) It's a mixture of both. Students will communicate verbally to some extent in the same strategy and nonverbally at the same time. And valuing all forms of communication is most important. In my practice as a bilingual teacher and teaching bilingual students, I've also understood that language can't be the sole focus. And the nonverbal cues also highlighted in that communication are just as important as the language, as the bilingualism, when we're communicating ideas. And so, as teachers, there's a law that we also have to pay attention to. So, it's not just that it's nonverbal or verbal communication, but it's also how we approach the teaching, right? Because we as teachers can definitely take over students' thinking and not necessarily pay attention to what they're actually saying. So, only valuing verbal communication would be detrimental to the student. Juanita: So, it has to be a little bit of both and a mixture of everything. I've had students [who] have tried to show me in gestures alone with no written comments on a piece of paper, and that sometimes can work. I've had instances where students can gesture with their hands and say they're pointing, and they're using both hands as, “This is how many I mean, and this is how I'm partitioning with my fingers. I'm doing three partitions, and I'm using three fingers, and I'm showing you three iterations of that with closing and opening my fists.” And so, there's just so much that kids can do with their body. And they're communicating ideas not just in a formal written format, but also using gestures. So, there's lots of ways that students can communicate, and I think teachers should pay attention to all of those ways. Mike: Yeah. The connection that I'm making is, we've done several podcasts, and I've been thinking a lot about this idea of strengths-based, or asset-based, instruction. And I think what you're saying really connects to that because my interpretation is, gestures, nonverbal communication, using manipulative tools, things that kids have either written or drawn, those are all assets that I need to pay attention to in addition to the things that they might use language to describe. Juanita: That's right. That's right. So, everything. ( laughs ) The whole student. ( laughs ) Mike: Well, I suspect you've given our listeners a lot to think about. For folks who want to keep learning about the practices that value nonverbal communication, what research or resources would you suggest? Juanita: Yeah, so I have two articles, one that's particular to bilingual pre-service teachers, and another one that I just explained within a whole group discussion. That's an article, titled, “Attending to others' mathematical ideas: a semiotic alternative to logocentrism in bilingual classrooms.” So, I can give you both links and you can share those along with the podcast. Mike: That sounds fantastic. We'll put a link to that up when we publish the podcast. I just want to thank you, Juanita. It was lovely to have you with us. I've learned a lot, and I sure appreciate you joining us. Juanita: Thank you. Well, thank you for having me. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. © 2023 The Math Learning Center | www.mathlearningcenter.org

Rounding Up Season 1 | Episode 10: Asset-Based Learning Environments Guest: Dr. Jessica Hunt Mike Wallus: Take a moment to think about the students in your most recent class. What assets do each of them bring to your classroom and how might those assets provide a foundation for their learning? Today we're talking with Dr. Jessica Hunt about asset-based learning environments. We'll talk about how educators can build an asset-based learning environment in their classrooms, schools, and school districts. Welcome to the podcast, Jessica. Thanks for joining us. Jessica Hunt: Thank you. I'm so excited to be here today. Mike: Well, I would love to start our conversation asking you to help define some language that we're going to use throughout the course of the podcast.  Jessica: Sure.  Mike: I'm wondering if you can just describe the difference between an asset-based and a deficitfocused learning environment. Jessica: I think historically what we see a lot of is deficit-based thinking. And deficit-based thinking focuses on perceived weaknesses of students—or even a group of students. And it focuses on students as the problem. And as a result, we tend to use instruction in an attempt to fix students or to fix their thinking. So, an asset-based learning environment means focusing on and beginning with strengths as opposed to what we think kids need or how to fix them. So, this means viewing kids as able and recognizing that the diversity of their thoughts, their culture, their experiences—all of these things are valuable and can actually strengthen and add meaning to classrooms and to instruction. I think assetbased learning environments involve a shift in our own mindset as teachers. And, of course, what we hope results from that is a shift in our practice. We talk a lot about growth mindsets for kids. I think I am referring to growth mindsets that teachers have about kids. We can ask, ‘What do students know and how can I use that? Or how can I build upon that through my teaching?' I've never met a kid that didn't bring something to instruction. Every student that I've met [has] had strengths that they bring to mathematics classrooms and to communities to expand their thinking and also that of their peers. Mike: It's fascinating listening to your description. I find myself thinking about how deficit-based many of the systems and structures … Jessica: Yeah. Mike: … and practices are, even though we do these things with positive intent.  Jessica: Yeah.  Mike: Can you just say more about that? How do you see deficit thinking filtering into some of the systems and then impacting the learning environments in our kids? Jessica: Sure. I think two ways that I see deficit thinking filtering into driving—and driving systems in classrooms—involve things like time and priorities. Time and how it's used in classrooms and schools is one area that deficit thinking can impact in a big way. How are systems recommending that teachers actually spend their time with students in the context of a particular day or a week or even a unit of instruction? And I ask that question because I think that it's one thing to state that we have asset-based approach. Yet it's quite another to consider the need to develop meaningful habits within classroom spaces that can really promote student strengths. Mike: So, one of the things that you just said really struck me, which is this idea of habits in the classroom. I'm excited to hear what you're going to say about that. Jessica: I think one of the key habits that we have in asset-based learning environments is this idea of listening to kids. I've never met a student that didn't have viable and valuable ideas about mathematics. The key for me is having the time and space to uncover and understand what those are. So, we've got to have a way to listen to students' thinking. When we do that, when we understand the reasoning and the strengths that they're bringing, that supports us in selecting instructional tools and strategies that leverage both their individual strengths and those that they bring to the group in order to promote learning. Mike: Let's pick up on that a little bit. This idea of listening to kids and understanding their thinking and understanding of what it means about the assets that they bring. For a person who might be listening, help them form an image of what that might look like in an elementary classroom. Talk to me a little bit about on a day-to-day basis, how might this idea of listening to kids or attending to kids' thinking—and really considering the assets—how might that show up? Jessica: One way it shows up is this focus on learning. And before I go on with that, I want to talk a little bit about how learning and a focus on it is a little different than focusing on performance. So, focusing on performance as opposed to learning, risks looking at change as something that's fast and quick as opposed to something that grows and endures. So, part of focusing on learning means that we're looking more at the process as opposed to only examining quick outcomes or products of what students are experiencing in classrooms. It's actually interesting to think about that in terms of educational equity because there's some research that actually suggests that performance gains don't necessarily equate to learning gains. Mike: I think that's fascinating. You're making me think of two things. One, and I'm going to reference this for people who are listening, is ‘Taking Action,' which is NCTM's work. Really trying to say what do some of the really critical principles of high-quality education look like in grades pre-K through 5? And they have a really specific focus on attending to what do we want kids to learn versus simply what's the performance. Jessica: Yes, absolutely. Mike: I also just wanted to key in on something you said, which is that performance can be short-lived, but learning endures. Jessica: It sure does. If we want to focus on learning, it means that we have to be intentional in our classroom practices. And I also think that links to a lot of things. Like you brought up NCTM, and a lot of the things that they advocate for. I think there are some natural linkages there as well. So, for me, being intentional, one key part of that is ensuring that students are doing the thinking so that teachers can listen to and promote that thinking. So, we want the placement of the learning and the thinking on the students for a good percentage of the instructional time. We want to ensure that we're immersing students in content rather than simply presenting it all the time. And I think another part of that listening involves positioning students and the ideas that they're bringing forward as competent. So, I think, together, what all of this means is that we're supporting students to make meaning for themselves, yet definitely not by themselves. Jessica: Teachers have an intentional, key role. And part of that intentionality involves things like slowing down and thinking carefully about how to structure learning experiences. And taking more time and planning and ensuring that students have access to multiple ways to engage in and represent and express their thinking with respect to those tasks and activities that they're using and drawing upon to learn. And I think that asset-based learning environments allow for that intentionality. It allows for that time and space and planning. And in teaching, it allows for that immersion and thinking and listening and positioning of students as the sense-makers, as the doers and thinkers of mathematics. Mike: I think the connection that I'm making is this idea that there are some shifts that have to happen in order to enable asset-based listening and intentionality. One of the things that comes to mind is it really starts with even how you structure or imagine the task itself. If you're posing a problem, that problem isn't accompanied by a ‘Let me show you how to find the answer.' That actually allows kids to think about it. And there might be some divergent thinking, and that's actually a good thing. We want to understand how kids are thinking so we can respond to their thinking. Jessica Absolutely. Mike: That's a big contrast to saying, ‘Let me show you a task, let me show you how to do the task.' It's pretty difficult to imagine listening in that kind of context because really what you're asking them to do isn't thinking about how to solve it. Does that make sense? Jessica: It sure does. And I think for me, or a hunch that I would have, is that that also goes back to this whole idea of teaching and listening and maybe even assessing, if you will, for what we think kids need versus what they're bringing us versus their strengths. I see some connections there in what you're seeing. Mike: Let's talk about that a little bit.  Jessica: Sure.  Mike: Particularly assessment, I think when I was getting ready for this episode, that was the first thing that came to mind. I found myself thinking about previous PLC meetings or data meetings that I've had where even if we were looking at student work, I have to confess that I found myself thinking about the fact that we were looking at what kids didn't understand versus what they did understand. And I tried to kind of imagine how those conversations would've looked from an asset perspective. What would it look like to look at student work and to compare student work and think about assets versus thinking about what do I need to remediate in the type of thinking that I'm seeing?  Jessica: Uh-hm. I hear you there. I think it speaks to something that if we really want to build assetbased learning environments, we need to make some shifts. And I think one of those shifts is how we look at and use data and assessment. Primarily, I think we need to assess strengths and not needs. I heard that a lot as you were talking. How can we focus on assessing strengths and not needs? I say that to a lot of people and they're like, ‘What's the difference?' ( laughs ) Or, ‘That seems so small.' (laughs) But I think it winds up being a really big deal. If you think about it, trying to uncover needs perpetuates this idea that we should focus on what we see as the problem, which as I mentioned earlier, usually becomes the students or particular group of students. And I think it's very problematic because it sets us up as teachers to keep viewing students and their ideas as something that needs to be fixed as opposed to assets that we can build from or learn from in the classroom. Mike: Yeah. One of the other ideas that we've talked about on this podcast in different episodes is the idea of relevancy and engagement. And it strikes me that these ideas about listening to kids for assets are pretty connected to those ideas about relevancy and engagement. Jessica: Yeah, most definitely. I think, again, figuring out, we sometimes call this prior knowledge, but I look at it as when kids come to school, they bring with them their entire experience. So, what are those experiences and what from their eyes are things that are relevant and engaging and things in which they are passionate about themselves? And what do they know about those things? And how might they connect to what others in the classroom know about those things? And how can we, to borrow a term, how can we ‘mathematize' those things ( laughs ) in ways that are beneficial for individual kids and for the community of learners in our classroom? Like, how can we make those connections? I don't think we can answer those types of questions when we use assessment from this place of, ‘What don't students know?' Or ‘How can I get them to this particular place?' If that makes sense.  Mike: It does.  Jessica: I think we can ask those questions from a strengths-based lens that is curious about and passionate about really getting at, again, this whole experience that kids are bringing with them to school. And how we can use that to not only better students learning, but better the classroom community and maybe even better the mathematics that kids are learning in that community. Mike: Absolutely. Jessica: That's, that's interesting to think about. Mike: So, you started to address one of the questions that I was going to ask, which is, I'm imagining that there are folks who are listening to the podcast and they're just starting to think about what are some of the small steps or the small moves that I might make? What small steps would you advise folks to think about if they're trying to cultivate an asset-focused learning environment? Jessica: It's an interesting question, and I would suggest putting into practice some of the bigger ideas that we're getting at in asset-based learning environments themselves. And the first is, look at your own strengths. And when I say who I'm referencing there, it can be a teacher, it can be a school, it can be a district. If you look at your own strengths first, look at how your practices, your structures, your priorities are uncovering and using strengths. And if they're not, why not? Kind of looking at what's there, what capacities do we currently have that we can build on toward asset-based learning environments? And I think I would pair that with just a commitment to, to action, if you will. You know, start small, but start now. If you're a classroom teacher for instance—I tend to go to that ( laughs ), that grade size a lot ‘cause I still very much, uh, identify as a teacher—start with one task or one day, or part of a day, where you can slow down and use your instructional time to listen for kids' strength. Jessica: What brilliance and valuable ways of reasoning are they sharing with you? And what kinds of activity or task or environment did you need to put in place to uncover that? What did you learn about it? What did you learn about yourself in this process? So, we learn about kids and then we learn about ourselves. It becomes sort of this beautiful back and forth between students and teachers where we're all learning about ourselves and about each other. And I think that learning piece is the third thing that I would suggest. Again, going back to let's focus on learning. Let's celebrate our own learning as teachers and schools and districts and et cetera. Reframing your practices and structures will take time. That's OK. But learn to celebrate the steps that you and your communities are taking toward this asset-based model of instruction. And know that, again, you know, when we work to do that, we enable kids as mathematical thinkers and doers. So, we take that problem off kids, and we place it as a challenge in our instructional design, in our experiences and our interactions between teachers and students. So, I think for me, I would really invite folks to take those small steps, uncover your own strengths, learn to listen, and celebrate your own learning. Mike: Before we conclude the episode, I'm wondering if you can recommend any resources for someone who wants to continue learning about an asset-based approach to elementary mathematics? Jessica: Yeah. There [are] so many good examples of this. I think about my own learning as a teacher and a teacher of teachers, ( laughs ) and a researcher. And I think about things like cognitively guided instruction or the work of the The Dream Project in early childhood or even TODOS, where I know they provide a lot of wonderful examples of asset-oriented resources. I'll also do a shameless plug ( laughs ) for my, for my own book, you know, myself … Mike: Plug away!  Jessica: … ( laughs ) and Jenny Ainslie put together, called, ‘Designing Effective Math Interventions: An Educator's Guide to Learner-Driven Instruction.' And that book came off of a project that I did with, uh, National Science Foundation support, where we looked at kids' thinking over time and designed some tasks and activities to support conceptual understanding of fractions. But there are those. Alnd, and so, so many more. But those are the ones that come to mind immediately. Mike: That's fantastic. And we'll share links to those things with the podcast.  Jessica: Great. Mike: I want to thank you so much for joining us, Jessica, it's really been a pleasure talking to you. Jessica: Oh, thank you. It's been an immense pleasure talking with you as well. And thank you for inviting me. I really appreciate it. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation. dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. © 2023 The Math Learning Center | www.mathlearningcenter.org

(5 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(10 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

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(10 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(5 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(10 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(5 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(10 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(5 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(10 hours) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

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(music) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

(music) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

#949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

#949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

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(music) #949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

#949 "ASMR mike" Let me bore you to sleep (Jason Newland) (6th January 2023)

This week we're exploring the fascinating and controversial topic of flat earth theory....again. This ancient belief, once relegated to the fringes of society, has seen a resurgence in recent years thanks to the power of the internet and social media. On this episode, we'll take a deep dive into the history of the flat earth movement and examine the arguments made by its supporters.  We'll explore the evidence (or lack thereof) supporting the idea that the earth is not a globe, but rather a flat, disc-shaped plane. Whether you're a believer or a skeptic, you won't want to miss this revisit. Join us as we challenge our assumptions about the world around us and explore the flat earth phenomenon. Did we change our minds? *Intro sound clip features comedian Dan Cummins If you have any questions or topics you'd like to see the society cover, please reach out at Contact@hushhushsociety.com   You can find all our audio, blogs and drop sweet ratings at www.hushhushsociety.com Find our Video Content on our Rokfin Leave us a review on Apple, our website, Podchaser or GoodPods You can grab Hush Hush merch and help support the show on Patreon Link up with the society on social media:   Facebook   Instagram   Twitter    Join our Discord and chat with us   TRANSCRIPT Flat Earth 2   [00:01:00]  Dave: Greetings, Hushlings. Welcome back to the Hush Hush Society Conspiracy Hour. Mike: Where we journey into the world of conspiratorial mysteries and dark truths Dave: I'm Declassified Dave Mike: and I'm Mystery Mike and as though is we're joined by our fellow globetard Slick Fronk Sanders. Fronk: The Earth is probably round how you doing? Dave: it's going. Are things going around today? Mike: Quick question flat Earthers. How do boomerangs work on your flat plane? Fronk: Boomerangs are flat.  Dave: that got him. If you didn't notice today, we returned to the great debate in this episode. Is the Earth round? Is the Earth flat? Fronk: Hushling's, uh, in case you weren't [00:02:00] aware, we visited this topic in season three and completely shat all over the flat plane and we believe we should revisit this mother of all modern conspiracies, seeing as though it's such a big part of conspiracy culture. Dave: it's getting even bigger, even though you guys probably most definitely are gonna take a second dumping in this one. Mike: not as bad as the first. Dave: Not  Fronk: Yeah. We'll see. We'll see. Mike: we've discussed how there are different phases to being a flat earther. I'm guess I'm still in stage zero and we were in stage one in May of 2021. let's go up around to stage two But before we search for the horizon and fall off the flat plane and search for God in the sky under the spotlight sun, you can always find us on our social medias, Facebook, [00:03:00] Instagram, and Twitter Dave: You can also find everything hush hush society on our website, www.hushhushsociety.com. From episodes to links to merchandise, and the ability to drop a review or leave us a voicemail. We hope we get some after this episode. Mike: Hmm. Please do. Dave: Yeah. Fronk: And we keep mentioning that we are now also a video podcast. You can not only. To us, but you can watch us, you can see our faces. You can get that expressional action that you might not get from just an audio recording. And to find those episodes, you just gotta go to Rock Fin. It's, it's very simple. Rock fin.com. There's even an app. And in the search bar you just put in Hush Hush Society. You'll find us nice and easy. And there you can find all of our videos. you hit the notification button. You get notifications when our videos come out. Check it out. Mike: And just one last thing before we move on to the flat plane, we just [00:04:00] want to give a quick shout out to our newest patron, Gabrielle May. Thank you so much. We appreciate you. Fronk: Just in case you're new to this, we're gonna do a quick little recap for you on what Flat Earth theory is, and essentially, in a nutshell, the earth is flat rather than round. Pretty self explanatory, although it's made its appearance throughout history. The theory gained popularity around 2009 and has continued to grow ever since. Dave: It is regarded as one of the most controversial conspiracy theories in existence. Why claim that our earth is flat and not a globe easy? That's because it looks flat and feels flat and is surrounded by 200 feet of ice blocking us from traversing across an infinite plane or falling off the edge. Sounds correct, right? Fronk: I mean, yeah, that's what I've been made to believe. That's that's what it seems like Mike: Yeah. Riding on the back of a turtle through the cosmos, but the cosmos [00:05:00] doesn't exist, so where's the turtle going? Anyways,  according to believers, NASA and the ruling elite protect the ice walls from people attempting to climb over and fall from the disc. Can't make it up. They also believe that earth's gravity is an illusion, and that objects are driven up by a mysterious force called dark energy, rather than spinning and being stuck to a surface, Fronk: But on the other hand, there are countless photographs, videos, and images from astronauts and the International Space Station that kind of seem like evidence to show that the Earth is round. But these are not considered real evidence and are allegedly faked by the government or the ruling elites Dave: Now before we move on, flat, earthers already pissed off at our description in the beginning, Fronk: probably. Dave: we wanted to pull you in, but we'll make it as [00:06:00] fair as possible with some of the talking points that we're going to go over.  Now, Hushlings, there is the flat Earth Society as well as thousands of others from around the globe in groups. In addition to independent researchers, even though there is evidence to contradict some of these arguments, they are dismissed as fabrications of around earth conspiracy, along with stars, planets, galaxies, space, and gravity, all being a part of the facade of where we live. Mike: That is my biggest thing when it comes down to a debate between a flat earth and someone who believes that we live on a globe, is that it always results. In a flat earth are saying, well, that's what you've been told. You've been lied to. You're believing a lie that's being told to you, which is the old faithful of all conspiracy theorists, is that you're being lied to. That's all well and good, but at what point do you turn around and say, the [00:07:00] science is being lied to you. Nasa, we know lies to us. We know they fabricate images. We know what they do. But again, that's more of an argument that NASA is filled with bunch of liars. But at what point do you look at it maybe there is evidence that it's a globe or maybe there is evidence that it's a flat plane. There has to be a certain cutoff point where you stop saying, well, you're being lied to. That's what they want you to believe. That's what they're fabricating the science. They're fabricating this. They're fabricating that. How, and this has always been my issue, how do you talk to a flat earth and say, what piece of evidence would it take for you to say that it's a globe Dave: Pictures. Mike: pictures? , but then you show them a picture of this is what our earth looks like. It's a globe. Or you show them video or you show them anything. Well, that's been fabricated. It's always like this deniability to go against what they believe in. Like you, you have to deny [00:08:00] it. You have to deny it because it shakes the entire foundation of what their belief system is, especially when it comes to a flat earth. But then they always revert back to, that's what the Bible says. That's what the Bible says. I'm sorry, we, we've been over the Bible many times. We all know that it's been changed a thousand times and it's a book.  Fronk: not only that, but that's what they're making the Bible say. That's what certain people are interpreting the bible to say, and you can make the Bible say a lot of different things depending on how you decide to interpret it as a person. And if you're interpreting it as, they're telling me about the flat earth and so be it, Dave: This episode is gonna focus a little bit more heavily on some of the things that Mike and Fronk just mentioned, talking about NASA and the why would they lie and why would they fake and indoctrinated us as kids to believe that it's a ball. , and these are major [00:09:00] talking points that I've learned over the last year and a half since we've done this, other than just the physical evidence. We have the physical evidence if you're going to go by the, mainstream. we'll go through a bunch of stuff. I think we'll talk about religion too. So Mike, save those nails, buddy. Mike: We'll look into some of what we just listed and more throughout this episode, and it strongly suggested you listen to our first crack at this crust to understand where some of the historical beliefs come from and a lot of other things about this theory, mainly the science. But let's give this another oscillation, shall we? We're gonna literally hit some of the proposed theories and then firmly spit some facts. be prepared to, uh, confirm or deny your belief. Fronk: Before we completely dive into the flat plane, we're gonna talk about the planet as we've been taught in a traditional sense. Our Native [00:10:00] Earth is a terrestrial rocky planet, correct? Yes or no? I mean, whether it's flat around truth,  It has a dynamic and active surface with mountains, valley, canyons, you name it. All the different geographical structures and a variety of other features. It has water covering 70% of its surface, as well as harboring thousands of life forms, and it has a unique orbiting satellite arm. Dave: it has a circumference. Remember this number Hushlings 24,901 miles. And it shares our solar system with eight, sorry, Pluto, eight other planets and is rotating at around thousand miles an hour while orbiting our home star. Now this is where flat Earthers start to deny our existence on a spinning ball. we're orbiting around our sun at 67,000 miles an hour, all while zipping around the center of the Milky Way, roughly at [00:11:00] around 490,000 miles an hour. And the biggest claim, you can't feel it.   Mike: Well, that's just what we're taught in school. Unfortunately, most of us didn't escape the clutches of the Rockefeller Education System. There's that name again. Yep. He created the General Education Board in 1902 at the cost of 129 million. It's a lot of money back in 1902. It's a lot of money today and provided major funding for schools across the nation and was very influential in shaping the school system. Also, he's quoted as saying, I don't want a nation of thinkers. I want a nation of workers. Sounds like my pause. Fronk: And that speaks some deep truth because school does indoctrinate the nation into the trap of society. Once you hit like 10th grade, you're already filling out college applications, colleges that you're gonna be in debt to for the rest of your life, that you're gonna have to work for the majority of [00:12:00] your life to pay off for that job that you'll be working for the rest of your life. And it's this endless cycle. So that's definitely perpetuated by some global elitist. I get that to an extent, maybe the indoctrination portion of it. Dave: Well, from the beginning. Which classroom have you ever been in that didn't have a globe?    Fronk: In 1928, John D Rockefeller Jr. Financed an expedition to the South Pole as a British secret service. Agent Rockefeller knew perfectly that no South Pole existed, but people were curious about the true shape of the world. From 1956 onward, Antarctica was completely controlled by the Pentagon. Hence the Antarctic Treaty. And anybody visiting this chunk of land without permission was shot on site. Admiral by who we've talked about extensively, died mysteriously in 1957 and perhaps had a timely demise before he could tell the truth about what the South Pole. Mike: When it comes to the[00:13:00] Antarctic treaty and being shot on sight, who is shooting these people on sight? Fronk: Snow snipers. Those drones from Star Wars that landed on Hoth Mike: , that's a lot of land to patrol in order to watch for people.  Dave: remember. Antarctica is 5.2 million square miles as well. Mike: That's what doesn't make sense to me. You're gonna be shot on sight and that's another part of the Antarctic treaty that I also don't understand. Who is physically stopping you from going there? The only thing that's physically stopping you from going to Antarctica is it costs a lot of money. To either charter a boat that would go there. most people don't go there. Most charter boats don't go there. You could do a flyover, but that's only partial. Who is physically stopping you besides your bank account? Dave: I did see a video recently of some guys on a boat that were stopped. I think they were stopped by the New Zealand Navy [00:14:00] or the Australian Navy, and they were turning him around and you can see like. Ice in the distance or something like that. And I don't know if there was just like an iceberg that was out there that they were near, but the allegations on TikTok was got turned around at the bottom of the world, cause I believe it's, there's some degree, and I'm gonna sound uneducated saying this, but I don't know the degree, I think, but there's some degree at the bottom of the world. That you can't go. But the Antarctic treaty, it contradicts itself because the Antarctic treaty was supposed to be a demilitarized zone. No military stuff. No commercial, nothing. It was supposed to be strictly for research. Fronk: So why is the Navy there? Of who? New Zealand? Dave: It was either New Zealand or Australia Fronk: So what is the New Zealand or Australian Navy doing there? Dave: Well, they're close to Antarctica Fronk: Yeah, but isn't a non-military zone. Dave: But there's only military scientists maybe not all military scientists. You got like, Noah [00:15:00] scientists and stuff, and I'm sure NASA is down there, the Nazis, they're all down there. You know, you  got everybody. Antarctica looks like a continent to me, and there's a lot of pictures of it. And are they fake? I am. I'm not on the plane, so I don't know. . Why would it matter and why would they lie? The largest argument of why these elites would lie to us is most likely there's more land, more resources, maybe even unlimited resource. And lands beyond the ice shelf or walls, as well as the suppression of how powerful of beings we are, which can kind of be a different argument that has nothing to do with flat earth as well. thoughts on that? Fronk: I could get behind both of those points to an extent in the shoes of a flat Earth, for example. Yes. If you told me that there was unlimited resources, we're talking oil, we're talking the purest water in the world. We're talking minerals that are used to power the world's [00:16:00] electronics, whatever, energy generating methods that we might have unlimited supply of that which would completely destroy not only the US dollar, but the world economy, which is what the alleged elites thrive off of. And if it's not money that they thrive off of it is leaching our fucking energy. And we've talked about that a lot. And if we were to unlock some sort of crazy. Secret about ourselves or humanity as a whole. That might be incredibly enlightening to a lot of people or disturbing. I could see it going either way, but if, if a bunch of people woke up and they were incredibly enlightened, that could be bad for the reptilian negative energy blood suckers. Dave: I don't think it would go well for anybody. I think we always do ask this question a lot when we talk about this as is, would it change our everyday lives? And we usually say no, but it would, because we [00:17:00] probably have a massive economic shutdown. religions would collapse. There'd probably be some type of total anarchy that would happen and then we'd have our own epiphanies of being like, not really upset that I was wrong, but shit I was lied to as well, part of the Doy group. And that would be a shitty day. would it end everything for me? No, it would change everything for sure. But I think the unlimited resources part, I could see somebody hiding that, , we did talk about Admiral Byrd and Admiral Byrd went through, supposedly into the hollow earth, could he have misinterpreted and gone through a crack and found more land. Who knows? In the writing The Iron Republic, written by EW Barrington and published also in 1902, another one of that year with the education system. It was published in Florida Magazine, and it said that an explorer went through a crack in the ice walls and found an advanced civilization after being lost for over a month at sea. So that [00:18:00] means he went through the ice walls and there was more ocean,  Mike: Have there ever been any, any pictures or video of the ice wall or beyond it? Fronk: Uh, people take pictures of. Ice shelves and try to say that they're the ice walls, but at the same time, those could very well just be ice shelves or very large icebergs Mike: Makes sense. Makes sense.  Dave: I wanna see a flight going around the whole whatever, 76,000 miles it's supposed to actually be. Just banking around the whole rim. But you can't go there because the military will shoot you down in a de militarized. Mike: I still think that there's plenty of ways to get there. And we talked, who do we talk with? That had went to Antarctica? Was it Mark Fronk: on a cruise with like their father. Yeah. Mark O'Connell. Yeah. Dave: Yep. Mike: O'Connell said that , he went to Antarctica with his family. Dave: San Diego Padre's pitcher's there right now.  Fronk: Yeah, but he, he also mentioned that it was like the only [00:19:00] part of Antarctica that they'll let a civilian on and it's like this tiny little peninsula and they've got the little, novelty pole.  Like you could go up and touch it and take a picture with it. Yeah. And they got little stuff, penguins and shit. Dave: could it just be a simple explanation why we don't bring people there? One, you'll die  Fronk: , yes, it's very extreme terrain, there's tons of extreme terrain that we're allowed to go to that you would probably die in if you weren't very well equipped. Mike: Yeah, it makes sense that the only reason that they would be stopping people from going there, besides the massive, endless amounts of resources that they're hoarding from us, would be that they just don't want people going out there and fucking dying.  This brings up another allegation that even the word extraterrestrial means extra terra or more land. Trying to hold some weight to the notion this has been taught to us. We see in the film The Next Level by David Weiss. [00:20:00] He meets with an older woman named Ruth. She's 102, God bless her, from Connecticut, who was in tears claiming that she was taught flat Earth in school, in Hamden, Connecticut, and now feels vindicated and better because of his truths. Dave: she was like, lost it. Mike: like real, real emotional about it. Dave: Yeah. Really emotional about it Mike: Okay. We just mentioned the Rockefeller education system and him saying that he doesn't want a nation of thinkers. He wants a nation of workers. , in the 1920s, if she was taught that the earth was flat, She would've been learning from that education system. Dave: True. Yeah, but I don't think that there's actually, I've looked and looked and looked and couldn't find any definitive evidence that was saying that they actually taught that in schools. Because even in 2022 curriculums across the country are not the same, even across the [00:21:00] same states, depending on the size of your state, they're not the same, especially when you get to advanced levels like college professors are teaching what they want within that curriculum, How in 1920 were they all taught the same thing when there was still tons and tons and tons, tons of schools. , that's the thing that gets me,  she's 102. Could she have just been like, yeah, I saw that once and she saw it on a cartoon in the seventies while she was in her sixties,  Fronk: nonetheless, I do find it difficult to wrap my head around because it was David Weiss who did that interview or whatever, and he brings up a lot of stuff about flat Earth. I listen to a bunch of his talks and shows that he went on to and whatnot, and he brings up all of these points and , he tells people to just, look into it. You gotta look into it yourself. You gotta do your research. , you go to do this research and obviously if you're looking into stuff like this, you're not going to [00:22:00] Google. You're not using Bing, like the go to search engine for anything that you can't find is duck, duck go. And he's been saying that Duck, duck go is starting to censor things of this nature. So, like Dave, I went looking for what the global education was like in the 1910s, the 1920s, and. Again, like you said, no definitive proof. Is it a censorship thing or is it the fact that it was just not taught as flat in the 1920s? Dave: There's also allegations that say that, it was the thirties and even in the sixties through certain education systems. , I almost bought David Weiss's app now. David had contacted us and let us know how he thought about us. I think in the next level, , it almost looks like somebody's trying to sell something and maybe this woman really did feel vindicated Ruth if she's still alive or not. but I don't know, check out the next level. It's an interesting take on flat earth and [00:23:00] there's a bunch of other proponents that I'd never even heard of that have some interesting talking points. Mike: my beef when it comes to David is he did reach out to us. He reached out to us a couple times, especially after our flat Earth episode. And essentially just berated us through email it's the usual argument that I, especially for some odd reason am on the receiving end of arguments with flat earthers is just yelling and anger and just being pissed off consistently. and he was not too happy, as Dave said with how we covered it in our talking points. He said, oh, it's the same talking points. Well, it's the same talking points with flat Earthers too. you talk about the Bible, you talk about nasa, you talk about, it's like, it's, it's the same talking points because we're talking about the same fucking topic.  Of course we're gonna have our sides to it and of, and flat earthers are gonna have their sides to it. It's just the way that it is. That's how you have constructive. [00:24:00] Conversations that go back and forth with conflicting beliefs. Dave: I feel like it's a lot of frustration that , you're just not getting it. Fronk: I feel like he rails Coke and like smashes Globes in his free time, like buys globes from Goodwill and just fucking destroys them in the parking lot and then drives home  Dave: beats them with Louisville slugs. Just smack. Smack.  Mike: I can't wait for our next email correspondence after this one. Fronk: dude. It's not gonna be an email. It's gonna be a voice message and he is gonna be all fucking jacked up out of his mind.    Dave: Before we move on to like the major talking points we gotta talk about what Mike mentioned earlier where a lot of the stuff that is talked about goes back to biblical cosmology and creationism.  Mike: Yeah. And that's always been my biggest talking point with discussions with flat Earthers is explain it to me I will give you my counterpoints and you'll give me your points and we can go [00:25:00] back and forth, but complete your, persuasion of trying to make me see that it's a flat plane. Complete your argument without using the Bible. Every single fucking time. Every single time it ends in, well, it says this in the Bible and it says this, it always ends up being that let's put it this way. I've never met a flat earth that wasn't also at the same time a Bible thumper. Dave: I've met two types. I feel like there are conflicting points to, flat earthers even they step on each other's toes a little bit. They might not, not get along, but I think there are some folks that definitely don't believe in the biblical cosmology and it's just a physical thing. But every time you go back to, if it's a physical thing, that's a structure that's not a planet. It brings me to the question, even a non-religious person. It brings me to the question, well then we're talking about who created it, [00:26:00] not just the science of planets and, gas and particles coming together for, from a accretion. We're talking a whole different thing. Now. We're talking about, well, if it's a structure , and this is not what we think it is and this is not what I think it is, then it had to have been manufactured structure. We build structures. using that type of verbiage, brings even me to being like, , now we're in the religious realm or the faith realm. Fronk: You want me to blow your mind right now? you know what's easier than creating a whole universe writing fucking lines of code. Bam, bam.  Mike: Yeah, there it is. There it is. We should just bring all arguments of flat earth back to simulation theory. Fronk: That's where I, that, yeah. Prove to me that it's even physical and then maybe I'll consider whether, the shape is round or flat. Dave: Let's talk about curves. Fronk: Right. All right. Let's talk about the voluminous crevices and curves that our mother Earth provides. Right. The idea of a flat [00:27:00] earth stems from a number of viewpoints, and the most fundamental is to rely on one's own sense, to determine the true nature of one's surroundings. The world appears flat. Clouds, bottoms look like they're flat. Water looks like it's flat, and the sun moves. The stars are always the same positioned exactly how they always were, and all of these sensory cues indicate that we do, in fact, live on a flat. Dave: I'm not an astrophysicist and I'm not a  Fronk: Are you  sure?  Dave: Maybe, maybe, maybe in my other existence, the 500 of 'em. I'm a failed astrophysicist, but I do have a telescope and I've had it for quite some time and I'm pretty good with it. And it's Fronk: the fuck? Dave: eh, the stars not moving. I know that there's a difference between absolute, uh, motion. A difference between [00:28:00] relative motion, and I'm pretty sure that the way that the stars move, but their whole argument is, is that since everything's spinning at astronomical speeds every night, we would see different stars because we're just whipping around and seeing different things. So why are the stars the same? And it does get you thinking, well, why are the stars the same? Well, I'm not a professional astronomer, so I can't really explain that. But I would say it has something to do with relative motion where everything's moving in conjunction instead of just this vortex of insane speeds..  Fronk: In my peanut globetard brain, I'm more so thinking the speed of light and how long it actually takes for the light from the stars that we're seeing to travel here. I mean, yeah, we've been seeing the same stars for thousands and thousands and thousands of years, but at what point were those stars emitting that light? How long have those stars been dead for, and how long is it gonna take for us to see new stars again? [00:29:00] I can't answer any of those questions for you, but I'm pretty sure that's. Dave: Valid point. Mike: Also in the grand scheme of time, humanity has been around a fucking blink in universal time. again to Fronk's point here, we're seeing the same stars because we're living 80 years and that's it. As opposed to the billions and billions and billions of years that the universe has existed and that that light has traveled and those stars have either been born, exploded, died, and disappeared. , we're seeing nothing, nothing. Dave: Well, that goes back to you being an insignificant being and that being suppressed. There's that argument. We'll have that later. We'll fight about it. Mike: there, there won't be an argument. We are insignificant beings.  Even if you took it back to a creationist argument, we are fucking insignificant. We are insignificant, we're [00:30:00] nothing. If we were something we would still commune with Gods, we would still commune with universal spirits. We would be. Something more than fucking meat sacks traveling through the world going, oh, I wonder what job I'm gonna have next, that I'm gonna work fucking 40 hours a week at and pull in a menial salary and take care of my 5.2 fucking kids, and then eventually retire at the ripe old age of 70 years old. And that's my life. How special am I Dave: Well, that's the system that you're locked in. Mike: system or not? Even if I had no job, even if I was just wandering, enjoying my life, going to these wonderful, exotic places, just doing everything that I wanted to do. At the end of it all 70 to 80 years, that's what I get. That's fucking it. in those 70 to 80 years, when am I seeing God? When am I [00:31:00] seeing a hint of any extraterrestrial, any, any extra dimensional, any religious, fucking spiritual guide? Anything. Anything.  when I'm not, fucked up on drugs, Dave: psychedelics. Fronk: God tier moment. Mike goes, have you ever given an ant food? Throw that bitch in there.  Dave: A lot of people see that as negative, and I don't really see it as negative that we're that insignificant. It's kind of the same argument that I make about the flight paths, which we'll quickly touch on is, well, the, the plane has to keep dipping down to keep going. Have you seen how small a plane is to how big the earth is? Mike: That's one thing that they don't understand is fucking perspective. You don't understand  perspective.  Dave: I'm glad you brought that up because what Frankie said a couple minutes ago about viewpoints perspective, seeing, if the clouds appear flat, water is flat, that's called using an empirical approach or an approach that relies on information [00:32:00] on your senses.  What's your feeble little human garbage eyes can see? And if you can't see the curve, then it doesn't exist. They use mathematics. I am. Stupid with math. The math is if the earth is round, there should be a degree of curvature, eight inches per mile squared. one mile would be eight inches, two miles, 32 inches, three miles, 72 inches, four miles, 128, and so on.  128 inches is about 10 feet of curvature. So that would be, four miles away now? 10 feet. A considerable amount when you're looking at a boat on. Water the water line to the top, say, let's say an aircraft carrier is probably 60 to 90 feet. You'd have to be at least around 20 miles to not just see the flight deck of that ship going over the horizon.  Then you got the whole, you got the bridge, you got everything else. You got all the radar you're probably looking at 120 feet at least to the top of, all of the structures on that ship. How many miles is that? . That's the thing. Another thing with the insignificance is [00:33:00] that we're tiny as fuck. Like how can we see anything? If you're five foot 10 and you're looking at something how far are you actually gonna see Mike: but what about the Zoom, Dave? What about the Zoom? Some of those cameras, they can zoom way, way, way, way in. They take those cameras and they zoom, zoom, zoom, and they go, well, that city is 150 miles away. There's no way that I should see it because of this curvature. And this camera is picking it up perfectly. So how do they work? Dave: I think they use the Chicago skyline for example. And I didn't do the experiment and look on Google Maps , and see the different distances, but you gotta remember the Sears Tower, whatever the fuck it's called now, it's like well over a thousand feet tall. and they're like, well, you can see the whole thing you. In those pictures that are shown as examples, you cannot see the entire Sears Tower. There is hundreds of feet of displacement in Chicago. Like New York has a [00:34:00] very tall fucking skyline. But you could still see those buildings and they're there, and on top of it, you're getting atmospheric disturbance. You're getting a layer of almost a mirage layer.  Mike: Dave was just going over the math of the entire situation, it's 67 feet per 10 miles. Now, before we move on, we have to mention that there are ball earthers or globes or globe tards that do argue that this equation is misused by flat earthers. And is the equation of calculating a parabola, not a full sphere. Dave: The guy who said that this is Misused was something that was found on the Michael Stata podcast and apparently himself and another guy that were on there, one was like an F 18 pilot, and then he's got certain hundreds and hundreds amount of hours as being a pilot. he had mentioned that the equation was misused and used the parabola as an example, that you're talking [00:35:00] about something like this instead of something that's a full circle even if you're talking about it on the curve, , it's still a parabola, even on that surface. Even though the equations are right and the math is right to calculate the curvature of the earth with its circumference that's known.  Might not be accurate. And uh, who did that? Aristophenes did that. And I know Flat Earthers is gonna say that guy didn't even fucking exist. which maybe he did, maybe he didn't. That was 2000 years ago. Who knows? Fronk: just to be fair to the flat earthers, right? We can't nitpick what false history we believe and don't, we do tend to say that history could have been falsified many times. If history has been erased at any point in time there is the possibility that this dude was made. Mike: using this model, a person standing on a spherical surface with eyes five feet, 11 inches above the ground, can [00:36:00] hypothetically see the ground up to about three miles away, but a person at the top of the Eiffel Tower at 896 feet can see the ground up to 36.6 miles away. Dave: Well, they're higher in altitude, Mike: Mm-hmm. . Mm-hmm. . Mm-hmm.  Dave: but the argument is that you can't see using the calculation, you wouldn't be able to see because it's dipping. I think the argument is wrong, and I'm not a mathematician and I'm not good at math, but from what my I see is that almost like some of these people are seeing it smaller than what it is. I don't think they're really getting how big this thing is and how small we are. So even at a 900 feet, Yes, you can see almost 10 times as much in distance, but you're also almost a thousand feet in the air,  Mike: Again,  perspective.   Fronk: If the degree of the [00:37:00] curvature is found to be the same everywhere on earth's surface, and the surface is in fact large enough, the constant curvature demonstrates that the earth is a. Now what about water? James Underdown, executive Director for the Center for Inquiry, Los Angeles worked with the Independent Investigations Group, a nonprofit dedicated to investigating exceptional claims using scientific methods. A boat based target with horizontal stripes was used in one of these tests. Dave: He's quoted as saying we sent a boat out on the water, and the farther it goes, the more the stripes disappear. That was supposed to demonstrate the curvature of the planet, but most flat earthers disagreed generating considerable debate. The biggest reason for these arguments with flat earth, obviously it comes from flat Earth, Dave(David Weiss), and it's all about perspective, as we said. The ground would never obscure distant objects on a flat earth. It should be possible to see all the way to the edge of the [00:38:00] world, right? That is the question that we would be asking. The answer we get is the atmosphere is opaque. Now, using the vernacular atmosphere is almost a conundrum in itself, and you ask, well, why did you use that? Well, we don't have another word for it.  Mike: Why not just make up a word like you fucking make up your own beliefs?  Just fucking do it. Just do it. . Make up a new word. It's very easy. It's done every day.   [00:39:00] Ad break [00:40:00]    Mike: Let's move on to another major fight in this, the position of the sun, sunrise and sunset. In case you were wondering, the sun is always above the Earth's surface in both models, Yet in the flat model, it travels in circles around the Earth's north pole, which is also, its. The seasons are caused by the expansion [00:41:00] and contraction of these circles. What about latitude?  Dave: What about latitude? I mean,  that would  Mike: about latitude  Dave: right? Mike: Hmm. Dave: The largest circumference of latitude on this planet would be the equator. Correct?  Mike: Yep. Dave: And then you have the tropic cancer and the tropic of Capricorn. The midpoints. I don't know that seems pretty, easy to explain. Maybe I'm just stupid. Could  be,  Mike: Globetard Dave: yeah. Fronk: Fucking idiot. Do some research Mike: Look into it. Fronk: where, show me where, show me where I could read about this that isn't on the app.  Mike: In the Bible, Fronk: Oh, yeah. Okay. Okay. All right. Here we go with the fucking Bible again. Mike: and books from the  17 hundreds  Fronk: They considered the sun to be much closer than 93 million miles and possibly even as far as 3000 miles or as close as 300 miles and moves in a circle or a helix pattern because the earth is supposedly accelerating upward, obviously toward the sun [00:42:00] at 9.8 meters per second because they don't believe in gravity, and that explains gravity away. with that being said, the sun must also be accelerating in the same direction as this hypothetical earth vortex. Make sense? You guys got that? Dave: instead of us spinning with things spinning around us and us spinning around something else and then that spinning around something else, which is relative there's a really big graphic that's always shown on every documentary, every video, and it's like the sun being shot out of a. With everything else just like around it, it looks like a DNA strand, most globe tards, know that that's not how motion works with celestial bodies. that one got me and always gets me, is every time that's shown. I'm like, oh God.  Fronk: other astronomical bodies moving in such a pattern? We have like really high powered telescopes Mike: Because space is not real.  Fronk: [00:43:00] Oh, shit. I forgot. I'm, I'm sorry. I'm sorry. You got me.  Okay. All right. All right. Right. All right. Dave: no space. No space. We have to remember that throughout this whole episode, there's no space. Fronk: Yes. Yes. Mike: if you take space out of the equation, introduce God in the Bible, and just ignore all known fucking science for the past like 300 years, you can be a flat earther. Fronk: wait is it no space or it's just the sun and the moon and the earth, or , is it None of that and it's just plain earth with our spinning moon, sun clock sort of thing happening, Which one is it? Do flat earthers believe either the barrel bore theory or the plate theory? Dave: Everything's contained in a system. Fronk: It's one in the same Dave: and everything above us is, I guess, the abyss, because there's a lot of arguments that, like with this Artemis program, whether it's fake or not, we'll talk about NASA in a little bit, but whether it's fake or not, Rockets [00:44:00] don't work in a vacuum apparently. but they're actually using, their own inertia to move in a vacuum. But I guess things don't work that way according to some. That brings us to sunrise and sunset. I don't want to get too far into this cuz this can take hours and hours and hours to argue about, let's talk about sunrise and sunset real quick.  Fronk: Unlike a bunch of these other points, the day and night cycles are actually kind of easily explained on a flat plane. The sun theoretically would move in circles above the North Pole. Or around the North Pole, and when it's over your head, it's day, and when it's not, it's nighttime. The light of the sun is then confined to a limited area on the earth, right? Because it's right above you. This claim never held any weight for me in particular because it can be debunked with science.  On top of this, all of the planets and stars aren't actually what they appear to be like [00:45:00] big rock balls in space or giant balls of gas, but they're actually luminaries. Yet. We also hear a lot of people say, well, we don't know what they. Dave: Stars and planets are one of the biggest things that cannot be explained yet. We can explain them with telescopes. We've been talking a lot about movement. We have to talk about heliocentric model, which is the one that we supposedly live in and not the geocentric model, which is the one that flat earthers live in. When we are confronted with the question of how the earth is able to orbit the sun, and it's not a sphere it's pretty simple. The earth actually doesn't orbit the sun, as we've been saying. This is so, because instead of the sun being the center of our solar system, our planet is actually the center of our solar system or controlled environment. Mike: In reality, we have Helio Centrism, also known as the Heliocentric Model. It's the astronomical model in which the earth and planets revolve around the sun at the center historically, [00:46:00] Helio Centrism was opposed to geo centrism, which placed the earth at the center. now we've hit the firmament. Fronk: In the cosmology of the flat earth. The disc shaped planet is covered by a dome whose edges stopped just beyond the roughly 145 foot high ice wall of Antarctica. And these stars are fixed on this dome while the sun and moon, which are only about 31 miles in diameter, revolve about a 3,100 miles above the earth. Dave: Now, as we said before in biblical cosmology, the firmament is a vast, solid dome or semi solid dome created by God during his creation in the first six days To divide the primal sea into upper and lower portions so that the dry land could appear, which surrounds the earth or frozen water, I've heard this a lot with the biblical cosmology stuff, is that it's explained during day one, day two, day three, and they even say in the Bible, God created the firmament. I [00:47:00] believe it's on ver bran's headstone, as we've mentioned previously. I think it's a lot of wordplay and interpretation,  Mike: We also mentioned back in Hollow Moon, if you've listened to that episode about the Zulu tribe, where the firmament or atmosphere rained down to earth.  Our flat earthers saying that the sky is liquid possibly. Clearly, we know that the Earth's atmosphere is 78% nitrogen, 21% oxygen, 0.9% argon and 0.1% of other gases. Dave: Now, quickly, recently, I've heard a lot of arguments in quite a few different shows and videos not just one proponent, but multiple proponents on this theory. And a lot of 'em will say, well, the atmosphere itself is just a different version of water as it is up in space, a whole different version of water. Because they use the example of if you go to the deep oceans or certain lakes, there's different [00:48:00] salinities of water. You'll have heavier water on the bottom, different pockets of water. the atmosphere works the same way and they say, because it has the same elements in it. Now, if our atmosphere is made up of 78% nitrogen, 21% oxygen, yes, there's hydrogen in that, because if we need water, we need H two O, which does happen in the atmosphere, Fronk: shit. That's why they sent U-boats to space it's water. Dave: oh. Fronk: Oh, Dave: That's it.  You got me.  Mike: done. We're done.    Final thoughts, boys? Fronk: Thank you Hushlings. Dave: Yeah, that's it. Mike: Okay, so we're talking about the firmament currently. Now I just want everyone to know the actual definition of a firmament. So the firmament is the vault or arch of the sky. The firmament isn't necessarily something that is physical. It is something that is viewed. the [00:49:00] arch from one horizon to the other is the sky. That is the firmament. So when everybody's saying, oh, firmament, they're talking about the firmament, they're talking about something that's physically there. No, that's a viewpoint. The firmament refers to horizon. To horizon. The arch of the sky as you see it from one end of your viewpoint to the other Dave: Makes sense. There's a lot of that too, where it said that you're, uh, you have a personal viewing bubble and I think that's misinterpreted as what you're actually, what you can see you go up a 1500 foot mountain, you look around, you can see 360 degrees.  Mike: that's your firmament. Dave: that's your firmament. Fronk: One bar from Suicide Boy's last album. One of them goes Dome. So good. I think she think the earth is flat mouth like the fucking firmament. She got my eyes rolling back. There you go.  Mike: it says it all. Fronk: [00:50:00] It says it all, it says it all your, your mouth has a firmament. Mike: Show me what that firmament do. Fronk: land ho. We have hit the ice walls and the absence of the poles along the edge of our local area exists a massive 150 foot ice wall. This ice wall is on the coast of Antarctica, and The wall is absolutely gargantuan, made up of solid water, ice that surrounds our world and holds our world's oceans in.   And the South Pole does not exist, whereas the North Pole is just a giant mountain called a hyperly that you can't visit. Dave: The ice walls were discovered by Sir James Clark, who was a British naval officer and polar explorer who was amongst the first adventure to Antarctica in an attempt to determine the position of the south magnetic pole between 1768 and 1779. [00:51:00] Upon confronting the massive vertical front of ice heat famously remarked. Mike: "It was an obstruction of such character as to leave no doubt in my mind as to our future proceedings for we might as well sail through the Cliffs of Dover as to penetrate such a mass. That's what she said. It would be impossible to conceive a more solid looking mass of ice. Not the smallest appearance of any rent or fisher. Could we discover throughout the whole of its extent and the intensely bright sky beyond it, but too plainly indicated. The great distance to which it wreaths, southward " Dave: apparently it took him three years or so to do one of the journeys and he circumnavigated the globe at 77,000 miles. what if he did it three times and did [00:52:00] 77,000 miles? That's the one thing that I've always thought is that, was it one trip  Fronk: And he just didn't know Mike: But again, in the 18 hundreds, let's say that this guy goes and he encounters an ice shelf, would he not think that was an ice wall? Dave: yeah, Fronk: like, oh shit. Well this is the edge of the world I suppose. Mike: there's no going past this. My ship can't go through that. Dave: I mean, yeah, that would be logical. Mike: I think this is what we said in the first one, a lot of these arguments for a flat earth revert back to like this 18 hundreds knowledge. Let's look at this book from the 18 hundreds. Look, they mentioned the firmament. Let's look at this. they talk about ice stones and blah, blah, blah. Fronk: The future is a lie. . The truth lies in the 18 hundreds. Reject modernity, Now all of this would of course, imply that Antarctica isn't at all what they say. And we've [00:53:00] mentioned this quite a bit about the Antarctic treaty already and the Antarctic bases and all of the secrets that they hide and you can't go there. You're not allowed There. Only scientists. Yeah. That's where they're hiding the edge of the.  Dave: Let's board a plane real quick and try to go to Antarctica. I know we say we can get there by ship, but two major arguments about airplanes with the flat earth theory is one, there's no round trip flights to Antarctica. And I think we covered this briefly in our first one where we had said, Antarctica fucking sucks. And that's probably why there's no round trip flights and how a lot of the Southern Hemisphere flights cannot be explained. And I believe we went over that a lot in our first episode. And I still stick by all of what I thought about that. Now, the other question that comes up with this theory  one, can you see curve in a commercial aircraft? And two, the aircraft always has to be pitching nose down after a [00:54:00] certain amount of time. Those two arguments come up major in this theory. So I wanna get your thoughts on do planes always have to tip downward as you're flying? Cuz you've all been on flights before, Fronk: No, the plane isn't nose diving or it doesn't feel like it anyway. It doesn't seem like it's nose diving by any means. Dave: but you would feel it. You can feel drop in altitude when you're starting to descend and you feel that, whew, almost that weird weightlessness when they drop a couple hundred feet or a thousand feet pretty quickly. You can feel turbulence, obviously. , I don't think that it necessarily pitches downward after a certain distance because I think, like I said earlier, planes are tiny and the earth is huge. So I don't think there's that much effect of a plane having to move when it's floating on top of a surface of air. Fronk: If a plane pitched downwards while at like max [00:55:00] altitude, wouldn't it just start losing altitude? Wouldn't you just be going towards the ground or am I being peanut brained? Dave: If planes were going in the straight path following the Earth's curve, then they would fly off into space. That's what they say. And I think it's simpler than that. Planes fly in a certain area from 35,000 to 50,000 feet, especially commercial aircraft in a certain layer of air that's thinnest. Which is why they can move as fast as they can, but I don't believe that they're pitching because they're so tiny that everything is going to appear flat at 35,000 feet cuz the earth is so big. Mike: , they're maintaining a certain altitude from the ground, so they're not pitching anything. They're just going with the natural atmosphere of the earth. Dave: Gravity.  Mike: Yeah.    Dave: The plane thing never, never made too much sense to me, especially with the flying off into space. If you didn't compensate for curvature, it's because the Plains Center [00:56:00] mass is always perpendicular with the ground and the plane is so insignificantly small. That you will not notice those changes. You notice left and right banks on planes, , you take a direction moving towards another city, you see it, you feel the whole plane go and you're looking towards the ground. If you're ascending, you feel that inertia you're getting pulled up into the air, especially on takeoffs. Or if you're descending, you feel that, oh, the pilot goes, we're gonna be descending in a couple minutes, and all of a sudden you feel that that drop, you feel that motion left, right, and vertical but you don't feel those nudges that they say that they're doing. So I don't think that that happens. I just think the center mass of that plane is fighting against gravity to keep it up. It's a boat in the sky. Mike: even if they did, that's a continuous compensation. So it's not like they're flying a certain distance and then going, oh, well I'm eight inches above where I was before. I need to adjust. Even if that was the truth, they would just make manual [00:57:00] adjustments as they went. So over that period of time, a half inch, a quarter inch, whatever you wouldn't even be able to tell in the first place if that was the case. Fronk: And that would only be if you were flying like across the world. I'm sure it's even less so if you're flying from somewhere on the east coast down to like Minnesota or something, it's gonna be even less noticeable if you're traveling somewhere that local. Dave: You're only traveling a couple hundred miles. Fronk: Yeah, exactly. Mike: I'm sure the figures are out there, but how many flat earthers are from America versus from the rest of the world? Dave: Good question. Mike: just wondering. Dave: I don't know the answer to that. I would say there's a lot in America. America is a very conspiracy driven country at the moment, and flat earth boils down to every other conspiracy. If you believe wholeheartedly in this, you believe everything else, the lies, everything is fake. Your entire [00:58:00] existence is fake. that's from what I get Fronk: That sucks. And then, and then from that point where do they go with that? They yell at other people about it or We're gonna briefly go over the eclipse aspect of flat earth theory. Now, we all obviously know what eclipses are. That's when the moon aligns with the sun and the earth and blocks out the sun. You know the deal. and remember that the moon is 400 times smaller than the sun. It's also about 400 times closer to the earth than the sun is. Is that coincidence that this astronomical phenomenon happens? Uh, Dave: Well, I can tell you from the flat earth side that that is almost impossible.  Mike: It's pretty impossible either way. Like it's pretty coincidental. I will give it to them that when you're talking about the sun and the moon being these like perfect distances and these perfect sizes and these per that's intriguing to say the least. I will give them. Dave: Which we did go over[00:59:00] Hollow moon theory if the moon was placed here, it was placed here on purpose, but then that would give weight to some type of, maybe not creationism, but some type of external control or external observation, which I think all of us are on the fence with that.  That could be, it could not be, Mike: Again, prove to me that any of this is real Dave: So there's two types of eclipses. There's solar and lunar eclipses. Now, the way solar eclipses work is that the moon orbits in between the sun and the earth. And when that occurs, obviously the moon blocks out the sunlight. You see the corona bought a bing. You have a solar eclipse, and the moon also casts a shadow on the earth. Now, a lot of the times it's told that the moon can't cast this little tiny pin prick shadow that goes across the earth. But if the moon is relatively 200,000 miles away, why couldn't it?  Mike: According to flat Earth theorists, this astronomical phenomenon is [01:00:00] actually a glimpse of a mysterious shadow object that orbits the sun and occasionally passes in front of the moon. From our point of view, could it be planet X Nibiru? No. This object is known as the anti moon. That's new Dave: another random object in our solar system. We could go on and on about eclipses, but we have to talk about one of the biggest fallacies of our education system. Gravity, Mike: not real. Dave: not real. Now, one of the most well agreed upon theories is general relativity. And it is the theory of gravitation developed by our boy Albert Einstein, who was apparently a conman according to flat earthers. And between 1907 and 1915, he figured all this out. The theory of general relativity says that an observe gravitational effect between masses results from their warping of space time. Gravity is still just a theory to us. I guess we can all be on the fence [01:01:00] on it cause we really don't get it. And I think scientists have , admitted that they don't get it,  Mike: Well, didn't recently they say that they had to like rework that entire thought process for some discovery that they had found that the theory of relativity had to be, had to be rethought or it was not necessarily wrong entirely, but partially, I guess., it had to do with the way that a black hole was working, where for the first time they saw a star coming out of a black hole. Fronk: Yeah, I saw that it was being regurgitated. They saw light coming out of a black hole. That's right. Mike: Things are happening, man. Whether you believe in space or not, it's. Pretty wild. Fronk: Newton's love gravitation states every point Mass attracts every single other point mass by a force acting along the line intersecting both points. I don't know what that means. The force is proportional to the product of the two [01:02:00] masses and inversely proportional to the square of the distance between them. Exactly. That's what I've been saying this whole Mike: Sounds about right. Thanks boys. Well, what is gravity? According to this theory, it's stated that the earth isn't pulled into a sphere because the force known as gravity exists in a greatly diminished form compared to what is commonly taught, which is that we're being pulled down to the center of the earth while. The flat Earth is constantly accelerating up at a rate of 32 feet per second squared or 9.8 meters per second squared. As we had previously mentioned, this constant acceleration causes what you think of as gravity, but it's actually caused by a universal accelerator known as dark energy or Etheric wind. Never heard of Etheric wind. That's interesting, Fronk: time's that post Taco Bell shit's my etheric wind. Dave: [01:03:00] Furthermore with this we hear words like density and buoyancy a lot in these theories arguments, which is why things fall to the ground that are heavier and explains rockets, which are thought to actually be filled with helium and have a pyrotechnic show. that proves that all things fall at 9.8 meters squared.   Dave: All right boys, we're getting towards the end of our flat earth expedition here. But we have to go back in the sky. That brings us to rockets and satellites. As we just mentioned. Proponents of flat earth theory believe that satellites totally exist, but cannot be seen from the ground and are actually held in the atmosphere by helium balloons. Hence why NASA is the largest consumer of helium and they sometimes crash into the planet, which we call them weather balloons. And I guess that would explain the weather balloon phenomenon.  Fronk: Satellites in low earth orbit are constantly fighting gravity. According to science, some are geographically fixed and keep their [01:04:00] orbit by balancing two factors, their velocity, which is the speed required to travel in a straight line and their gravitational pull to the earth. To resist the stronger gravitational pole, a satellite orbiting closer to the earth requires more velocity. And of course, we're not going to get out of this debriefing without a little bit of NASA sprinkled in that bitch. Mike: Yes, good old nasa, our friends over there, professional cgi. It's widely assumed that humans have never left the Earth's atmosphere. In fact, we've never left earth and entered space because we lack the ability to do so in the first place unless you're a Nazi and a U-boat. Most of what society has been taught about space is completely made up or greatly exaggerated. By the government and or the elites. There's also the claim that humans have never landed on the moon. I'm with that, and that the infamous moon landings witnessed by the entire world in [01:05:00] 1969 were a sham. Fronk: Okay. I'll give them that. A major claim is that any pictures from the Apollo 11 mission that show that our planet as a sphere in the distance were fabricated by the government and nasa and NASA's mission is not to hide the shape of the earth or trick people into thinking it's round or anything else of the sort. Dave: Well, that's what NASA says, right?  We obviously know that there's some type of space travel conspiracy, whether it's more advanced or it doesn't exist. Possibly Nasa's mission is to create the illusion of space travel in order to, cover for the military, and their dominance in space. One thing we forgot to mention that I thought of real quick when you guys were talking is the quick notion on gravity. There's a lot of flat earthers that will say, well, can you jump, when you jump off the earth, you a hundred, 200 pound person jumping off the earth. Do you come back [01:06:00] down? And was it easy to jump? Then why is gravity so strong? Fronk: that's the whole argument of like, why does Gravity hold our planet's, oceans On  Dave: Yeah. Yeah. If it can  hold all this water and all this mass,  why can you jump off your roof and hit the ground? Mike: Because there is a different pull depending on the mass of the object.  Dave: Mike wins a gold star Fronk: gold sticker for you. Mike: boys, let's get into our final thoughts. Everything that was on Reddit, we've been through, we've done this whole thing. I wanna know the final thoughts as we get into stage two of becoming a flat earth. are we now believing that gravity is not real? The sun is a, lamp and uh, and we live on a flat plain, surrounded by an ice wall. Dave, are you a flat earther? Dave: No. sadly, I am not a flat earther. I think it's an [01:07:00] interesting theory that opens up a lot of more conspiracies and there are some valid questions, but I think a lot of it has to do with our lack of actually being able to see things because we are restricted beings. Uh, the one thing about flat earth theory that I find really fascinating is the suppression of information, the hidden things. And I think that's the conspiratorial part that really pulls me, believing that it is a different shape or an infinite plane or a snow globe, or, flatterers is gonna get so mad at me for saying that because we don't believe it's a snow globe. It doesn't look like a pancake. They all have different theories and a lot of it goes back to religion. A lot of it goes to creationism. A lot of it goes back to every other conspiracy you've ever heard of. So for me, still, I still think we live on a planet. the definition of planet is what we live on. Is it a perfect sphere? I think that's proven that it's not a perfect sphere.[01:08:00] I'm not a scientist, but I've done research and research and research and supposedly it takes up to two weeks or so to become a flat earth. I've been doing this research since like the end of July, and I'm still not convinced. wanted to give it a fair shake. Didn't wanna be a douche bag. Would invite any flat earth to come on and talk to us. We'd love to have you on, but You didn't get me yet. Mike: I will take my final thoughts, a complete left turn here. I don't care. I don't care whether it's a giant paella pan or if we live on a dodge ball. I, I don't care. I don't care. Maybe it's the blue pilled part of my brain that still exists. I don't give a shit. It doesn't change anything. I'm still gonna wake up in the morning and have to go to work, have to pay my taxes, and eventually I'm gonna fucking die. That's just the way that it is. I don't care if we live on a flat plane, I don't care if we live on a globe. It's just the way that [01:09:00] it is. but I don't think that we live on a fly plane. I'm just gonna say that I don't think that I, I do think that there is a lot of cover up of our former history. That much I believe is true. I do believe that NASA is filled with a bunch of liars and they do fabricate things including, setting up these videos where they're watching astronauts float around, but the water stays in a cup. That's an interesting one. , I do think that they do composite images together and they are a bunch of liars that I completely agree with. . I love you whether you're a flat earth or not, but no, it's a no for me. Fran, give us your final thoughts. Did you become a flat earther in this episode?   Fronk: No, I didn't. , I'm not gonna go off on a limb and say that I tried to give flat earth theory, the benefit of [01:10:00] the doubt, but I tried to stay open-ended, especially towards like the beginning of the episode. I was just trying to like see it from both sides and I still do to an extent. And you're right in saying that their best argument is the space shit and nasa, but, that can't be all you're going off of here, because that, lends to so much other shit besides just the shape of the planet.  And not only that, if you're like sold on the shape of the planet, then you've been deceived. You know what, I'm gonna pull a flirter and tell you what you've been taught on. The internet is wrong, and it's all code. You've been tricked into thinking that what we live on is physical and that it has shape. There is no shape. I've never even been out of the country. You can't even convince me that Australia's real, let alone the, the, the fucking shape of the  Mike: you're partial flat earther because they don't believe that Australia is real either. Fronk: [01:11:00] Oh, no. Australia's not real Mike: listen, if you're in Australia and you, uh, you live there full time, reach out to us. Send us an email. Even better a voicemail, because I just want to hear the accent. Send us a voicemail and say, Hey, yeah, I exist. I'm here. This is a real place. Dave: Clearly they exist. They're number three on our Spotify Mike: That's right. Thanks Australia. Fronk: No, I, I never tried to doubt Australia. It was a metaphor, but Dave: Our Hustralians down under, Mike: That's hilarious. Dave: , if we offended you we're sorry. Well, I partially am. Mike: I, I, listen, I tried this episode. I think that I was better than the first episode. I didn't sit there and say anybody was an idiot or any of that stuff. like I said, you believe what you wanna believe, but on, at the end of the day, I don't think that it really matters. Fronk: And if it makes you feel [01:12:00] special, by all means,

「芳茲滴雞精」年節推出「日月養生雞魚饗宴禮盒」。除了超人氣「日月養生滴雞精」還有百位護理師推薦「日月養生滴魚精」。香醇無腥味！禮盒內附匠人手作「天目釉品茗杯」，下單滿額再抽黃金999金條，詳情請點擊鏈結：https://go.fstry.me/3S2ZQrx —— 以上為播客煮與 Firstory Podcast 廣告 —— 「不好吧～我今天穿得很隨便耶」 英文怎麼說？ 朋友突然揪你下班出去，可是今天真的隨便抓個衣服就穿出門了耶 XD “我穿得很邋遢”、“我昨天沒洗頭”、“我今天素顏” 的英文怎麼說呢？ 這一集的文化閒聊，Duncan 跟我們分享， Duncan 約會的時候會特別精心打扮嗎？會穿什麼樣的風格呢？ 快來聽這一集內容，聽聽看我今天穿得很隨便的英文怎麼說。 Duncan 的線上課程「英語腦進化論」， 現在正在火熱預購中（歡呼～～）： https://lihi1.com/6xs97 我們的聽眾結帳前輸入 duncan300，優惠價格再扣 300 元喔！ 我們跟 MixerBox 合作，推出「這句英文怎麼說」專屬的贊助方案囉！ 有每個禮拜會寄給你一次 podcast 電子報 ＆ 幕後花絮腳本的輕鬆學習方案， 也有來跟我們一起錄音的互動方案，和用 8 折優惠購買我們的線上課程方案喔。 歡迎點進我們的贊助方案看看有沒有你喜歡的內容喔： https://pse.is/3zu4hx 快速幫你複習一下這集的主題句 ＆ 單字： 不好吧～我今天穿得很隨便耶 Sorry, I'm not dressed to go out. I'm dressed too casually. I'm not dressed for company. 補充學習 我穿得很邋遢 （drab / shabby） I'm dressed poorly. I look awful. 我昨天沒洗頭 I didn't wash my hair yesterday. 我今天素顏 I'm not wearing makeup. 情境對話 Duncan：Hey, tonight I'll see Tina, the girl I want you to meet. Are you free? Mike：Ah, sorry, I'm not dressed to go out. Duncan：Why? You look about the same as usual. Mike：Let's do a different day. Next time, give me some advance notice, so I can prepare. 學英文吧網站https://ivybar.com.tw/?c=3 或追蹤 iVY BAR 學英文吧的 IG，上面圖文版 podcast 複習也很棒喔！https://pse.is/39vede 現在我們也有影音版的 Podcast 實境秀喔https://pse.is/3ahupl Powered by Firstory Hosting

Rounding Up  Season 1 | Episode 2 – Posing Purposeful Questions  Guest: Dr. DeAnn Huinker  Mike Wallus: Educational theorist Charles De Garmo once said, ‘To question well is to teach well. In the skillful use of the question, more than anything else, lies the fine art of teaching.' Our guest today, DeAnn Huinker, is one of the co-authors of ‘Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K–5.' We'll talk with DeAnn about the art and the science of questioning and the ways that teachers can maximize the impact of their questions on student learning. DeAnn, welcome to the podcast. It's great to have you.  DeAnn Huinker: I'm happy to be here, Mike. I'm looking forward to our conversation today.  Mike: So, I'd like to start by noting that NCTM (National Council of Teachers of Mathematics) has identified posing purposeful questions as a high-leverage practice in ‘Principles to Actions,' and then again in 2017 with the publication of ‘Taking Action.' And I'm wondering if you can make the case for why educators should see purposeful questions as a critical part of this practice.     DeAnn: Yeah, certainly. Let's just jump right in here. As we think about purposeful questions and why we as teachers need to be more intentional and strategic in the questions we use … I was honored to be a member of the writing team for ‘Principals to Actions.' And in writing that document, we were really tasked with identifying a set of high-leverage teaching practices for mathematics. We reviewed the research from the previous 25 years ( chuckles ), and it was really clear: There's been a lot of research on teacher questioning. And what are the characteristics of effective questioning. So, as I think about making this case for purposeful questions, a couple things come to mind. First of all, researchers have estimated that teachers ask up to 400 questions each day in the classroom. I mean, that's more than one question every minute for the entire school day.  Mike: That's incredible ( sniffs ).  DeAnn: ( chuckles ) I know. That's a lot of questions. Also, if we think about it, it's not just how many questions we ask, but what questions. Because that depth of student learning is really dependent on the questions we ask them because our questions prompt them to consider and engage with the specific mathematical ideas that we're helping them to learn. The other thing I'd like to add to this, is that our questions also set the tone for what it means to learn and do mathematics.  Mike: Hmm. DeAnn: Are we asking questions about getting answers or are we asking questions that let students know we value and respect their inquiries into mathematical ideas into problem-solving, and that we really are about helping them make sense of mathematics? I think it's essential that we critically examine the types of questions we ask and how we can use them to best serve our students.  Mike: That's a really interesting way to think about it. That the questions we ask are really signaling to kids, ‘What is mathematics?' In some ways we're informing their definition of mathematics via the questions that we ask.  DeAnn: Yeah, I absolutely agree with you.  Mike: Well, I think one of the most eye-opening things for me to think about lately has been just learning more about the different categories of questions and the different purposes that they can serve. So, I'm wondering if you can briefly sketch out some of the types of questions teachers could put to use in their classrooms.  DeAnn: So, in ‘Principals to Actions,' we really looked at a lot of different frameworks that people have established over the years for questioning. And we kind of boiled it down to four specific types that are particularly important for mathematics teaching. One is to gather information. For example, can students remember the names for different types of triangles? Another is to probe student thinking. This is when we want them to further explain, elaborate or clarify their thinking. Uh, third type—which is my favorite category—are questions that make the mathematics visible. In other words, these are questions that prompt students to consider and explicitly discuss the underlying math concepts. Or that we want them to make connections among math ideas and relationships. Let me give you an example. If I were going to ask students to explain how to represent 3 × 5 with an array, they would have to consider more deeply the meaning of each of those numbers and that expression, and how that would connect to the representation. So, we're really getting at the mathematics there, not perhaps the problem or tasks that cause them to think about 3 × 5.  Mike: I see. I see.  DeAnn: Fourth category [is] questions that encourage students to reflect and justify. And I think of these as the why questions. Why does it work to solve 4 × 6 by adding 12 + 12? So, those are the four categories that we identified in ‘Principles to Actions.' But since that time, in the ‘Taking Action' book at the elementary level, my co-author and I decided to add a fifth category, because these questions really are emerging in classrooms often. So that fifth category is asking questions that encourage students to engage with the reasoning of other students. Many people refer to these as talk moves. For example, if we think about these talk moves that teachers use in their classrooms or that we need to use more often in our classrooms, an example would be, ‘Who could add on to what Mateo just said?' Or another example would be, ‘Could someone describe or put into their own words the strategy that Jasmine was just telling us about?' Those talk moves are the ones that really get students to listen to and start to have conversations with each other.  Mike: It's interesting because what comes to mind is, there are multiple reasons why that's such an important thing to do in the classroom. In addition to engaging with the reasoning, what it makes me think is it also gives the teacher the opportunity to position a child who may potentially have been marginalized as someone who has math knowledge or whose ideas are valuable.  DeAnn: As I was thinking about talking with you today, Mike, I got thinking about that same idea, which is how do we use questions to position students as capable and as having mathematical authority? And I think this is actually a new area in mathematics education that we need to explore in research further. Just by saying, ‘Can you repeat what Jasmine just said?' I'm actually marking her idea as probably something we should all listen to and consider more deeply.  Mike: Absolutely.  DeAnn: I definitely agree that we can use questions to position students as capable in math classrooms, which is something that's greatly needed these days. And that also helps students develop a more positive math identity in themselves and even fosters their math agency and capability in the classroom.  Mike: So, for me at least, personally, my perspective on questions really changed after I read the ‘5 Practices for Orchestrating Productive Mathematics Discussions' that was written by Margaret Smith and Mary Kay Stein. And after I read that, I really found myself investing a lot more time in preplanning my questions. So, what are your thoughts about whether or how teachers should approach preplanning questions?  DeAnn: In the five practices model, the first practice is to anticipate. This involves anticipating student responses to the kind of key math task of the lesson, and also planning questions so that you, as the teacher, are ready to respond to your students.  Mike: Uh-hm.  DeAnn: Practice of anticipating is preplanning. And I would strongly suggest having those questions written down on a piece of paper so that we are ready to refer to them during the lesson, because it's going to keep us on track, and it's going to give us those tools to help press students to talk more about the mathematical ideas that we want to surface.  Mike: I think part of what really is illuminating for me is, we're anticipating how students might think, and then really, we're digging into what's a response that can help advance their thinking regardless of the angle that they're coming at the task from. So, it's, in some ways, what we're talking about preplanning questions, is really kind of a differentiation strategy to some degree. DeAnn: Perhaps we want to talk a little bit more about the use of the math teaching practice talks about asking both assessing questions and advancing questions?  Mike: Yeah.  DeAnn: So, let's dig into that a little bit.  Mike: Yeah.  DeAnn: The teaching practice from NCTM says we should be using purposeful questions to both assess and advanced students' reasoning and their sense-making about important math ideas and relationships. So, assessing questions are those that really draw out students' current understanding and strategies. And then advancing questions are those that really move students forward in their thinking and understanding—and pushes or presses them or pulls them along towards those learning goals for the lesson. So, that has probably been one of the main things that has really evolved in my thinking in working on ‘Principles to Actions,' is thinking more deeply about these assessing questions and the advancing questions that we need to be posing in our classrooms.  Mike: It strikes me that of the two—they're both important. But it may be that planning advancing questions is the more challenging task for an educator. Talk to me a little bit about preplanning or thinking in advance about advancing questions.  DeAnn: Certainly. So, first as we think about assessing questions, those tend to be more the recalling information, probing student thinking.  Mike: Uh-hm.  DeAnn: As teachers, I think we're pretty good at that. We can all say, ‘Well, how did you think about that? How did you figure that out?' But the advancing questions are much more difficult because that means we, as teachers, have to know: Where are we going with this task and what's the math we want? So, in thinking about this … Or, for example, I was recently working with a group of teachers. And what they did is they worked in grade-level groups and even preplanned the questions they were going to use in an upcoming lesson. And it was really true that yes, assessing questions they had. But we took a lot of time to kind of unpack and think about these advancing lessons. So, I'm going to kind of share, like, three steps here to think about this.  DeAnn: One, you really need to know the math learning goals for the lesson because the advancing questions need to be about the mathematics students are learning. Two, it's helpful to work through the math task that the students are going to be doing in the lesson cause that's going to help you anticipate and approach the task and think about, ‘OK, what might be happening in their work?' And then third, we can preplan those questions that should be specific to the task, to the anticipated student work, and most importantly to the mathematics.  Mike: Uh-hm.  DeAnn: If you can do that with someone, it's so invaluable to brainstorm and bounce ideas off each other.  Mike: I was thinking about what you were saying. And it's striking the difference between an advancing question that's, as you said, about the mathematics that we're trying to advance, versus a question that might move a child toward mimicking a strategy for a right answer right now, but that isn't actually in the long-term advancing the mathematics that we want. That really, for me, is jumping out as something that … it's a line that we want to help people see the difference between those two things, particularly in the moment. And I think that's why, as you were talking, DeAnn, the idea of, let's write some of these things down so that we have them on hand. Because in the moment it's often difficult to make those kinds of judgements when you're in a public space with a whole bunch of children in front of you. That's a superhuman task at some times ( chuckles ). So, there's certainly no stigma to writing it down. In fact, it's a strategy that makes a ton of sense for teachers.  DeAnn: Yeah, definitely agree. There's nothing wrong with having those questions on a piece of paper, on a clipboard, carrying that with you, pausing, taking a moment. ‘What might be some questions I want to ask here?' I mean, asking questions is really a skill we develop as teachers, and we need to use tools and resources to, kind of, help us.  Mike: Well, I was going to say, the other thing that's really hitting me, DeAnn, is the connection between the learning goal and the question; how clearly we see the learning goal and the different levels of progression that kids will make as they're approaching the learning goal. And advancing means recognizing the meaning of a child's thinking at a given time and thinking about what's the next move, regardless of where they're at. Move children toward that deeper understanding.  DeAnn: Yeah. Perhaps it would be helpful if we share some examples.  Mike: Let's do that.  DeAnn: All right. So, assessing questions—as we were talking, it's like, ‘Tell me about your thinking? Can you explain your picture to me? Can you tell me about the tape diagram you drew and used to solve this problem?' Just getting into that kid's thinking and where they're currently at. But then the advancing questions really move students' thinking forward. As you were saying, kind of along this continuum. So, we have to be ready to guide them, kind of step by step, to kind of scaffold that thinking, right? So, I might ask a question, ‘What equation could you write for that problem?' Maybe they got the answer, but what would be an equation they could write? Because perhaps my learning goal is to help them make a connection between those different representations, the context and the equation. I might see that a child has written an equation, but then I might say, ‘Could you label what each of those numbers means in your equation?' Because I really want to make sure they understand the mathematical meaning of each of those numbers.  Mike: Absolutely.  DeAnn: Just asking kids questions, like ‘How are your strategies similar or different?' That's also going to make them think a little more [deeply]. So, all of these advancing questions, really the goal is sense-making and more depth of understanding.  Mike: That totally makes sense. I'm wondering if we can pivot a little bit and talk about the types of teacher moves that might accompany an assessing or an advancing question? What might I do after I ask an assessing question, as opposed to say, asking an advancing question?  DeAnn: So, with assessing questions, the goal of them is really to understand where the student is currently at. So, I would ask an assessing question, and as the teacher I would stay and listen. So, we could assume students are working individually or small groups.  Mike: OK.  DeAnn: So, I might ask an assessing question of a child or a small group and stay and listen because I'm trying to figure out, really to understand, what they did ( chuckles ) and why they did that. Whereas an advancing question, I would be more likely to pose the question to the individual child or small group and then walk away and say, ‘I'll be back in a minute or two to see what you've done or what you're thinking about.' So, it's kind of like giving them time to pause and ponder and consider that question. Mike: This is fascinating because I wonder if for a lot of people that might feel counterintuitive, that you would pose the advancing question and walk away. Tell us a little bit more about the why behind that choice.  DeAnn: Our goal really is to help students become independent math learners in the classroom. By asking the question and then saying, ‘I'll be back in a couple minutes; think about that or show me what you've done,' we want them to be able to figure out how to proceed with a task on their own so that they don't become dependent upon us as teachers. But they really develop that agency in themselves to try things out, whether they're right or wrong, but at least that they're making some progress in the task.  Mike: You know what it makes me think, DeAnn, is that asking an advancing question and walking away might feel foreign to the educator, and it might at least initially feel kind of foreign to the child as well. But over time, it will start to feel like the culture of the classroom, and the child will actually get to a point where it's like, ‘Oh, my teacher believes that I have the ability to think about this and come up with an idea.' And that's a real gift to a child. It does what you were talking about earlier, which is: Question sets the culture and helps children think about what is it to be learning about math.  DeAnn: Yeah. We've also talked about that other type of question to encourage students, to engage with the reasoning of each other. That also really helps with those advancing questions and that tone in the classroom. Cause you could ask a question as a teacher and then say, ‘Why don't you talk with each other for a while about this?' Or ask one student to explain to another student some of their ideas. So, we can, again, use those talk moves when students are working in partners in small groups to learn from each other.  Mike: I'm struck by the idea that this conversation we're having about questioning is also really pretty tightly connected to, how do we support children when they need to engage with productive struggle? And I'm wondering if you could talk about the connection between high-quality advancing or assessing questions, and helping kids manage and engage in productive struggle at the end.  DeAnn: Thinking back to ‘Principles to Actions,' we identified eight high-leverage teaching practices for mathematics. And one of them is using purposeful questions. But another one is supporting productive struggle. So, the connection I think you're kind of alluding to here, Mike, really is they go hand in hand. We can use our questioning to encourage students to persevere in the mathematics that they're doing. But those questions, again, [mean] we are, first of all, trying to understand where the student is at by asking those assessing questions. And then we can encourage them to kind of, like, this bridge, right? With those advancing questions we're trying to get them to consider some of the mathematical ideas that might actually not even be on their horizon for them right now. So, if we say, ‘How could you put this fraction on a number line?' Or ‘How do you know this fraction is greater than or less than one?' We're asking a question to really make that math idea visible and to get them to consider it. And then we're pausing and giving them time and space to consider it and figure out how to proceed on their own. If I, as a teacher, tell them what to do next, that means I'm owning the math, I'm being the authority, and I'm not valuing struggle as part of the learning process.  Mike: Mm, yes. Yes, absolutely. Well, before we close, I want to dig into one more question type. And this is the one that I think really is just kind of transcendent. It transcends the task at hands and digs into students' understanding of big ideas. And it's the one that you would describe as making mathematics visible. Can you talk a little bit about the importance of these types of questions and perhaps some examples that would help people kind of envision what they look like in an elementary classroom?  DeAnn: So, you asked about these questions [that are] really making the math visible. As I think about that, what comes right to mind is a fascinating study conducted by Michelle Perry and her colleagues. They actually looked at the questions and examined very closely the questions teachers ask in a first-grade classroom for mathematics. And they compared the questioning of teachers in Japan, Taiwan, in the United States. Well, unfortunately they found that teachers in the U.S. ask significantly [fewer] questions that require high-level thinking than in Japan and Taiwan. In fact, teachers in those countries tend to ask questions that transcend the problem at hand. I love that phrase. The question goes beyond the surface of the task to really transcend that problem at hand, to get at the underlying math ideas, math concepts, and connections that we want students to make. And they found that teachers in Japan and Taiwan went beyond the surface to really make the math visible for students to consider. And really kept students engaged at higher cognitive levels of thinking.  Mike: That is fascinating. What it reminds me of is, I think it was Jim [James] Hiebert and [James] Stigler wrote about the idea of the mathematics classroom as a cultural activity, in that there's this kind of underlying script of what it means to be a student or a teacher in a mathematics classroom. And I think what we're really talking about in some ways is the role of questioning in building a different vision of what a mathematics classroom is or what it means to be an educator of mathematics.  DeAnn: Yeah. I think that ties right back to our earlier sharing about productive struggle. We think if students don't know the answer quickly that it's our job to step in and tell them how to do it.  Mike: Uh-hm. We're almost coming full circle though, in the sense that I think the promise of high-quality questioning—be it assessing or advancing—is that we're really, by considering the ways that students might think about a task and then considering the ways that you can assess that and advance their thinking from wherever they may be, we really are helping teachers see a different way. And I think that's the power of what you're describing when you talk about strong questioning, DeAnn.  DeAnn: Yeah.  Mike: So, we talked a little bit about what to do next. But I would love for you to take a moment to weigh in on the question of wait time. What are your thoughts about wait time and its value and how that can work in a classroom to support children?  DeAnn: So far today, we've been talking a lot about like the types of questions that teachers ask. But the implementation of those questions is also something we need to think a little bit more about. So, [there are] two types of wait time. Wait time is when I ask a question as a teacher, and how long do I wait until I call on a student? The research on wait time really shows that as teachers, we tend to wait less than a second.  Mike: That's incredible.  DeAnn: Yeah. We provide no processing time to our young learners to really formulate those ideas in their head and then be able to share back. So, just by reminding ourselves to pause for 3 seconds makes a huge difference in the learning that goes on in a classroom. Those 3 seconds, what happens is we find out that more students will respond to our questions. The length of students' responses increases. And those questions or those responses from students where they say, ‘Oh, I don't know,' decrease. So merely waiting 3 seconds makes a huge difference. And as teachers, we just don't deal well with silence, and thinking time, and processing time. So, I think it's always a good reminder to just monitor the amount of time we give students to process ideas after we ask a question.  Mike: You know, as a person who works in math education, when I'm at a dinner party or in mixed company with people, and I ask them, ‘Tell me about your memories of elementary school mathematics.' There are a few common things that always come up. One is typically, as I'm sure won't surprise you, the idea of memorizing my facts. And the other theme that kind of goes along with that is this sense that I wasn't good at math because I didn't know the answer right away. And the connection I'm making is, maybe that's because we didn't give you enough time to actually process and think. If we simply expand our time and give kids 3 seconds or 4 or 5, rather than 1, how different would that experience of mathematics be for children? How many folks would actually feel differently about mathematics and maybe, perhaps, not associate mathematics with just being the first and being the fastest to find the answer.  DeAnn: So, again, we're talking about using our questioning to kind of establish that tone and the expectations in the classroom about what it means to learn and do mathematics. And we shouldn't be in such a hurry ( chuckles ) for students to respond. We as adults need our processing time. Our young learners, [who] are first encountering many of these new ideas in mathematics, we need to give them time to think and to process and make connections before we expect them to respond to any of our questions.  Mike: The piece about 1 second is just so striking. It's odd because I suspect people imagine that by coming back that quickly, they're actually supporting the child. But you're actually doing the opposite ( chuckles ). You're teaching them: One, if you haven't had it in a second, what's wrong with you? And then two: You're also fostering dependency. It's fascinating how, what I think comes from a desire to help, is actually debilitating. DeAnn: It really speaks to the need to reestablish not only norms for students in our classrooms, but really for ourselves as teachers.  Mike: Definitely. Well, I just wanted to say thank you so much for this conversation. It's really been a pleasure to have you join us and hopefully we'll have you back at some time in the future.  DeAnn: And thank you, Mike. I've really enjoyed talking about the importance of purposeful questions for teachers to consider more deeply in their classroom practice.  Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability.  © 2022 The Math Learning Center | www.mathlearningcenter.org