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Today, the usual suspects knee-jerked higher Thursday on Trump's latest peace declaration as crude oil dropped, while the other usual suspects (software as a service) were some of the worst performers ahead of Adobe's earnings release after the close. Also, a strong discussion of the status for gold, copper, crude oil and El Niño with Saxo Head of Commodity Strategy Ole Hansen, a look at macro and FX and much more. Today's pod hosted by Saxo Global Head of Macro Strategy John J. Hardy. Links FT suggests that the quantum computing revolution may be coming sooner than we think. Jesse Felder on the Thoughtful Money podcast, pointing out some concerning trends within the AI phenomenon and suggesting we are near a bubble top. A recent Matt Stoller substack post, mostly just encouragement to follow his work and to read his book Goliath and to point out his link to this old post from May of 2009 about Wall Street's capture of Washington - something that Treasury Secretary Bessent has promised to do something about. The new Kevin Warsh Fed will have a critical role to play if this is ever to amount to anything. About twice per week (in normal times, hopefully soon to resume), you will find links discussed on the podcast and a chart-of-the-day over at the John J. Hardy substack. Read daily in-depth market updates from the Saxo Market Call and the Saxo Strategy Team here. Please reach out to us at marketcall@saxobank.com for feedback and questions. Click here to open an account with Saxo. Intro music by AShamaluevMusic DISCLAIMER This content is marketing material. Trading financial instruments carries risks. Always ensure that you understand these risks before trading. This material does not contain investment advice or an encouragement to invest in a particular manner. Historic performance is not a guarantee of future results. The instrument(s) referenced in this content may be issued by a partner, from whom Saxo Bank A/S receives promotional fees, payment or retrocessions. While Saxo may receive compensation from these partnerships, all content is created with the aim of providing clients with valuable information and options.

Ohio Hot Bed for Drive-Ins; Senior Pranks Going TOOOOO Far; Cheez-It Marker Event Ideas; Guinness World Record Idea; LingeRAT; Rounding Up to the Nickel; Ohio May Mayhem; Wing It THURSDAY, with the Versailles Poultry Days

Andy Tulin from The Post Presence sits down to discuss what's wrong with his favorite team (the Liberty) and we gallivant across the league to get his thoughts on which teams are contenders and which teams are frauds. Check out his daily WNBA Roundups at https://the-post-presence.beehiiv.com/

Dr. Jenny Bay-Williams, Productive Ways to Build Fluency with Basic Facts ROUNDING UP: SEASON 4 | EPISODE 18 This summer we're replaying favorite listener episodes from the first four seasons of Rounding Up—like this one from Season 1. We'll return with all new episodes in early September. Ensuring students master their basic facts remains a shared goal among parents and educators. That said, many educators wonder what should replace the memorization drills that cause so much harm to their students' math identities. Today on the podcast, Jenny Bay-Williams talks about how to meet that goal and shares a set of productive practices that also support student reasoning and sensemaking.  BIOGRAPHY Jennifer Bay-Williams is a professor of mathematics education at the University of Louisville. She has authored over 40 books and 100 journal articles and book chapters that focus on making mathematics meaningful to all students. She is an international leader in the field of mathematics education, frequently speaking at state, national, and international conferences and serving on national boards.  RESOURCES "Eight Unproductive Practices in Developing Fact Fluency" article by Gina Kling and Jennifer M. Bay-Williams Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention book by Jennifer M. Bay-Williams and Gina Kling Math Fact Fluency companion website by Kentucky Center for Mathematics TRANSCRIPT Mike Wallus: Welcome to the podcast, Jenny. We are excited to have you.  Jennifer Bay-Williams: Well, thank you for inviting me. I'm thrilled to be here and excited to be talking about basic facts.  Mike: Awesome. Let's jump in. So, your recommendations start with an emphasis on reasoning. I wonder if we could start by just having you talk about the why behind your recommendation and a little bit about what an emphasis on reasoning looks like in an elementary classroom when you're thinking about basic facts.  Jenny: All right, well, I'm going to start with a little bit of a snarky response: that the non-reasoning approach doesn't work.  Mike and Jenny: (laugh)  Jenny: OK. So, one reason to move to reasoning is that memorization doesn't work. Drill doesn't work for most people. But the reason to focus on reasoning with basic facts beyond that fact, is that the reasoning strategies grow to strategies that can be used beyond basic facts. So, if you take something like the making 10 idea—that 9 plus 6, you can move one over and you have 10 plus 5—is a beautiful strategy for a 99 plus 35. So, you teach the reasoning upfront from the beginning, and it sets students up for success later on.  Mike: That absolutely makes sense. So, you talk about the difference between telling a strategy and explicit instruction. And I raise this because I suspect that some people might struggle to think about how those are different. Could you describe what explicit instruction looks like and maybe share an example with listeners?  Jenny: Absolutely. First of all, I like to use the whole phrase: "explicit strategy instruction." So, what you're trying to do is have that strategy be explicit, noticeable, visible. So, for example, if you're going to do the making 10 strategy we just talked about, you might have two 10-frames. One of them is filled with nine counters, and one of them is filled with six counters. And students can see that moving one counter over is the same quantity. So, they're seeing this flexibility that you can move numbers around, and you end up with the same sum. So, you're just making that idea explicit and then helping them generalize. You change the problems up and then they come back and they're like, "Oh, hey, we can always move some over to make a ten"—or a twenty, or a thirty, or whatever you're working on. And so, I feel like, in using the counters, or they could be stacking Unifix cubes or things like that. That's the explicit instruction. It's concrete.  And then, if you need to be even more explicit, you ask students in the end to summarize the pattern that they noticed across the three or four problems that they solved. "Oh, that you take the bigger number, and then you go ahead and complete a ten to make it easier to add." And then, that's how you're really bringing those ideas out into the community to talk about.  For multiplication, I'm just going to contrast. Let's say we're doing [the] add a group strategy with multiplication. If you were going to do direct instruction, and you're doing 6 times 8, you might say, "All right, so when you see a six," then a direct instruction would be like, "Take that first number and just assume it's a five." So then, "Five eights is how much? Write that down." That's direct instruction. You're like, "Here, do this step. Here, do this step. Here, do this step." The explicit strategy instruction would have, for example—I like, for eights, boxes of crayons because they oftentimes come in eights. So, but they'd have five boxes of crayons and then one more box of crayons. So, they could see you've got five boxes of crayons. They know that fact is 40, they—if they're working on their sixes, they should know their fives. And so, then what would one more group be about?  So, just helping them see that with multiplication through visuals, you're adding on one group, not one more, but one group. So, they see that through the visuals that they're doing or through arrays or things like that. So, it's about them seeing the number of relationships and not being told what the steps are.  Mike: And it strikes me, too, Jenny, that the role of the teacher in those two scenarios is pretty different.  Jenny: Very different. Because the teacher is working very hard (chuckles) with the explicit strategy instruction to have the visuals that really highlight the strategy. Maybe it's the colors of the dots or the exact 10-frames they've picked and have they filled them or whether they choose to use the Unifix cubes and how they're going to color them and things like that. So, they're doing a lot of thinking to make that pattern noticeable, visible. As opposed to just saying, "Do this first, do that second, do that third." Mike: I love the way that you said that you're doing a lot of thinking and work as a teacher to make a pattern noticeable. That's powerful, and it really is a stark contrast to, "Let me just tell you what to do."  I'd love to shift a little bit and ask you about another piece of your work. So, you advocate for teaching facts in an order that stresses relationships rather than simply teaching them in order. I'm wondering if you can tell me a little bit more about how relationships-based instruction has an impact on student thinking.  Jenny: So, we want every student to enact the reasoning strategies. So, I'm going to go back to addition, for example. And I'm going to switch over to the strategy that I call "pretend-to-10", also called "use 10" or "compensation." But if you're going to set them up for using that strategy, there's a lot of steps to think through. So, if you're doing 9 plus 5, then in the pretend-to-10 strategy, you just pretend that 9 is a 10. So now you've got 10 plus 5 and then you've got to compensate in the end. You've got to fix your answer because it's 1 too much. And so, you've got to come back 1. That's some thinking. Those are some steps. So, what you want is to have the students automatic with certain things so that they're set up for that task. So, for that strategy, they need to be able to add a number onto 10 without much thought.  Otherwise, the strategy is not useful. The strategy is useful when they already know 10 plus 5. So, you teach them this, you teach them that relationship—10 and some more—and then they know that 9's 1 less than 10. That relationship is hugely important, knowing 9 is 1 less than 10. And so then they know their answer has to be 1 less. 9's 1 less than 10. So, 9 plus a number is 1 less than 10 plus the number. Huge idea.  And there's been a lot of research done in kindergarten on students understanding things like 7's 1 more than 6, 7's 1 less than 8. And they're predictive studies looking at student achievement in first grade, second grade, third grade. And students—it turns out that one of the biggest predictors of success is students understanding those number relationships. That 1 more, 1 less, 2 more, 2 less. Hugely important in doing the number sense.  So that's what the relationship piece is, is sequencing facts so that what is going to be needed for the next thing they're going to do, the thinking that's going to be needed, is there for them. And then build on those relationships to learn the next strategy.  Mike: I mean, it strikes me that there's a little bit of a twofer in that one. The first is this idea that what you're doing is purposely setting up a future idea, right? It's kind of like saying, "I'm going to build this prior knowledge about ten-ness, and then I'm going to have kids think about the relationship between 10 and 9." So, the care in this work is actually really understanding those relationships and how you're going to leverage them.  The other thing that really jumps out from what you said [is] this has long term implications for students' thinking. It's not just fact acquisition; it's what you said: Research shows that this has implications for how kids are thinking further down the road. Am I understanding that right?  Jenny: That's absolutely correct. So just that strategy alone. Let's say they're adding 29 plus 39. And they're like, "Oh hey, both of those numbers are right next to the next benchmark. So instead of 29 plus 39, I'm going to add 30 plus 40, [which equals] 70. And I got, I went up 2, so I'm going to come back down 2. And I know that 2 less than a benchmark's going to land on an 8." So that, again, it's coming back to this relationship of how far apart numbers are, what's right there within a set of 10, [which] helps then to generalize within tens or within hundreds.  And by the way, how about fractions?  Mike: Hmm. Talk about that.  Jenny: (laughs) It generalizes to fractions. So, let's take that same idea of adding. Let's just say it's like, 2 and seven-eighths plus 2 and seven-eighths. So, if we just pretended those were both 3s because they're both super close to 3, then you'd have 6, and then you added on two-eighths too much. So, you come back two-eighths, or a fourth, and you have your answer. You don't have to do the regrouping with fractions and all the mess that really gets bogged down. And it's a much more efficient method that, again, you set students up for when they understand these number relationships. When you get into fractions, you're thinking about, "How close are you to the next whole number?" maybe, instead of to the next tens number.  Mike: It strikes me that if you have a group of teachers who have a common understanding of this approach to facts, and everyone's kind of playing the long game and thinking about how what they're doing is going to support what's next, it just creates a system that's much more intentional in helping kids not only acquire the facts, but build a set of ways of thinking.  Jenny: Mike, that's exactly it. I mean, here we are, we're trying to make up for lost time. We never have enough time in the classroom. We want an efficient way to make sure our kids get the most learning in. And so, to me that is about investing early in the fact strategies. Because then actually when you get up to those other things that you're adding or subtracting or multiplying or whatever you're doing, you benefit from the fact that you took time early to learn those strategies. Because those strategies are now very useful for all this other math that you're doing. And then students are more successful in making good choices about how they're going to solve those problems that are, oftentimes—especially when, I like to mention fractions and decimals at least once in a basic facts talk because we get back, by the time we get into fractions and decimals—we're back to just sometimes only showing one way. The sort of standard algorithm way. When, in fact, those basic facts strategies absolutely apply to, almost always, more-efficient strategies for working with fractions and decimals.  Mike: I want to shift a little bit. One of the things that was really helpful for me in growing my understanding is the way that you talk about a set of facts that you would describe as foundational facts and another set of facts that you would describe as derived facts. And I'm wondering if you can unpack what those two subsets are and how they're related to one another.  Jenny: Yeah. So, the foundational facts are ones where automaticity is needed in order to enact a strategy. So, to me, the foundational fact strategies are their names. Like the doubling strategy—or double and double again, some people call it. Or add a group for multiplication. And the addition ones of making 10s and pretend-to-10 strategies. And in those strategies, you can solve lots of different facts. But there's too much going on (laughs) in your brain if you don't have automaticity with the facts you need.  So, for example, if you have your 6 facts, and you're trying to get your 6 facts down. And you already know your 5s, like, automaticity with your 5s, then that becomes a useful way to get your 6s. So, if you have 6 times 8, and you know 5 times 8 is 40, then you're like, "I got one more 8, [which equals] 48." That's an added group strategy.  But if you're not automatic with your 5s, this is how this sounds when you're interviewing a child. They're going to use add a group strategy, but they don't know their 5s. So, then they're like, "Let's see. 5 times 8 is 5, 10, 15, 20, 25, 30, 40. Now, what was I doing?" Like, they can't finish it because they were skip-counting with their 5s. They lose track of what they're doing, is my point. So, the key is that they just know those facts that they need in order to use a strategy. And that, going back to, like, the pretend-to-10, they got to know 10 and some more facts to be successful. They have to know 9's 1 less than 10 to be successful. So, that's the idea is, if they reach automaticity with the foundational fact sets, then their brain is freed up to go through those reasoning strategies.  Mike: That totally makes sense.  I want to shift a little bit now. One of the things that I really appreciated about the article ["Eight Unproductive Practices in Developing Fact Fluency" by Gina Kling and Jennifer M. Bay-Williams] was that you made what I think is a very strong, unambiguous case for ending many of the past practices used for fact acquisition—worksheets and timed tests, in particular. This can be a tough sell because this is often what is associated with elementary mathematics, and families kind of expect this kind of practice. How would you help an educator explain the shift away from these practices to folks who are out in the larger community? What is it that we might help say to folks to help them understand this shift?  Jenny: That's a great question, and the real answer is it depends, again, on [the] audience. So, who is your audience? Even if the audience is parents, what do those parents prioritize and want for their children? So, I feel like there's lots of reasons to do it, but to really speak to what matters to them. So, I'm going to give a very generic answer here. But for everyone, they want their child to be successful. So, I feel that that opportunity to show, to give a problem, like 29 plus 29, and ask how parents might add that problem. And if they think 30 plus 30 and subtract 2 to get to the answer or whatever, then that gives this case to say, "Well this is how we're going to work on basic facts. We're building up so that your child is ready to use these strategies. We're going to start right with the basic facts, learning these strategies. These really matter." And the example I gave could be whatever fits with the level of their kid. So, it could be like 302 minus 299. It's a classic one where you don't want your child to implement an algorithm there; you want them to notice those numbers are 3 apart. And so, there's this work that begins early. So, I think that's part of it.  I think another part of it is helping people just reflect on their own learning experiences. What were your learning experiences with basic facts? And even if they liked the speed drills, they oftentimes recognize that it was not well-liked by most people. And also, then they really didn't learn strategies. So, I feel like we have to be showing that we're not taking something away; we're adding something in. They are going to become automatic with their facts. They're not going to forget them because we're not doing this memorizing that leads to a lot of forgetting. And, bonus, they're going to have these strategies that are super useful going forward.  So, to me, those are some of the really strong speaking points. I like to play a game and then just stop and pause for a minute and just say, "Did you see how hard it was for me to get you quiet? Do you see how much fun you were having?" And then I just hold up a worksheet (laughs). I'm like, "And how about this?" You know, again, that emotional connection to the experience and the outcomes.  Mike: That is wonderful.  Since you brought it up, let's talk about replacements for worksheets and timed tests.  Jenny: Mm-hmm.  Mike: So, you advocate for games, as you said, and for an activity-based approach. I think that what I want to try to do is get really specific so that if I'm a classroom teacher, and I can't see a picture of that yet, can you help paint a picture? What might that look like?  Jenny: I love that question because there's lots of good games and lots of places. But again, like I said earlier, this thinking really deeply about what game I'm choosing and for what—what do my students need to practice? And then being very intentional about game choice is really important.  So, for example, if students are working on their 10 and some more facts, then you want to play a game where all the facts are 10 and some more facts. That's what they're working on. And then maybe you mix in some that aren't. Or you play a game with that and then they sort cards and find all the, solve the 10 and some more, or there's lots of things they can do. They can play Concentration, where the fact is hidden and the answer is hidden and things like that. So, you can be very focused. And then when you get to the strategies, you want to have a game that allows for students to say, allow their strategies.  So, I'm a big fan of, like, sentence frames, for example. So, there's games that we have in our Math Fact Fluency[: 60+ Games and Assessment Tools to Support Learning and Retention] book [by Jennifer Bay-Williams and Gina Kling] that are in other places that specifically work on a strategy. So, for example, if I'm working on the pretend-to-10 strategy, I like to play the game Fixed-Addend War, which is the classic game of War, except there's an addend in the middle, and it's a 9, to start. And then each of the two players turns up a card. So, Mike, if you turn up a 7, then you're going to explain how you're going to use the pretend-to-10 strategy to add it. And I turned up a 6, so I'm going to, I'm going to do this then I'll, you can do it. So, I turned up a 6. So, I'm going to say, "Well, 10 and 6 is 16, so 9 and 6 is 1 less, [which equals] 15.' I've just explained the pretend-to-10 strategy. And then you get your turn.  Mike: And I'd say, "Well, 7 and 10, I know 7 and 10 is 17, so 7 and 9 has to be 1 less, and that's 16." Jenny: Yeah. So, your total's higher than mine. You win those two cards, you put them in your deck, and we move on. So, that's a way to just practice thinking through that strategy. Notice there's no time factor in that. You have a different card than I have. You have as much time, and we're doing think-aloud. These are all high-leverage practices. Then we get to the games where it's like, you might turn up a 6 and a 5 where you're not going to use the pretend-to-10 strategy for that. You've got to think, "Oh, that doesn't really fit that strategy because neither one of those numbers is really close to 10. Oh, hey, it's near a double; I'm going to use my doubles." So, you sequence these games to—if you start with one of those open-ended games, it might be too big of a jump because students aren't ready to choose between their strategies. They have to first be adept at using their strategies. And once they're adept at using them, then they're ready to play games where they get to choose among the strategies.  Mike: So, you're making me think a couple things, Jenny. One is, it's not just that we're shifting to using games as a venue to practice to get to automaticity. You're actually saying that when we think about the games, we really need to think about, "What are the strategies that we're after for kids?" And then make sure that the way that the game is structured, like, when you're talking about the pretend-to-10, with the fixed addend. That's designed to elicit that strategy and have kids work on developing their language and their thinking around that particularly. So, there's a level of intent around the game choice and the connection to the strategies that kids are thinking about. Am I understanding that right?  Jenny: That's it. That's exactly right. That's exactly right. And a huge—a lot of intentionality so that they have that opportunity in a no-pressure, a low-stress, think-through-the-strategy [way]. If they make a mistake, their peer or themselves usually correct it in the moment, and they get so much practice in. I mean, imagine going through half a deck of cards playing that game.  Mike: Yeah.  Jenny: That's 26 facts. And then picture those 26 facts (laughs) on a page of paper. And then—and again, in the game that you've got the added benefit of think-aloud, and then you're hearing what your peer has said.  Mike: You know, one of the things that strikes me is, if I'm a teacher, I might be thinking, like, "This is awesome, I'm super excited about it. Holy mackerel, do I have to figure these games out myself?" And I think the good news is, there's a lot of work that's been done on this. I know you've done some. Do you have any recommendations for folks? There's, of course, curriculum. But do you have recommendations for resources that you think, help a teacher think about this or help a teacher see some of the games that we're talking about?  Jenny: Well, I'm going to start with my Math Fact Fluency book because that is where we go through each of these strategies, each of the foundational facts sets and the strategies, and for each one supply a game. And then from those games they're easily adaptable to other settings. And some of the games are classic games. So, there's a game, for example, called Square Deal. And the idea is that you're covering a game board, and you're trying to make a square. So, you get a 2-by-2 grid taken, and you score a point or 5 points or whatever you want to score. Well, we have that game housed under the 10 and some more facts. So, all the answers are, like, 19, 16, 15, and the students turn over a 10 card and another card, and if it's a 10 and a 5, they get to claim a 15 spot on the game board.  Well, that game board can be easily adapted to any multiplication fact sets, any other addition [sets]. I like to do a Square Deal with 10 and some more, and then I like to do Square Deal with 9 and some more. There's my (laughs) effort, again, to come back to either pretend-to-10 or making 10. Where they're like, "Oh, I just played 10 and some more. Now we're doing the same game, but it's 9 and some more." So, I feel like there's a lot of games there. And there is a free companion website that has about half of the games ready to download in English and in Spanish.  Mike: Any chance you'd be willing to share it?  Jenny: Yeah, absolutely. So, you can just google it. The Kentucky Center for Mathematics created it during COVID-19, actually, as a gift to the math community. And so, if you type in "Kentucky Center for Math" or "KCM Math Fact Fluency companion website," it will pop up.  Mike: That's awesome.  I want to ask you about one more thing before we close because we've really talked about the replacement for worksheets, the replacements for timed tests. But there is a piece of this where people think about "How do I know?" right? "How can I tell that kids have started to build this automaticity?" And you make a pretty strong case for interviewing students to understand their thinking. I'm wondering if you could just talk again about the why behind it, and a little bit about what it might look like.  Jenny: So, first of all, timed tests are definitely a mistake for many reasons. And one of the reasons—beyond the anxiety they cause—they're just very poor assessment tools. So, you can't see if the student is skip-counting or not, for example, for multiplication facts. You can't see if they're counting by 1s for the addition facts. You can't see that when they're doing the test, and you can't assume that they're working at a constant rate; that they're just solving one every, you know, couple of seconds, which is the way those tests are designed. Because I can spend a lot of time on one and less time on the other. So, they're just not, they're just not effective as an assessment tool.  So, if you flip that. Let's say they're playing the game we were talking about earlier, and you just want to know, "Can they use the pretend-to-10 strategy?" That's your assessment question of the day. Well, you can just wander around with a little checklist (chuckles), you know? "Yes, they can." "No, they can't." And so, a checklist can get at the strategies, and a checklist can also get at the facts, like, "How well are they doing with their facts?" So, once they do some of those games that are more open-ended, you can just observe and listen to them and get a feel for that. If they're playing Square Deal with whatever fact, you know. So, what happens is, you're like, "I wonder how they're doing with their 4s. We've really been working with their 4s a lot.' Well, you can play Square Deal or a number of other games where that day you're working on 4s. The [game] Fixed-Addend War can become Fixed-Factor War, and you put a 4 in the middle. So adaptable games and then you're just listening and watching.  And if you're not comfortable with that approach, then they can be playing those games, and you can have students channeling through where you do a little mini-interview. It only takes a few questions to get a feel for whether a student knows their facts. And you can really see who's automatic and who's still thinking. So, for example, a student who's working on their 4s, if you give them 4 times 7, they might say, "28." I call that automatic. Or they might, they might do 4 times 7, and they pause, and they're like, "28." Then I'm like, "How did you think about that?" And they're like, "Well, I doubled and doubled again." "Great." So, I can mark off that they are using a strategy, but they're not automatic yet. So that to me is a check, not a star. And if I ask, "How did you do it?" And they say, "Well, I skip-counted." Well then, I'm marking down they skip-counted. Because that means they need a strategy to help them move toward automaticity. Mike: I think what strikes me about that, too, is, when you understand where they're at on their journey to automaticity, you can actually do something about it as opposed to just looking at the quantity that you might see on a timed test. What's actionable about that? I'm not sure, but I think what you're suggesting really makes the case that I can do something with data that I observe or data that I hear in an interview or see in an interview.  Jenny: Absolutely. I mean this whole different positioning of the teacher as coaching the student toward their growth; helping them grow in their math proficiency, their math fluency. You see where they're at and then you're monitoring that in order to move them forward instead of just marking them right or wrong on a timed test. I think that's a great way to synthesize that.  Mike: Well, I have to say, it has been a pleasure talking with you. Thank you so much for joining us today. Jenny: Thank you so much. I am, again, thrilled to be invited and always happy to talk about this topic.  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.

Kristin Frang, Understanding the Roots of Fluency with Addition & Subtraction ROUNDING UP: SEASON 4 | EPISODE 16 Research suggests that supporting students' fluency with addition and subtraction hinges on understanding how children's mathematical thinking develops. So what are the concepts and ideas that play a part in fluency with combinations to 10, 20, and beyond?  Today, we'll explore this question with Kristin Frang, director of instructional programs at Integrow Numeracy Solutions.  BIOGRAPHY Kristin Frang is the director of instructional programs for Integrow Numeracy Solutions. She designs resources and services that support states, districts, schools, and individuals in transforming numeracy education. RESOURCES "Understanding Units Coordination" Season 4, Episode 11 of the Rounding Up podcast Integrow Numeracy Solutions website blog  email address On Track to Numeracy book by Lucinda "Petey" MacCarty, Kurt Kinsey, David Ellemor-Collins, and Robert J. Wright TRANSCRIPT Mike Wallus: Welcome to the podcast, Kristin. It is so great to be talking with you today.  Kristin Frang: It's great to be here. I feel so honored to be on this podcast.  Mike: Before we dive into a conversation about addition and subtraction, I'd like to do a bit of grounding. So you're currently the director of instructional programs for Integrow Numeracy Solutions. I wonder if briefly you could tell the listeners: What is Integrow Numeracy Solutions, and what's its mission?  Kristin: Yeah. Integrow Numeracy Solutions' mission is to transform numeracy education by connecting research with practice and empowering educators to advance student mathematical thinking and success. But I really want to bring that mission to life through a story, just a quick story, if I can.  Prior to my role with Integrow, I was a K–12 mathematics consultant. And one of the things that I did was, when the Common Core [State Standards] were released, I worked with teachers to transition to the then-new standards. We studied many documents together, including progression documents that were included in the standards, and teachers were honestly fascinated by this idea of a progression and that they were embedded into the standard. But I remember an instance where we had been studying these progressions and a teacher came up and said to me, "I know where my students are at; I can see them in these progressions. But how do I get them to the next stage?"  And I didn't have an answer (laughs) at that point. I was a former middle school and high school teacher. I was working with elementary teachers. I was studying, just like them, these progression documents, and I could only categorize the reasoning that was in front of us. And so that next step to say, "Oh, this is what I would do and bring into action in the classroom," I didn't have an answer for. And so that's really where I was introduced to Integrow—formerly [the] US Math Recovery Council, but now Integrow Numeracy Solutions. And at the heart of our mission to empower educators is to bring research to the classroom in accessible and practical ways that advance student reasoning. We do this in professional learning, we do it in supplemental resources, and we also hire and train educators to deliver high-dosage tutoring for students to accelerate their learning.  Mike: I want to just linger on something you said, which was—and I really appreciate both the truth of the statement you made and also the vulnerability, which is to say—I think for many teachers, there's this experience of, "I can see my students in these progressions, but I'm not sure what to do when it comes to making moves to shift where they're at or help them move." And I think that's a profound truth for so many teachers. And I think it's really important that folks like you, who are doing this work, acknowledge that that's a place you were in once as well because that's so true for so many of us.  Kristin: Yeah. There's always a new thing where we're watching students, we're thinking about the next steps. And so often it boils down to categorizing the things that students are doing now, but not often figuring out: What are the true actions that we take with real children who are in front of us to get them to progress in their own reasoning? We can tell them the next step, but my belief system that is aligned with Integrow Numeracy Solutions is that the most powerful thing is to help students have those experiences and create that understanding themselves. And to do that, it's more complex than just knowing what the next benchmark is for them.  Mike: I think that's a helpful introduction. And I also find it to be a good segue for all the questions that I wanted to explore today. So let me start here: It feels important to acknowledge that supporting students' addition and subtraction fluency actually hinges on understanding how children's mathematical thinking develops. So I wonder if you can talk about some of the concepts and the ideas that play a part in fluency when it comes to combinations of 10, combinations to 20, and even beyond.  Kristin: Yeah. The words that we hear associated with fluency right now are "flexibility," "efficiency," "accuracy." So we've moved on from just speed, which I think is a really positive place for us to be in education. But at the heart of flexibility, efficiency and accuracy is a quantitative understanding of arithmetic. I'm really glad that you had Amy Hackenberg on [the podcast] recently who discussed this concept of units coordination because throughout what we'll talk about, you'll see units coordination come out, but she's definitely the expert to explain it. Just a nod. Just listen to that episode [Season 4, Episode 11]. It was amazing.  Thinking, though, specifically about fluency—fluency isn't just knowing all of these combinations. In the early stages of counting, students view a number simply as a count or result of a count of single items, and there's this critical shift in developing a unit as a fundamental tool of measurement. And that's the act of unitizing where a student conceives of a collection of items as one unit that's simultaneously made of smaller units.  It is a common progression that once a student counts on, that then we would shift to building strategies to solve addition and subtraction within 20, and then of course with 100, and beyond, and then in other domains. But this is all happening in first and second grade for that addition and subtraction to 20 fluency. So attending to this numerical composite—understanding that when a child says "7" and sees that that represents counting from 1 to 7 without having to count—is a really big cognitive shift in their mathematical understanding and can be undermined with, "Oh, now that they're counting on, we're going to tell them these strategies." And so we really do need to have some intentional instructional strategies to make sure that we're developing that first, that numerical composite, before we try to develop all these strategies for addition and subtraction to 20. Because that is the basis for children to move from a counting-based strategy to compose units.  So when they can use a quantity like, "Oh, 8 plus 5, I can break apart this 5 into smaller parts and I can give some of those parts to the 8." So children at that point have to simultaneously hold 5 as a single unit while recognizing the 2 and the 3 make up the 5, but they can be moved to the 8 as well. That's really sophisticated.  Mike: So I want to mark that because I think the notion that this is really sophisticated is important for folks to understand because I'll be vulnerable and honest: I didn't recognize the complexity of what children were grappling with when I started teaching, particularly as a person who was teaching kindergarten and first grade. I really saw my job as helping to build a set of rote procedures like counting and number sequence and memorizing combinations and the outcome of being able to count and the outcome of being able to quickly recall those. I think that's not in question, but understanding the mechanics and the evolution of kids' thinking that's going on, that's a big deal. This whole notion that you have a unit and the unit is composed of smaller units. And one of the things that you said that feels like a really big deal that could be lost is the idea that shifting from a counting-based strategy to a strategy that depends on this notion of units that have smaller units inside and that are also still a unit—that's such a big deal. In order to go from counting everything to counting on to being able to look at a number like 8 and say that it has a 5 and a 3 inside of it—all of that is connected to this notion of units inside of units. And I'm so glad you mentioned that.  Kristin: Yeah. The mental actions that students are doing, making those visible, when we see children do it developmentally, we just assume it's easy. But the shifts that they're making in their understanding of units to move from that pre-numerical stage of "Everything is a 1 and I have to repeat it" to "Now this word can stand in for the count" to "Now I can embed units inside of other units." There's so much happening, and they're so young at that age; we have to remember that too.  Mike: So let's talk about some other important components of developing fluency. What else is an important primer for how people are thinking about this?  Kristin: Yeah. Another important component is supporting students in developing the cognitive structures that allow students to anchor their understanding and quantitative meaning and develop that sophisticated reasoning. Many researchers, many authors have written in different ways and different names about these structures. So like a "mental structure," "mental residue," "mental tools," "patterns of thought." To name a few people, Zaretta Hammond, Betty [K.] Garner, Karen [S.] Karp are some people I've read and appreciate their thinking around that.  So it's more than just allowing students to use manipulatives to solve problems. There's an intentionality in how we use tools and an explicit process used by educators to bring their mathematical world to life. So first, identifying key settings that emphasize mathematical structures. So the tool in front of them has a big role to play in the "math"—I put that in quotations—in the "math" that they see. 10-frames that highlight a quantity of 10, but also can show other quantities within 10, such as, like, a five or a double. It has an added layer of boxes that contain a number. Some contain a number or a counter and others are empty. So there's ways that kids are coming to understand quantity with the structure.  Similarly, a bead rack can show a five structure, a double structure, depending on your representation. They can help kids think about exchanges and really kind of that movement of quantity in a real physical way. Using linking cubes, do you use them all in one color? Are you strategic about the color that you use to bring out mathematical structures for them?  So once we think about the key setting and the structure that we're trying to help kids reason about, we want to pose intentional questions that orient students to those structures. So how do they see that 5 inside? How are we going to bring that out? It's obvious to us, but are they seeing that or are they seeing something different in the tool? Are they reasoning about something different? And so the intentionality behind how we question students during those activities also aids to building their cognitive structures. So it's not the tool itself that is the 8. It's that the child is seeing the 8 and they're seeing the 5 and the 3 in some empty boxes.  And finally, I think the step that we miss a lot, especially in problem-based instruction or any kind of inquiry-based instruction, is this explicit time where we connect the symbols in formal mathematics directly to represent the child's thinking and the tool that they've been playing around with. So it's not just about knowing I can get an answer on the 10-frame, but it's [that] I'm abstracting that series of actions, and I'm then connecting it to this quantity that I've written in a symbol. And are there connections between those things? And if those things aren't happening—kids are doing all those parts and pieces, but really developing the cognitive structure that they can then themselves use and take with them, I think that's what's so powerful when we talk about fluency is they can take a cognitive structure with them and fill in the mathematics in the future [when] maybe they don't have an educator in front of them asking those questions. But if they've been through those processes, then they have that structure to fill in.  Mike: There's a lot that you just said that I think is important and we could probably linger on a lot of it. But on the front end of this conversation, you said it's one thing to be able to see students in a progression, and it's another thing to think about, "What's my role or what are the tools that I have to help them shift?" What I heard in that last part, particularly is this notion of almost like a translation between the physical materials kids are engaging with and the meaning that they're making of that, and then helping them to abstract that in a way where we have symbols that are representing either actions or quantities and the relationships that are happening. That part of the teacher's job and part of the moves that teachers have in their toolbox is this notion of translation—taking what I'm seeing kids doing and how what I'm hearing them say or do to make meaning of it, and then helping them make that abstraction is kind of one of the tools that's really important in a teacher's toolbox when they're thinking about helping kids make moves.  In preparation for our interview, one of the things that stayed with me was you described how your own understanding of the meaning and the importance of fluency had shifted over time. And I'm wondering if you can talk about what you used to think and what is it that you think now about fluency. Could you talk about your own personal journey?  Kristin: For sure. I used to think that knowing facts, just knowing them in a very static way—like I know the answer to 5 plus 3, I keep coming back to that fact—reduces the cognitive load when they were getting into higher grade levels. Well, they don't need to think about that problem, and they can think about what we're doing in seventh grade math or in algebra.  But what I've come to understand is that the ways that students know their facts—more specifically how they're able to work with the units and the way they conceptualize the units that they are given, how they break them apart, how they put them back together—that's what matters as they go. So not just knowing the answer, but that these things can be taken apart and put back together.  Anderson Norton is a researcher that I really love to listen to. And I listened to him at an Integrow conference once. And he talked about developing mathematics through repeatable mental actions. So this kind of relates back to those cognitive structures. One example of a group of mental actions is this idea of composable, reversible, and associative. So when I think about 8 plus 5, 5 is composed of a 2 and a 3, and I can reverse that to focus on the unit of 2, and then I can associate that quantity with the 8 to make a new unit while keeping intact the unit of 5. That's really complex, but that idea transcends the domains of mathematics. Now, I'm not an expert in units coordination research, so I hope I represented that correctly, but I've certainly experienced students struggling to keep track of different units as they work. So thinking about exponent rules, and they break apart these powers and they're writing them and they're learning all these patterns, but they're struggling to keep track of the units that they're working with. Factoring functions in algebra. We're asking them to break apart something and put it back together in these different forms, and they're losing track of these units. So these actions of composable, reversible, and associative have implications in many domains of mathematics. So the bottom line is we want to develop not the fact itself, but the mental action behind that fact. Anderson Norton, I hope I did that justice.  Mike: I want to name something that I think is really important, particularly given the fact that your background is actually in secondary [education]. So what I take from this is this idea of working with units and the mental actions, that transcends arithmetic. It transcends whole numbers and even rational numbers. And it pays dividends and it keeps paying dividends in middle school and high school as kids are working in an algebra context. And I think that's worth saying out loud because it means that doing this work with elementary students to develop fluency is a bit of a twofer in the sense that you do get kids who end up with a bank of facts that they know, but they also have this underlying understanding of units and actions that pays dividends for them in the long run. Mathematics education, students' learning experience, is not a sprint or a series of handoffs. It's really a marathon. And those early experiences, they pay dividends and they keep paying dividends. I think that's really important because it reminds us, particularly as elementary educators, that we're part of a larger project.  Kristin: Not only part of a project, but part of building a lifelong interest in mathematics as an actual body of research that's dynamic and not a set of things to memorize and learn so that mathematics does become applicable in these different fields because the way that I approach a problem as an expert mathematician is that I take things apart, I put them back together. That transcends many careers. It's not just about being a math teacher or a math professor. It's about coming to understand that I have autonomy and how I see relationships of things, whether they're numbers or shapes or maybe parts that I'm working on in some sort of creative field that I'm in, but that I can do all of these things and that I can be curious and repeat those actions and see how they play out in that particular study.  Mike: That's well said.  Well, let's talk about the what, the why, the how of combinations to 10 and 20. To begin, I want to note that we use the term "combinations," and I'm wondering if you can say more about what you mean when you refer to combinations and why they matter.  Kristin: Yeah. I mean combinations not to literally mean "addition," but that combination is the idea of this relationship between parts and wholes. So that 2, 3, and 5 have this kind of additive relationship. I can put these parts together to make the whole; I can take a part out of the whole and be left with a part. I can have a part and wonder what part I need to make the whole. And so we sometimes talk about these in curriculums as "fact families," but the emphasis should be on the relationship of the parts to the whole and not filling out that kind of mimicking of like, "I know the four sentences because I know this thing." So, "If I know this, I also know this." It feels really nuanced, but in action really quite specific.  Mike: So I think that's really helpful and it really does lead me to my next question about how we help kids build their fluency with combinations to 10 and 20 and beyond. So given the why that you just articulated, it seems like the how is going to be substantially different from the ways that many, if not most, adults learn to build fluency. Can you talk about that, Kristin?  Kristin: We start from key combinations first. We consider a set of combinations that would be really useful in a lot of contexts. And I think many listeners will be familiar with those key combinations: doubles. Combinations of 10, of course. 5 plus because I have five fingers and then I can add some more on it, and I'm showing some finger patterns. So those are things we normally work on with students anyways. But starting again, going back to my original statement from a quantitative perspective—so not the memorization of those facts, but that I really come to understand them as quantities that are useful to me. And then building from those key combinations—I also want to name before I build onto that, is that some kids just have other facts that are interesting to them that they bring. So it might be their age, it might be the combination of their siblings' ages. And so we don't want to ignore that we introduce key combinations to students, but that students also have combinations that are useful to them naturally.  So once we have a set of those key combinations that we've come to think about and reason about, we can then build things that we don't know. We can transfer that. So 5 plus 3 can help me think about 4 plus 3. If I have a mental structure of a 10-frame or a bead rack that helps me think about, "Oh, there's just going to be one less counter on the top, and so I'm going to take that [counter] away." So that idea of taking the 1 out of the number is a really important mental action of them disembedding that quantity.  In addition, when we think about the 5 plus, the doubles, the partitions, we're thinking about combinations that will also transcend into multidigit combinations. So addition, subtraction—whether we're working with whole numbers or decimals, we can make tens, we can make hundreds, we can make wholes, we can make zeros. And those combinations of 10 are going to be really useful for us.  Mike: I'm struck by the fact that the combinations and also the mental actions that accompany them, as you said, they really do scale up quite nicely. And it seems like they scale up in the sense that they can get used to understand and solve problems with larger whole numbers, but they can also scale in the sense that ideas will help kids, but they can also scale in the sense that the ideas can really help kids when they encounter fractions and decimals. I wonder if you could talk about that idea just a little bit.  Kristin: Yeah. So thinking about a combination of 10 in this missing part. So 99 plus can help us when we're thinking about, that 99 is 1 away from 100. It can also help us think about 99 one-hundredths or 9 tenths as being one part or one unit away from a benchmark number that's really helpful for us. And so, it's just that the unit itself is different. So instead of just a whole, I'm one whole unit away from 100, I might be 1 tenth of a unit away from one whole, so the unit is just changing.  The view of mathematics this way, again, is very dynamic. We're creating a world where children are thinking about units and units away across domains, across number systems. And if we come to regard units as things that we can act on, whether it's a single object or a group of objects or a shape—we can put them together, take them apart and reassociate them—I can think of a lot of my mathematical knowledge in this way and not as a static set of information that I learned. And so then I'm able to transfer that because I've done that mental action or I've thought about something being a unit away.  Mike: That's fascinating because I'm going to go back to this whole notion of the relationship between 3 and 2 and 5. So 3 is 2 units away from a unit of 5 and three-fifths are 2 one-fifths away from a unit of five-fifths or one whole. This notion of units away from or units that combine to make other units, I really get now whether it's whole numbers or fractions, we're really talking about a unit that we've defined and then how many other units or how can we—how did you describe that? What was the language you used before about pulling a unit out? Was it "disembed"?  Kristin: "Disembed," yeah.  Mike: That really plays regardless of the type of unit we're talking about.  Kristin: Yeah. And remember back where we said this quantity had a meaning, so 7 stood for something. When we disembed, that unit still has meaning in the context of the original unit. So that's a really important point about disembedding is that it's not just that you take a part out, it's that part still has a relationship to the whole and you don't lose that relationship.  Mike: As I hear you talking, there seem to be some themes that are jumping out. One is the importance of key fact combinations and the mental actions. Another is the role visual models play in learning those combinations. And I think finally, I hear you indicating that it's important for students to make connections between different representations of the same combination. Tell me what I understood properly. Tell me what you'd revise or add to the summary that I just offered.  Kristin: Yes. I think we get a false sense that a student understands a concept when they're recognizing pattern, and that could be that they're recognizing pattern in a really intentional setting. Maybe they're using a 10-frame. But is that same relationship present in another setting? Success should not be measured by one instance of a child recognizing that pattern. And so one way of knowing that a child knows this is to see it in many contexts. And I think that's why it's so important for us to acknowledge the research around multiple representations in mathematics. And showing that knowledge in these multiple ways really does say that this is a connected set of knowledge that I can refer to as a child and not just be successful on this one day. That doesn't mean that that experience where they're recognizing the patterns is not important, but that can't be the measure of their success.  So this also becomes challenging in our system that values assessment events so heavily and measuring against a set benchmark. And I just want to name that because that's a real challenge for teachers. And of course we want to develop this rich set of knowledge, and sometimes we have to say that this is the system that we live in. But the true measure of that knowledge is being able to take that knowledge and transfer it into these multiple representations or in these multiple spaces and be able to use that. And that's why we talk so much about fluency being flexible and not just about accuracy.  Mike: You have me thinking more deeply than I have in a long time about the structure of some of the visual models and the physical materials that children use when they're engaged with the Bridges curriculum. I wonder if we could get specific and talk about a few of the visual models that support student learning. Are there features that make some models particularly valuable?  Kristin: One I want to mention that we might not have talked about is just a child's fingers. I think sometimes we think child's fingers are not models for them because they're counting by 1 and we tend to want students to move to more efficient strategies. But these fingers actually become really efficient tools. We can exchange fingers, we can move them very easily. We have control, and they're always with us. And so the finger use itself, I think, is a really powerful tool for us to encourage students to use in very sophisticated ways.  Mike: I mean, we literally have units of 1, units of 5, and a unit of 10 at our fingertips in front of us. I'm so glad you called that out because that's a tool that students can make use of, that teachers can make use of and that we can think of in a slightly different way than we had in the past when I just thought about fingers as a counting-by-1 resource, when actually fingers, [a hand], and hands, plural, are 1s, 5s, and 10s right there in front of you.  Kristin: And they can stand in for other units if we're really sophisticated with sequences. So a 1 can be a 7 if we wanted it to be, and we can think really creatively about that. I mean, I think that depends on some other skills. But yeah, we have 1s, 5s, and 10s built right into our hands.  Mike: That's exactly right. And you're making me think about the fact that when I skip-count or when I see students skip-count, oftentimes what's happening is I'm speaking the unit out loud and I'm holding up one finger to stand in for that unit on my hand to keep track of the number of units. So I totally hear what you're saying.  Kristin: Yeah, very sophisticated. And then there's even more complex content, right? So thinking about hours and elapsed time, and we're crossing different kinds of numerical systems where you go from a 12 to a 1 is very complex, and then we can have these fingers as units as well to help us keep track of things. So of course, frames are a really powerful tool. Frames—specifically, 10-frames, 5-frames, 20-frames—provide an extra structure for students, especially when they're really thinking hard about some quantity pieces. So they might not be completely solid in that unit, but we don't have to say, "Oh, you have to count on first before we're going to try to explore some other patterns." Those things can be developing simultaneously. So frames provide this box that contains the unit for them and it becomes this really obvious count for them. They can see those individual discrete items, but they can also see what's missing really clearly because they're empty.  Bead racks are a great support as well when you're thinking about that relational network that we want students to develop and not count by 1s. So we can exchange beads, and we can exchange quantities, and we don't have to exchange beads one by one. Sometimes frames, when we get to a space, it's inconvenient to have to move five counters at the same time where in a bead rack, you can just slide those five over or three over at the same time.  I also want to mention linear bead racks. So taking that stacked bead rack and making it align really helps students think about a continuous model, which transfers to a number line and the idea of units being measurement. So we were talking about, "It's one away," and so really conceptualizing that kind of next decade of numbers and one bead away. That's developing that idea of relative magnitude that's extremely helpful when we get to middle school and all of a sudden we're working in negative numbers.  Mike: We're reaching the end of our time together. And before we go, I'm wondering if you could share contact information for Integrow Numeracy Solutions with our listeners. I'd really love to be able to offer that because we've just touched the surface of some of the ideas that you help educators explore in some of the training and the support that you all offer.  Kristin: Yeah. If you'd like to find out more about us, a great place to go is our website, which is www.integrowmath.org, all one word. And we have a lot of different things you can explore from our events. There is actually, if you add a backslash "blog" to that [www.integrowmath.org/blog], you can go to our blog and read some of the ways that we think about our professional learning and some of the topics that I talked about today. If you want to reach out directly, feel free to email info@integrowmath.org and someone will get you to the right place based on your question.  Mike: And for listeners, we'll put a link to both of those in the show notes. Before we leave, Kristin, I'll just ask one last question. Are there any recommendations that you have for folks interested in learning more about the ideas we've talked about today? It could be books, websites, articles, or even just a suggested practice for someone who wants to get started.  Kristin: Yeah. For sure, take a look at the blogs on our website. They're little snippets of pieces of our trainings that you can take right with you into the classroom. Some ideas that I've talked about—help with bead racks, ideas around multiplication and division, and supporting students to think about those units. Our new publication, On Track to Numeracy from [Lucinda] "Petey" MacCarty, Kurt Kinsey, [David Ellemor-Colons, and Robert J. Wright], is designed to be an accessible, relatable and practical tool focused on supporting classroom teachers. It not only has the progressions that I started this podcast off talking about, but it has those teaching tests and progressions that help us answer the question of, "What do I do next now that I can understand where my students are?" Mike: I think it's a great place to stop, Kristin. I want to thank you so much for joining us. It's really been a pleasure talking with you.  Kristin: Thank you for having me. I've had a great time.  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.  © 2026 The Math Learning Center | www.mathlearningcenter.org

Jeff and Andy find every mock draft they can for the Browns and break down the differences in the top picks for the team at 6 and 24.

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It's a big day for the All About Nothing studio! Barrett Gruber breaks in his new microphone to discuss the high-stakes House Judiciary Committee hearing featuring Attorney General Pam Bondi. The hosts dive into the combative testimony, Bondi's "washed-up lawyer" barbs, and the DOJ's controversial handling of the Epstein files, where redaction failures have once again put survivors at risk.Back home in South Carolina, the guys address the sobering news of ICE moving into Columbia and what the expansion of 287(g) agreements means for local law enforcement and community trust.Plus: Bill breaks down the ethics of retail "round up" donations—is it charity or just a corporate tax write-off? The duo also reflects on recent celebrity news, the symbolic "monks' journey for peace," and the ongoing debate surrounding Donald Trump's mental health and controversial public statements.Key Topics: #PamBondi #EpsteinFiles #ICEColumbiaSC #RetailEthics #Trump2026 #AttorneyGeneralBondi #SouthCarolinaPolitics #PodcastTech #AllAboutNothingPodcastZac King | LinktreeBarrett Gruber | LinktreeBill Kimler | LinktreeThe All About Nothing: Podcast | LinktreeBlack White Blue in the South | Instagram, Facebook | LinktreeDr. Jumelle Brooks | LinktreeClick here for Episode Show Notes!As always, "The All About Nothing: Podcast" is owned and distributed by BIG Media LLC!Check out our network of fantastic podcasts!Click Here to see available advertising packages!Click Here for information on the "Fair Use Copyright Notice" for this podcast.Mentioned in this episode:ZJZ Designs - St Patrick's Day ShirtsZJZ DesignsEverplay Spring 2026 LeaguesCheck out Everplay Sports and Social for the full list of the 2026 Spring Leagues and 2026 Late Spring Leagues!Everplay Sports & Social LeagueBIG Media Copyright 2026BIG Media LLC

Tyler Brûlé, Emma Nelson and guests look back at the week’s news, live from the French capital. We also turn to Paris Men’s Fashion Week with Matthieu Zucconi.See omnystudio.com/listener for privacy information.

Looking for a winter car fix without a long road trip? We map out a string of Texas car museums that punch above their weight, from Austin's rock-and-roll-infused collection to the Hillsboro time capsule and Woody's Classic Cars and Baseball Museum. The highlight is the Permian Basin Petroleum Museum's Chaparral Gallery, where engineering legends meet live demonstrations that keep these racers in motion, not mothballed. We wrap the route with Bill's Backyard Classics in Amarillo—a grassroots trove of hot rods, muscle, and trucks that feels personal and welcoming.Then we slide behind the wheel of the 2026 Lincoln Aviator Black Label. Think clean, American luxury with modern lighting, rich leather, and a ride that floats without losing composure. The twin-turbo V6 serves smooth, V8-like thrust, but we press on two fronts: efficiency that begs for a hybrid and driver-assist features that demand constant attention. We talk usability, eye-on-road alerts, and why partial automation should reduce cognitive load, not raise it. Pricing and rivals like the MDX, GX, and XC90 help frame where the Aviator shines and where it needs polish.Ownership realities get real with a concise recall roundup across brands—airbags, cameras, battery cables, and more—followed by a tour of the market's mood via Hemmings sold prices. From a budget-friendly C4 Corvette to a premium 1959 Cadillac 62, a sleeper Studebaker pickup, and a surprisingly strong Firebird, we unpack what drives value: condition, taste, and story. Local cruise-ins and Monster Jam bring the community energy, while two trends shape the future: dealers reconditioning older, higher-mileage cars to address affordability, and modern salvage networks that make parts sourcing smarter and faster. We close with Honda's new minimalist logo for its electrified era—a small emblem with big signaling power.If you love car culture that stretches from museum halls to test-track impressions and neighborhood meets, you're in the right garage. Subscribe, share with a fellow enthusiast, and leave a review to tell us which segment you want more of next.Be sure to subscribe for more In Wheel Time Car Talk!The Lupe' Tortilla RestaurantsLupe Tortilla in Katy, Texas Gulf Coast Auto ShieldPaint protection, tint, and more!Disclaimer: This post contains affiliate links. If you make a purchase, I may receive a commission at no extra cost to you.---- ----- Want more In Wheel Time car talk any time? In Wheel Time is now available on Audacy! Just go to Audacy.com/InWheelTime where ever you are.----- -----Be sure to subscribe on your favorite podcast provider for the next episode of In Wheel Time Podcast and check out our live multiplatform broadcast every Saturday, 10a - 12nCT simulcasting on Audacy, YouTube, Facebook, Twitter, Twitch and InWheelTime.com.In Wheel Time Podcast can be heard on you mobile device from providers such as:Apple Podcasts, Amazon Music Podcast, Spotify, SiriusXM Podcast, iHeartRadio podcast, TuneIn + Alexa, Podcast Addict, Castro, Castbox, YouTube Podcast and more on your mobile device.Follow InWheelTime.com for the latest updates!Twitter: https://twitter.com/InWheelTimeInstagram: https://www.instagram.com/inwheeltime/https://www.youtube.com/inwheeltimehttps://www.Facebook.com/InWheelTimeFor more information about In Wheel Time Podcast, email us at info@inwheeltime.com

Dr. Todd Hinnenkamp, Enacting Talk Moves with Intention ROUNDING UP: SEASON 4 | EPISODE 9 All students deserve a classroom rich in meaningful mathematical discourse. But what are the talk moves educators can use to bring this goal to life in their classrooms?  Today, we're talking about this question with Todd Hinnenkamp from the North Kansas City Schools. Whether talk moves are new to you or already a part of your practice, this episode will deepen your understanding of the ways they impact your classroom community.  BIOGRAPHY Dr. Todd Hinnenkamp is the instructional coordinator for mathematics for the North Kansas City Schools.  RESOURCES Talk Moves with Intention for Math Learning Center Standards for Mathematical Practice by William McCallum  5 Practices for Orchestrating Productive Mathematics Discussions by Margaret (Peg) Smith and Mary Kay Stein  TRANSCRIPT Mike Wallus: Before we begin, I'd like to offer a quick note to listeners. During this episode, we'll be referencing a series of talk moves throughout the conversation. You can find a link to these talk moves included in the show notes for this episode. Welcome to the podcast, Todd. I'm really excited to be chatting with you today. Todd Hinnenkamp: I'm excited to be here with you, Mike. Talk through some things. Mike: Great. So I've heard you present on using talk moves with intention, and one of the things that you shared at the start was the idea that talk moves advance three aspects of teaching and learning: a productive classroom community, student agency, and students' mathematical practice. So as a starting point, can you unpack that statement for listeners? Todd: Sure. I think all talk moves with intention contribute to advancing all three of those, maybe some more than others. But all can be impactful in this endeavor, and I really think that identifying them or understanding them well upfront is super important.  So if you unpack "productive community" first, I think about the word "productive" as an individual word. In different situations, it means a quality or a power of producing, bringing about results, benefits, those types of things. And then if you pair that word "community" alongside, I think about the word "community" as a unified body of individuals, an interacting population. I even like to think about it as joint ownership or participation. When that's present, that's a pretty big deal. So I like to think about those two concepts individually and then also together. So when you think about the "productivity" word and the "community" word and then pairing them well together, is super important. And I think about student agency. Specifically the word "agency" means something pretty powerful that I think we need to have in mind. When you think about it in a way of, like, having the capacity or the condition or state of acting or even exerting some power in your life. I think about students being active in the learning process. I think about engagement and motivation and them owning the learning. I think oftentimes we see that because they feel like they have the capacity to do that and have that agency. So I think about that, that being a thing that we would want in every single classroom so they can be productive contributors later in life as well. So I feel like sometimes there's too many students in classrooms today with underdeveloped agencies. So I think if we can go after agency, that's pretty powerful as well. And when you think about students' math practice, super important habits of what we want to develop in students. I mean, we're fortunate to have some clarity around those things, those practices, thanks to the work of Dr. [William] McCallum and his team more than a decade ago when they provided us the standards for mathematical practice. But if you think about the word "practice" alone, it's interesting. I've done some research on this. I think the transitive verb meaning is to do or perform often, customarily or maybe habitually. The transitive verb meaning is to pursue something actively. Or if you think about it with a noun, it's just a usual way of doing something or condition of being proficient through a systematic exercise. So I think all those things are, if we can get kids to develop their math practice in a way it becomes habitual and is really strong within them, it's pretty powerful. So I do think it's important that we start with that. We can't glaze over these three concepts because I think that right now, if you can tie some intentional talk moves to them, I think that it can be a pretty powerful lever to student understanding. Mike: Yeah. You have me thinking about a couple things. One of the first things that jumped out as I was listening to you talk is there's the "what," which are the talk moves, but you're really exciting the stage with the "why." Why do we want to do these things? And what I'd like to do is take each one of them in turn. So can we first talk about some of the moves that set up productive community for learners? Todd: Yeah. I think all the moves that are on my mind contribute, but there's probably a couple that I think go after productive community even more so than others. And I would say the "student restates" move, that first move where you're expecting students to repeat or restate in their own words what another student shared, promotes some really special things. I think first it communicates to everyone in the room that "We're going to talk about math in here. We're going to listen to and respectfully consider what others say and think." It really upholds my expectation as an educator that we're going to interact with and understand the mathematical thinking that's present so that student restates is a great one to get going.  And I would also offer the "think, turn, and learn" move is a highly impactful one as well. The general premise here is that you're offering time upfront. Always starting with "think," you're offering time upfront. And what that should be communicating to students is that "You have something to offer. I'm providing you time to think about it, to organize it, so then you're more apt to share it with either your partner or the community." It really increases the likelihood that kids have something to contribute. And as you literally turn your body and learn from each other—and those words are intentional, "turn" and "learn"—it opens the door to share, to expand your thinking, to then refine what you're thinking and build to develop both speaking and listening skills that help the community bond become stronger. So in the end it says, "I have something to offer here. I'm valued through my interactions." And I feel like that there's something that comes out of that process for kids. Mike: You talked about the practice of "think, turn, learn." And one of the things that jumps out is "think." Because we've often used language like "turn and talk," and that's in there with "turn and learn," but "think" feels really important. I wonder if you could say more about why "think"? Let's just make it explicit. Why "think"? Todd: Sure. No, and I'm not trying to throw shade at "turn and talks" or anything like that, but I do think when we have intention with our moves, they're super impactful relative to other opportunities where maybe we're just not getting the most out of it. So that idea of offering time or providing or ensuring time for kids to think upfront—and depending on the situation, that can be 10 seconds, that can be 30 seconds—where you feel like students have had a chance to internalize what's going on [and] think about what they would say, it puts them in an entirely different mode to build a share with somebody else. I'm often in classrooms, and if we don't provide that think time, you see kids turn and talk to each other, and the first part is them still trying to figure out what should be said. And it just doesn't seem like it's as impactful or as productive during that time as it could be without that "think" first. Mike: Yeah, absolutely.  I want to go back to something you said earlier too, when you were describing the value that comes out of restating or rephrasing, having a student do that with another student's thinking. One of the things that struck me is there were points in time when you were talking about that and you were talking about the value for an individual student who's in that spot.  Todd: Mm. Mike: But I also heard you come back to it and say, "There's something in this for the group, for the community as well." And I wonder if you could unpack a little bit: What's in it for the kid when they go through that restating another student's [idea], or having their [own] idea restated, and then what's in it for the community? Todd: Sure. Well, let's start with the individual, Mike. And I think that with what we know about learning and how much more deeply we learn when we internalize something and reflect on it and actually link it to our past learning and think about what it means to us, is probably the most important thing that comes out of that. So the student that's restating what another student says, they really have to think about what that student said and then internalize it and make sense of it in a way where they can actually say it out to the community again. That's a big deal! So to talk about the impact on the community in that mode, Mike, when you get one or two [ideas], and maybe you ask for a couple more, you now have student thinking in four different forms out in the community rather than, say, one student sharing something and a teacher restating it and moving on. And I just love how those moves together can cause the thinking to linger in the classroom longer for kids. Often when I'm in classrooms, the kids actually learn it more when somebody else says it rather than me. And it kind of ties to that where, like, they just need to hear other kids thinking and start to process that a little bit more on their level. And we get to shore that up too as teachers. We can shore up whatever's missing if we need to later. But I think the depth that comes from thinking about it, putting it out in the community, having more kids think about [it] is pretty powerful. Mike: I think what's cool about that is the idea that there's four or five ideas floating around and how different that is than [when] a kid says something, the teacher restates it and moves on. I might not have made sense of it on the first kid's description or the teacher's description, but when those things linger around, there's a much better chance that I'm going to make sense of it. Todd: Yeah. And I agree, Mike.  And what's really important in that process as well is the first move I always talk about is "wait." You literally have to wait. When the student restates something, we've got to let that sit for a little bit for it to really be something that other kids can grasp onto and then give them time to process what they heard and then ask if someone could restate. At that point, it's causing all this cognition in the brain, and it's making me think about what I understand and what I don't understand about what was said. And it just starts to build and make a huge difference over time. Mike: Yeah. I'm glad you said that because I'm a person who talks to think, but that is not true of a lot of folks.  Todd: (laughs) Mike: A lot of people need time to think… Todd: Sure. Mike: …before they talk. And so I think it's really important to recognize that that wait time is really an opportunity for mental space. And if we don't do that, it actually might fall flat. Todd: Totally agree. I'd see it day in and day out in classrooms I'm in, where if we can offer that time to let that concept or thinking permeate across the room for a little bit longer, it's a whole different outcome. Mike: Nice.  I'm wondering if we can pivot and talk a little bit about moves that support student agency and their mathematical practice. They really do feel like they're kind of interconnected. Todd: Yeah, I think they are somewhat interconnected as I think about them. And I see agency as like a broader concept, like really that development of capacity to act or have power in a situation. But when you think about math practices—thinking about the standards for mathematical practices—it's a little more specific. So when you think about the math practice of perseverance, I think we have to think about the move [called] wait time that I just talked about. When used with intention, I think it can communicate to kids, "I've got confidence in you. You have something to offer. I believe in you and that you're capable of contributing here." I just think that we have to think about our use of wait time and the messages that kids get from that and be careful not to squelch their opportunity to grow in those situations. Mike: OK. I have a follow-up. You're making me think about ways to do wait time well and ways to do wait time that might have an unintended consequence. So walk me through a really productive use of wait time—what the language is that the teacher uses or how they manage what can feel uncomfortable for most of us. Todd: Sure. And I will be very upfront that anytime you start to use wait time, if you haven't before, there's going to be some discomfort. (laughs) You think about, if you're a person that always wants to fill that space or feel like you need to because students aren't quite contributing, then you start to shift your practice to cause there to be a little more extended wait time, there's going to be some discomfort that plays out in that situation.  So I think honestly, Mike, part of it is having the right question or the right prompt, and setting up the expectation and upholding it over time. I talk a lot with teachers about establishing and maintaining productive community. I think that we have to establish it over time and then maintain it. And what I mean by that is if you start to use wait time, you're establishing that norm in your classroom, is that I'm always going to give you time to think, and that's super important in here because we want to make sure that we get the most out of the experience. The maintaining part of it, I believe, is where we uphold that over time. We don't start to back off if kids don't then share their thinking. We can't always fill that space. And I think sometimes an inappropriate use of wait time is if we do it pretty well, but then we rescue when there's a time that kids aren't sharing something. So I do believe that no matter what classroom you're in, there is always one kid that can give you at least a nugget that you can go with. So I think as much as you can wait and try to draw that out before interjecting is super important. Mike: Yeah. You make me think about a scenario that I encountered a fair amount when I was teaching elementary, which was: I'd ask a question and there were two or three kids who immediately put their hand up. There were quite a few that were still thinking, and it was really uncomfortable for me, but I think also for some of the kids who had their hands up, that I didn't immediately call on them, that I actually waited and let the question marinate… Todd: Yes. Mike: …and the end product was great. I had more kids who had something to say because they had that space. But it was a little uncomfortable, especially for those kids who were like, "Wait, I know it immediately. Why aren't you calling on me? Todd: (laughs) Yes. And I think it's super important what you just shared, Mike, because in our practice, we have to be aware that the day-to-day practices or actions that we enact in our lessons, they're impacting everything from community, agency, practice. All the things that we're talking about today are sometimes just suddenly being impacted either positively or negatively. And I think the scenario you described about your practice is, like, you were intentional about it. You became aware, you realized that there's a handful of kids that I'm probably letting drive the discourse maybe more than I need to. And you're right: You've got other kids in classrooms that I'm in that are really waiting to talk and never have the chance. And I do feel like those are the kids that are going to have a hard time staying caught up with everybody because they're not getting that opportunity to develop some of those habits. Mike: Yeah. It makes me think about when I was a kid as well. I was not the fast kid, right? I was thinking about it, but I was not the first kid with my hand up.  You've really got me thinking about how wait time is a real subtle way of saying, "You're not necessarily the most competent person just because you have your hand up first." There's no added bonus that says, like, "You're the best just because your hand's up first. Everybody can contribute. You might need a little bit of time to process. That's super normal in a math class." Todd: Yes, it is. And you go back to what we discussed earlier about being a valued contributor in the community, and you think about what those kids feel once they experience that wait time and then their ideas being the ones that drive the discourse or that are highlighted or presented. That's where you draw that in, and if you can have 50% of your kids be the ones that are feeling that, then you got to shoot for 60, and then 70, and so on. But you gotta start to expand the number of kids that talk and share and restate and do all the things around discourse, but wait time is a super powerful tool to do that. Mike: Another thing that you shared when I saw your presentation was the idea that you can pair talk moves in a sequence and that those sequence talk moves can have a powerful impact on kids. And I'm wondering if you can talk a bit about some of the ways that educators can sequence talk moves to have maximum impact. Todd: Sure. Yeah. And I'm not necessarily suggesting that there is an always or a 100% correct way to line them up and sequence them, but I do think there's some [that], if you can go after them in particular instances in your professional practice, I think it's going to change your practice, I think more quickly and more deeply. And the same goes with a lesson. I think right off the bat, we first must wait. We have to start to build that into our practice where we wait. So if we offer a prompt [or] pose a question, let it sit for a second. I always talk about 4 to 6 seconds would be about how long you'd want to just let it sit for a little bit. Then, if you've got the right question and the right prompt, I think you could just say, "OK, now I'm going to give you some time to think and then I'm going to have you turn and actually learn with a partner. So I want you to think about the prompt that's on the board. What would you share with your partner?" And literally you give them time to think and then you can turn and learn.  So at that point, I think it's important that you're walking about the community, listening in, getting a feel for what's being discussed, because I think at that point you can have a feel for maybe what you might want to go to next, what insight you want to make sure is surfaced that is aligned to the learning goal of the day. That's how you get all that headed in the right direction. So you gotta lean in and figure that out. And I think at that point you could ask someone to share. "OK, who can share what you and your partner talked about?" See what happens; see what you get. You can be strategic if nobody offers. You can just say, "Hey, would you end up sharing? I listened to what you had. Would you mind sharing?"  And then I think at that point you could use a "Do you agree or disagree and why?" So here's their thinking on this situation. So I want you to really think about it. Do you agree with what they're sharing or not? And then I'm going to ask you why. Let that sit. Give them some time to think. Let that play out. I think at that point you could offer the floor to whoever wants to argue about that and try to convince the community that they agree or disagree and why.  And then I think, even, (laughs) I guess to keep going, Mike, I think you could at that point use the "tell us more," when that student's offering the reasoning on why they agree or disagree, and you don't feel like it's enough or maybe there's other kids in the room not quite understanding where they're going. "OK. So tell us a little bit more. Keep going." And offer that space and time for them to do that.  So yeah, there's several ways that you can sequence them, but I really think you have to figure out the learning goal, be intentional about the discourse and how you can get it headed in the right direction and also slow it down enough that there's some depth to it as well. Mike: We had a guest on [Rounding Up] earlier this season, and he was talking about the importance of "agree or disagree." He called it "pick a side," but I think the idea is the same. Todd: Oh yeah. Yeah, same concept. Mike: And I wonder if you could talk about, what is it about agree [or] disagree that you think is particularly powerful for kids? Todd: Sure, Mike. Do you agree [or] disagree? It does make you take a stand. Like you have to understand the situation well enough to be able to say, "Hey, I agree with this thinking because..." fill in the blank. I think it puts you in a position where you've got to weigh everything that's playing out in the discourse and then actually understand it well enough to be able to then communicate about it. Your approach may be different than the thinking that was shared, but if you can understand it well enough and then state whether you agree or disagree and why, that's some pretty deep understanding. I mean, there's some high value in that if you can get to that point. Mike: Absolutely. I get the sense that a fair number of these talk moves might start to feel pretty organic. They might happen almost like muscle memory when an educator starts to use them, but you really have me thinking about planning for talk moves. Do you have any guidance for an educator who might be trying to think about, "Hey, I want to purposefully integrate some of these moves into my practice." What would it look like to plan for that? Todd: Sure. I think first of all, when you talk about muscle memory, that's a great way to put it. Some of these moves may not be strong in a professional practice for a person right now, but the more you get to using them and trying them out and implementing them and seeing what they'll do for productive community agency math practice, you're going to start to develop a level of growth in your practice that I think is going to be tremendous. But as you think about being intentional with them as you plan a lesson and go after a particular learning goal for a lesson, the one thing that comes to mind for me is really Dr. Peg Smith's work around the five practices and orchestrating discussions, right? You think about anticipating and then selecting and sequencing and connecting for sure all come to mind in that. So I guess I would go as far as saying, as we prepare for what students may say or do, we can intentionally think about the moves that might be most impactful in different scenarios. For instance, let's just say [there's a] a third grade student; you're working on a model to represent multiplication. The student draws a model to represent a multiplication scenario. You can plan to project or show the model and then simply use the think, turn, and learn move. You can show the student thinking, ask students to not talk upfront. We need to give people individual time to think. And then I want you to think about what you see and then I want you to turn and learn with your partner about that. So I think at that point, with that move being used, you're going to get a lot of discourse around whether the model is an appropriate representation or not. I think there's going to be depth in what kids take away from the experience. And you can go back to that as like, OK, so if I know that a kid says this and just says, "Well, it looks like there's this many rows and this many arrays," [then] the tell us more move is a great one there. "Tell us more. What do you mean by that?" Then they have to extend to give more depth to their thinking and then refine it a little bit more.  So I think as you think about the learning goal, there's certainly ways that you can think about any of these talk moves, and in a way where you want to make sure that the right move is being used to get you closer to the goal of sense being made and such. So yeah. Mike: I want to come back to something that you touched on in the beginning, but it feels like a through line, which is: These talk moves are about building engagement and math, but really they're about so much more. What do you see as the long-term payoff for kids who experience this type of a learning experience? Todd: Well, (laughs) it often feels counterintuitive when I'm in schools and talking about these things because I think we've shifted into a mode where professional learning communities are so honed in on that exact math content standard, what do we want kids to know, be able to do? How will we know? What are we going to do when they don't? And I really believe that the more I'm in these situations, Mike, I'm understanding that we can't shift that learning like we want to until we deal with some of these that—I call them more general pedagogy practices, like discourse and talk moves with intention. Those are more general practices, not a content-specific practice teaching kids how to find a common denominator so they can add fractions and such. But I really think if we can get at some of these general pedagogy things to build up community, agency, math practice—all those things that I think will transcend time—I often talk about it, we're going after something bigger than just the priority standards or the most important standards within our state. We're going after things that are deeper, bigger, pay off more later in life than we may even realize that we're experiencing in the moment. Mike: Yeah. I mean, things like flexibility, problem solving, citizenship are all pieces that really jump out when I listen to you talk about that, Todd. Todd: Sure. No, you think about—and I mean, as we were talking about productive community earlier, I always offer them: Is there anything different you would want in your classroom or your school? You think about the words "productive" and "community," can we all come together and think about things in a way where we're contributing, we're all valued, we're producing together. And that's not something that I think we spend a lot of time talking about in schools now that it's so specific to content and how kids do on state assessments and such, but these things transcend all that. Mike: Absolutely.  We're at that point in time where I could probably keep chatting with you about this for hours, but you are a busy school educator and you gotta get out of here. I'm wondering though, if you could leave listeners with a thought or a question or maybe a nudge related to their practice, what would you share? Todd: I first would say I just think it's important to always be reflecting on whose talk is driving the experience. As you think about everything we've talked about today, Mike, is the student talk driving it? Is their reasoning driving it or is it ours? And I think understanding that these talk moves with intention and what they go after and using them consistently with intention, it just starts to shift the balance to favor more student-to-student discourse. And I think it presents as, in turn, more developed community, agency and math practice. And I just think that you get more out of that than [a] high quantity of teacher-to-student discourse or student-to-teacher discourse. So I always offer [to] just pick out a move, try it for a week, find a wing person, collaborate around that, share ideas. How'd it go? What were your barriers? What did you see happening? Just these small shifts I think can create some big opportunities for people down the road. Mike: I think that's a great place to stop. Thank you so much for joining us, Todd. It's really been a pleasure chatting. Todd: Mine as well. Thank you, 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. © 2026 The Math Learning Center | www.mathlearningcenter.org

Jake founded Serval in April 2024— by Dec 2025 he'd raised a $75M Series B from Sequoia at a $1B valuation.He didn't look for a "wedge" or a "niche." He looked at ServiceNow—a $160B, 20+ year-old incumbent that everyone IT team relies on—and rebuilt it from the ground up in a YEAR. In this episode, Jake reveals the audacity behind building a full-platform replacement from Day 1, why he spent months building in the dark with zero revenue, and how he achieved a 50% demo-to-close rate on six-figure enterprise deals.Why You Should ListenHow to go from incorporation to a $1B valuation in just 18 months.The psychological shift in sales calls that proves PMF.How to build a demo so compelling that 50% buy on the spot.Why you no longer need to find a small wedge to win post Gen AI.The specific question that stops customers from giving you generic feedback.Keywordsstartup podcast, startup podcast for founders, hypergrowth, zero to one, unicorn startup, Sequoia Capital, replacing legacy software, enterprise sales strategy, ServiceNow competitor, Jake Stauch00:00:00 Intro00:03:25 Why "Hair on Fire" Problems Matter00:06:58 Learning What Winning Feels Like at Verkada00:14:05 100+ Customer Discovery Calls00:18:12 The One Question That Unlocks Real Pain00:23:48 Why No-Code Workflows Fail00:28:45 Taking Risks on AI Model Improvements00:35:49 From $0 to Six-Figure ACVs in 6 Months00:39:00 The Strategy to Rip and Replace ServiceNow00:47:30 The "Rounding Up" Signal of PMFSend me a message to let me know what you think!

Welcome to the Tech Latest podcast. Every Tuesday, our tech experts Katey Creel and Shotaro Tani deliver the hottest trends and news from the sector.In this special year-end episode, Katey and Shotaro look back at the year's top tech stories, as well as predict the sector's trends in 2026. They discuss advancements in generative AI, the rise of robotics, new developments in energy technology and China's push toward chip self sufficiency.== == == == == == == ==Check out this episode's ⁠⁠⁠⁠featured story below: ⁠⁠⁠⁠Is DeepSeek next in line for a TikTok-like U.S. ban?As AI threatens jobs in the US, India enjoys a hiring boostChina's Pudu takes robot dogs outdoors to fuel growthJapan bets big on ultrathin, ultralight solar panelsIn silicon wafers, China's emerging local stars rattle global giants== == == == == == == ==And ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠register for our weekly #techAsia newsletter here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠.⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Find more of our tech coverage here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠.And for the Asian business, politics, economy and tech stories others miss, ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠please subscribe to Nikkei Asia here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠.Thanks for listening!

Will Leitch has you covered with the moves you missed over the Thanksgiving break, including one of the premier starting pitchers coming off the board. Then it's time to check in on the free agency rumor mill, focusing in on the biggest bats. To learn more about listener data and our privacy practices visit: https://www.audacyinc.com/privacy-policy Learn more about your ad choices. Visit https://podcastchoices.com/adchoices

H1 - Segment 1 - Mon Nov 17 2025 - Big ol Monday Afternoon welcome After my Georgia bulldogs beat Texas. What did we start seeing going up right up there in Charlotte NC Operation Charlotte's Web Rounding up record numbers of illegal aliens

In Season 2 Episode 6, Kenny and Rabbi Bernath review many of the wines they had over the last couple months, covering many of the new wines and regions available in the kosher marketplace.They discuss such wines as Chablis Grand Cru, Vernaccia di San Gimignano, a Premier Crus Beaune, and many others.Rabbi Bernath talks about his special house guest, Dr. Moises Cohen of Elvi Winery. Kenny immediately gets jealous.In this wide-ranging episode, Kenny and Rabbi Bernath get back to what they do best: shooting the breeze between two great friends and chatting kosher wine.Support the showEmail your questions and comments to kosherwinepodcast@gmail.com

Voters in Kansas and Missouri went to the polls yesterday to decide on a range of issues, including how many days kids should be in school and whether they should abandon their current form of government. Today, we bring you election results from across the metro.

Today on the Jimmy Barrett Show:Rounding up and rounding downLocal elections

Rick Caruso was floated as the solution to revitalize Santa Monica's struggling 3rd Street Promenade, while the massive West Hollywood Carnival was crowned California's biggest Halloween party. Conway called out people stepping on dogs in upscale restaurants. Across the U.S., businesses like McDonald's are “rounding up” receipts as banks and retailers face a penny shortage due to the U.S. Mint halting production. Elex Michaelson previewed “The Story Is…” on CNN, featuring Mayor Karen Bass and comedian Matt Friend, with John Kobylt set to appear Monday. And the Dodgers face a must-win World Series matchup against Toronto. 

Ross Halls and Tom Cann are back with our Ipswich Town Women's podcast after a historic first WSL 2 win. The duo discuss a tough three game week for Joe Sheehan's side, who had started it away at Charlton, earning a point at the Valley. Then it was cup action as they were beaten 5-1 by WSL side Leicester City, but switching focus back to the league against Portsmouth. Plenty of talking points from the 3-2 win was discussed as the Blues earned their first three points of the season. Kings of Anglia is sponsored by Stardust Spirits. Get 20% OFF with promo code KOA at https://www.stardustspirits.co.uk/ Introducing our new sponsors at Molecular! Get 10% OFF with promo code KOA10 at https://www.molecular-uk.com/ Subscribe on our website to watch the video version of the podcast - https://www.eadt.co.uk/subscribe/ You can shop the KOA range here - (kings-of-anglia.myspreadshop.co.uk) 

Stocks  heading into the fall with Nvidia earnings in the books, and the Fed's Jackson Hole conference in the rearview. So what's the next catalyst that will move markets? Our traders debate what they see in store for stocks. Plus Gap reporting results, with other big names like Dick's, Best Buy, and more delivering quarterly numbers. How the retail space is faring, and the names to watch.Fast Money Disclaimer

The Middle Fork Greenway is one of the most significant ongoing economic development projects in the High Country, connecting the towns of Boone and Blowing Rock by 6.5 miles of trail. Each July, Blue Ridge Conservancy conducts its Round Up for the Middle Fork Greenway, which gives local businesses and their customers an opportunity to directly impact this project through fundraising and education.On this week's Mind Your Business, we visit with Wendy Patoprsty, Director of the Middle Fork Greenway. She provides an update on ongoing construction and planning, new pocket parks and features, and how public art is being used to enhance this special corridor. Mind Your Business is written and produced weekly by the Boone Area Chamber of Commerce. This podcast is made possible thanks to the sponsorship support of Appalachian Commercial Real Estate.Catch the show each Thursday afternoon at 5PM on WATA (1450AM & 96.5FM) in Boone.Support the show

NEVER EVER SKIP THE GYM!Membership Specials https://swolenormousx.com/membershipsDownload The Swolenormous App https://swolenormousx.com/swolenormousappMERCH - https://papaswolio.com/Watch the full episodes here: https://rumble.com/thedailyswoleSubmit A Question⁠ For The Show: https://swolenormousx.com/apsGet On Papa Swolio's Email List: https://swolenormousx.com/emailDownload The 7 Pillars Ebook: https://swolenormousx.com/7-Pillars-EbookTry A Swolega Class From Inside Swolenormous X: https://www.swolenormousx.com/swolegaGet Your Free $10 In Bitcoin: https://www.swanbitcoin.com/papaswolio/   Questions? Email Us: Support@Swolenormous.com

This week Sam, English Dan, Andrés and Santi Bauzá review Argentina's two World Cup qualifiers – a win away to Chile and a draw at home to Colombia – and cast our eyes over the other games in the campaign as well, with Brazil and Ecuador confirming their places at next year's tournament and Chile eliminated. We also discuss Franco Mastantuono's transfer to Real Madrid and answer listeners' questions.

Tuesday's “What's Buggin' You” segment for 6-3-25

On this week's Keepin It Real, Cam Marston stands at the register at a coffee shop and what comes out of his mouth is a complete surprise to him. ----- Last week I bought a coffee and a T-Shirt at a coffee shop. And at that awkward moment when the person at the register spins the pad around for me to sign and enter a tip amount, I asked the guy “How much should I tip you for this?” I've never asked that question before. The moment I thought about asking it was after I had said it. Tipping has gotten out of hand. A few weeks back at a hotel in Colorado, every transaction at the hotel automatically included a 25% tip and then space on the bill to add more. At the hotel coffee shop, I'd buy a coffee, they'd hand me an empty cup and point me to the coffee pots across the way, and then ask for a tip. Then ask me to “round up” for some sort of something, adding more money to the transaction. You and I are paying a lot more for what we used to get and then doing the work ourselves. More and more people want you and me to add money to our transactions for doing their job. I know I sound old and curmudgeonly but, dang it, it's getting out of hand. That's why this transaction at the coffee shop stood out. “How much should I tip you for this?” I asked. The guy said, “Nothing. I've done my job. I poured you a coffee and rung you up in the register. You don't even want a bag for your T Shirt. There is no tip necessary.” I wept. I tell people that if I order food or drink standing up I don't tip. You shouldn't tip for service if you're standing. That's what I say. That's my rule. However, follow me around you'd see that I seldom obey my own rule. That awkward moment when the person at the register is waiting for you to add your tip so they can complete the transaction. They're watching and I give in nearly every time. I'm weak. Similarly, my wife and I recently changed homeowners insurance. I then got an email to download their contractor's app and a page of instructions about how to use their app to take photos and videos of my house so they can confirm the insurance quote. In addition to downloading the app, it would require complex passwords, two-step authentications, and, likely headaches and time on the phone with their service team. Though branding it as a simple tool that wouldn't take much time, they were asking me to do their job. I simply replied to the email that I'm not going to do it. That's their job, that's what I'm paying them for. I could sense the eye-rolls on the other side and they said they'd send out a representative to collect the information. A small win. If you agree with me, if you're frustrated about paying more and more for what you're getting and doing their job along the way, let me hear from you. Send me a donation and I'll continue to beat this drum on our behalf. And don't forget to round up. I'm Cam Marston and I'm just trying to Keep it Real.

MLS Season Pass reporter Andrew Wiebe joins Jonathan and Manny to discuss the week that was across the league, the latest Loons matches, and predictions going into the weekend.See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Ben and Donnie spend the opening hour of the show recapping Thursday night's NBA Playoffs action as well as Thursday's slate of MLB matchups on the diamond!

William Zahner, Understanding the Role of Language in Math Classrooms ROUNDING UP: SEASON 3 | EPISODE 17 How can educators understand the relationship between language and the mathematical concepts and skills students engage with in their classrooms? And how might educators think about the mathematical demands and the language demands of tasks when planning their instruction?  In this episode, we discuss these questions with Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University. BIOGRAPHY Bill Zahner is a professor in the mathematics department at San Diego State University and the director of the Center for Research in Mathematics and Science Education. Zahner's research is focused on improving mathematics learning for all students, especially multilingual students who are classified as English Learners and students from historically marginalized communities that are underrepresented in STEM fields. RESOURCES Teaching Math to Multilingual Learners, Grades K–8 by Kathryn B. Chval, Erin Smith, Lina Trigos-Carrillo, and Rachel J. Pinnow National Council of Teachers of Mathematics Mathematics Teacher: Learning and Teaching PK– 12 English Learners Success Forum SDSU-ELSF Video Cases for Professional Development The Math Learning Center materials Bridges in Mathematics curriculum Bridges in Mathematics Teachers Guides [BES login required] TRANSCRIPT Mike Wallus: How can educators understand the way that language interacts with the mathematical concepts and skills their students are learning? And how can educators focus on the mathematics of a task without losing sight of its language demands as their planning for instruction? We'll examine these topics with our guest, Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University.  Welcome to the podcast, Bill. Thank you for joining us today. Bill Zahner: Oh, thanks. I'm glad to be here. Mike: So, I'd like to start by asking you to address a few ideas that often surface in conversations around multilingual learners and mathematics. The first is the notion that math is universal, and it's detached from language. What, if anything, is wrong with this idea and what impact might an idea like that have on the ways that we try to support multilingual learners? Bill: Yeah, thanks for that. That's a great question because I think we have a common-sense and strongly held idea that math is math no matter where you are and who you are. And of course, the example that's always given is something like 2 plus 2 equals 4, no matter who you are or where you are. And that is true, I guess [in] the sense that 2 plus 2 is 4, unless you're in base 3 or something. But that is not necessarily what mathematics in its fullness is. And when we think about what mathematics broadly is, mathematics is a way of thinking and a way of reasoning and a way of using various tools to make sense of the world or to engage with those tools [in] their own right. And oftentimes, that is deeply embedded with language.  Probably the most straightforward example is anytime I ask someone to justify or explain what they're thinking in mathematics. I'm immediately bringing in language into that case. And we all know the old funny examples where a kid is asked to show their thinking and they draw a diagram of themselves with a thought bubble on a math problem. And that's a really good case where I think a teacher can say, “OK, clearly that was not what I had in mind when I said, ‘Show your thinking.'”  And instead, the demand or the request was for a student to show their reasoning or their thought process, typically in words or in a combination of words and pictures and equations. And so, there's where I see this idea that math is detached from language is something of a myth; that there's actually a lot of [language in] mathematics. And the interesting part of mathematics is often deeply entwined with language. So, that's my first response and thought about that.  And if you look at our Common Core State Standards for Mathematics, especially those standards for mathematical practice, you see all sorts of connections to communication and to language interspersed throughout those standards. So, “create viable arguments,” that's a language practice. And even “attend to precision,” which most of us tend to think of as, “round appropriately.” But when you actually read the standard itself, it's really about mathematical communication and definitions and using those definitions with precision. So again, that's an example, bringing it right back into the school mathematics domain where language and mathematics are somewhat inseparable from my perspective here. Mike: That's really helpful. So, the second idea that I often hear is, “The best way to support multilingual learners is by focusing on facts or procedures,” and that language comes later, for lack of a better way of saying it. And it seems like this is connected to that first notion, but I wanted to ask the question again: What, if anything, is wrong with this idea that a focus on facts or procedures with language coming after the fact? What impact do you suspect that that would have on the way that we support multilingual learners? Bill: So, that's a great question, too, because there's a grain of truth, right? Both of these questions have simultaneously a grain of truth and simultaneously a fundamental problem in them. So, the grain of truth—and an experience that I've heard from many folks who learned mathematics in a second language—was that they felt more competent in mathematics than they did in say, a literature class, where the only activity was engaging with texts or engaging with words because there was a connection to the numbers and to symbols that were familiar. So, on one level, I think that this idea of focusing on facts or procedures comes out of this observation that sometimes an emergent multilingual student feels most comfortable in that context, in that setting.  But then the second part of the answer goes back to this first idea that really what we're trying to teach students in school mathematics now is not simply, or only, how to apply procedures to really big numbers or to know your times tables fast. I think we have a much more ambitious goal when it comes to teaching and learning mathematics. That includes explaining, justifying, modeling, using mathematics to analyze the world and so on. And so, those practices are deeply tied with language and deeply tied with using communication. And so, if we want to develop those, well, the best way to do that is to develop them, to think about, “What are the scaffolds? What are the supports that we need to integrate into our lessons or into our designs to make that possible?”  And so, that might be the takeaway there, is that if you simply look at mathematics as calculations, then this could be true. But I think our vision of mathematics is much broader than that, and that's where I see this potential. Mike: That's really clarifying. I think the way that you unpack that is if you view mathematics as simply a set of procedures or calculations, maybe? But I would agree with you. What we want for students is actually so much more than that.  One of the things that I heard you say when we were preparing for this interview is that at the elementary level, learning mathematics is a deeply social endeavor. Tell us a little bit about what you mean by that, Bill. Bill: Sure. So, mathematics itself, maybe as a premise, is a social activity. It's created by humans as a way of engaging with the world and a way of reasoning. So, the learning of mathematics is also social in the sense that we're giving students an introduction to this way of engaging in the world. Using numbers and quantities and shapes in order to make sense of our environment.  And when I think about learning mathematics, I think that we are not simply downloading knowledge and sticking it into our heads. And in the modern day where artificial intelligence and computers can do almost every calculation that we can imagine—although your AI may do it incorrectly, just as a fair warning [laughs]—but in the modern day, the actual answer is not what we're so focused on. It's actually the process and the reasoning and the modeling and justification of those choices. And so, when I think about learning mathematics as learning to use these language tools, learning to use these ways of communication, how do we learn to communicate? We learn to communicate by engaging with other people, by engaging with the ideas and the minds and the feelings and so on of the folks around us, whether it's the teacher and the student, the student and the student, the whole class and the teacher. That's where I really see the power. And most of us who have learned, I think can attest to the fact that even when we're engaging with a text, really fundamentally we're engaging with something that was created by somebody else. So, fundamentally, even when you're sitting by yourself doing a math word problem or doing calculations, someone has given that to you and you think that that's important enough to do, right?  So, from that stance, I see all of teaching and learning mathematics is social. And maybe one of our goals in mathematics classrooms, beyond memorizing the times tables, is learning to communicate with other people, learning to be participants in this activity with other folks. Mike: One of the things that strikes me about what you were saying, Bill, is there's this kind of virtuous cycle, right? That by engaging with language and having the social aspect of it, you're actually also deepening the opportunity for students to make sense of the math. You're building the scaffolds that help kids communicate their ideas as opposed to removing or stripping out the language. That's the context in some ways that helps them filter and make sense. You could either be in a vicious cycle, which comes from removing the language, or a virtuous cycle. And it seems a little counterintuitive because I think people perceive language as the thing that is holding kids back as opposed to the thing that might actually help them move forward and make sense. Bill: Yeah. And actually that's one of the really interesting pieces that we've looked at in my research and the broader research is this question of, “What makes mathematics linguistically complex?” is a complicated question. And so sometimes we think of things like looking at the word count as a way to say, “If there are fewer words, it's less complex, and if there are more words, it's more complex.” But that's not totally true. And similarly, “If there's no context, it's easier or more accessible, and if there is a context, then it's less accessible.”  And I don't see these as binary choices. I see these as happening on a somewhat complicated terrain where we want to think about, “How do these words or these contexts add to student understanding or potentially impede [it]?” And that's where I think this social aspect of learning mathematics—as you described, it could be a virtuous cycle so that we can use language in order to engage in the process of learning language. Or, the vicious cycle is, you withhold all language and then get frustrated when students can't apply their mathematics. That's maybe the most stereotypical answer: “My kids can do this, but as soon as they get a word problem, they can't do it.” And it's like, “Well, did you give them opportunities to learn how to do this? [laughs] Or is this the first time?” Because that would explain a lot. Mike: Well, it's an interesting question, too, because I think what sits behind that in some ways is the idea that you're kind of going to reach a point, or students might reach a point, where they're “ready” for word problems.  Bill: Right. Mike: And I think what we're really saying is it's actually through engaging with word problems that you build your proficiency, your skillset that actually allows you to become a stronger mathematician. Bill: Mm-hmm. Right. Exactly. And it's a daily practice, right? It's not something that you just hold off to the end of the unit, and then you have the word problems, but it's part of the process of learning. And thinking about how you integrate and support that. That's the key question that I really wrestle with. Not trivial, but I think that's the key and the most important part of this. Mike: Well, I think that's actually a really good segue because I wanted to shift and talk about some of the concrete or productive ways that educators can support multilingual learners. And in preparing for this conversation, one of the things that I've heard you stress is this notion of a consistent context. So, can you just talk a little bit more about what you mean by that and how educators can use that when they're looking at their lessons or when they're writing lessons or looking at the curriculum that they're using? Bill: Absolutely. So, in our past work, we engaged in some cycles of design research with teachers looking at their mathematics curriculum and opportunities to engage multilingual learners in communication and reasoning in the classroom. And one of the surprising things that we found—just by looking at a couple of standard textbooks—was a surprising number of contexts were introduced that are all related to the same concept. So, the concept would be something like rate of change or ratio, and then the contexts, there would be a half dozen of them in the same section of the book. Now, this was, I should say, at a secondary level, so not quite where most of the Bridges work is happening. But I think it's an interesting lesson for us that we took away from this. Actually, at the elementary level, Kathryn Chval has made the same observation.  What we realized was that contexts are not good or bad by themselves. In fact, they can be highly supportive of student reasoning or they can get in the way. And it's how they are used and introduced. And so, the other way we thought about this was: When you introduce a context, you want to make sure that that context is one that you give sufficient time for the students to understand and to engage with; that is relatable, that everyone has access to it; not something that's just completely unrelated to students' experiences. And then you can really leverage that relatable, understandable context for multiple problems and iterations and opportunities to go deeper and deeper.  To give a concrete example of that, when we were looking at this ratio and rate of change, we went all the way back to one of the fundamental contexts that's been studied for a long time, which is motion and speed and distance and time. And that seemed like a really important topic because we know that that starts all the way back in elementary school and continues through college-level physics and beyond. So, it was a rich context. It was also something that was accessible in the sense that we could do things like act out story problems or reenact a race that's described in a story problem. And so, the students themselves had access to the context in a deep way.  And then, last, that context was one that we could come back to again and again, so we could do variations [of] that context on that story. And I think there's lots of examples of materials out there that start off with a core context and build it out. I'm thinking of some of the Bridges materials, even on the counting and the multiplication. I think there's stories of the insects and their legs and wings and counting and multiplying. And that's a really nice example of—it's accessible, you can go find insects almost anywhere you are. Kids like it. [Laughs] They enjoy thinking about insects and other icky, creepy-crawly things. And then you can take that and run with it in lots of different ways, right? Counting, multiplication, division ratio, and so on. Mike: This last bit of our conversation has me thinking about what it might look like to plan a lesson for a class or a group of multilingual learners. And I know that it's important that I think about mathematical demands as well as the language demands of a given task. Can you unpack why it's important to set math and language development learning goals for a task, or a set of tasks, and what are the opportunities that come along with that, if I'm thinking about both of those things during my planning? Bill: Yeah, that's a great question. And I want to mark the shift, right? We've gone from thinking about the demands to thinking about the goals, and where we're going to go next.  And so, when I think about integrating mathematical goals—mathematical learning goals and language learning goals—I often go back to these ideas that we call the practices, or these standards that are about how you engage in mathematics. And then I think about linking those back to the content itself. And so, there's kind of a two-piece element to that. And so, when we're setting our goals and lesson planning, at least here in the great state of California, sometimes we'll have these templates that have, “What standard are you addressing?,” [Laughs] “What language standard are you addressing?,” “What ELD standard are you addressing?,” “What SEL standard are you addressing?” And I've seen sometimes teachers approach that as a checkbox, right? Tick, tick, tick, tick, tick. But I see that as a missed opportunity—if you just look at this like you're plugging things in—because as we started with talking about how learning mathematics is deeply social and integrated with language, that we can integrate the mathematical goals and the language goals in a lesson. And I think really good materials should be suggesting that to the teacher. You shouldn't be doing this yourself every day from scratch. But I think really high-quality materials will say, “Here's the mathematical goal, and here's an associated language goal,” whether it's productive or receptive functions of language. “And here's how the language goal connects the mathematical goal.”  Now, just to get really concrete, if we're talking about an example of reasoning with ratios—so I was going back to that—then it might be generalized, the relationship between distance and time. And that the ratio of distance and time gives you this quantity called speed, and that different combinations of distance and time can lead to the same speed. And so, explain and justify and show using words, pictures, diagrams. So, that would be a language goal, but it's also very much a mathematical goal.  And I guess I see the mathematical content, the practices, and the language really braided together in these goals. And that I think is the ideal, and at least from our work, has been most powerful and productive for students. Mike: This is off script, but I'm going to ask it, and you can pass if you want to.  Bill: Mm-hmm. Mike: I wonder if you could just share a little bit about what the impact of those [kinds] of practices that you described [have been]—have you seen what that impact looks like? Either for an educator who has made the step and is doing that integration or for students who are in a classroom where an educator is purposely thinking about that level of integration? Bill: Yeah, I can talk a little bit about that. In our research, we have tried to measure the effects of some of these efforts. It is a difficult thing to measure because it's not just a simple true-false test question type of thing that you can give a multiple-choice test for.  But one of the ways that we've looked for the impact [of] these types of intentional designs is by looking at patterns of student participation in classroom discussions and seeing who is accessing the floor of the discussion and how. And then looking at other results, like giving an assessment, but deeper than looking at the outcome, the binary correct versus incorrect. Also looking at the quality of the explanation that's provided. So, how [do] you justify an answer? Does the student provide a deeper or a more mathematically complete explanation?  That is an area where I think more investigation is needed, and it's also very hard to vary systematically. So, from a research perspective—you may not want to put this into the final version [laughs]—but from a research perspective, it's very hard to fix and isolate these things because they are integrated. Mike: Yeah. Yeah. Bill: Because language and mathematics are so deeply integrated that trying to fix everything and do this—“What caused this water to taste like water? Was it the hydrogen or the oxygen?”—well, [laughs] you can't really pull those apart, right? The water molecule is hydrogen and oxygen together. Mike: I think that's a lovely analogy for what we were talking about with mathematical goals and language goals. That, I think, is really a helpful way to think about the extent to which they're intertwined with one another. Bill: Yeah, I need to give full credit to Vygotsky, I think, who said that. Mike: You're— Bill: Something. Might be Vygotsky. I'll need to check my notes. Mike: I think you're in good company if you're quoting Vygotsky.  Before we close, I'd love to just ask you a bit about resources. I say this often on the podcast. We have 20 to 25 minutes to dig deeply into an idea, and I know people who are listening often think about, “Where do I go from here?” Are there any particular resources that you would suggest for someone who wanted to continue learning about what it is to support multilingual learners in a math classroom? Bill: Sure. Happy to share that.  So, I think on the individual and collective level—so, say, a group of teachers—there's a beautiful book by Kathryn Chval and her colleagues [Teaching Math to Multilingual Learners, Grades K–8] about supporting multilingual learners and mathematics. And I really see that as a valuable resource. I've used that in reading groups with teachers and used that in book studies, and it's been very productive and powerful for us. Beyond that, of course, I think the NCTM [National Council of Teachers of Mathematics] provides a number of really useful resources. And there are articles, for example, in the [NCTM journal] Mathematics Teacher: Learning and Teaching PK– 12 that could make for a really wonderful study or opportunity to engage more deeply.  And then I would say on a broader perspective, I've worked with organizations like the English Learners Success Forum and others. We've done some case studies and little classroom studies that are accessible on my website [SDSU-ELSF Video Cases for Professional Development], so you can go to that. But there's also from that organization some really valuable insights, if you're looking at adopting new materials or evaluating things, that gives you a principled set of guidelines to follow. And I think that's really helpful for educators because we don't have to do this all on our own. This is not a “reinvent the wheel at every single site” kind of situation. And so, I always encourage people to look for those resources.  And of course, I will say that the MLC materials, the Bridges in Mathematics [curriculum], I think have been really beautifully designed with a lot of these principles right behind them. So, for example, if you look through the Teachers Guides on the Bridges in Mathematics [BES login required], those integrated math and language and practice goals are a part of the design. Mike: Well, I think that's a great place to stop. Thank you so much for joining us, Bill. This has been insightful, and it's really been a pleasure talking with you. Bill: Oh, well, thank you. I appreciate it. Mike: And that's a wrap for Season 3 of Rounding Up. I want to thank all of our guests and the MLC staff who make these podcasts possible, as well as all of our listeners for tuning in. Have a great summer, and we'll be back in September for Season 4.  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  

Reflecting on a 4-0 win over Stourbridge and Derby County Womens' season as a whole.

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  

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After a poignant weekend in the boxing world, Sean and Lukie come together to honor the legacies of George Foreman, Colin Hart, and Livingstone Bramble. Their reflections delve into the evolving landscape of boxing and journalism, capturing the essence of a transforming era. The episode also recaps the exciting bouts from the past two weekends and offers an enticing preview of the thrilling fights on the horizon. Learn more about your ad choices. Visit podcastchoices.com/adchoices

Happy love celebration week!! In honor of how much we LOVE our patreon subscribers, Trace and Julian answer two winners of our Patreon polls! It takes two

Last stretch of the preseason! OSG and yours truly round up the news from the Dynamo: Jack McGlynn coming to Houston, reviewing their preseason results so far, Josh Wolff joining the technical staff, rumors, loans, and more. We also have some updates from Houston Dynamo 2 involving a new head coach and season schedule ahead of the 2025 MLS NEXT Pro season.Timestamps:2:46 Marcelo Santos appointed as head coach for Houston Dynamo 26:20 Dynamo 2 schedule released9:00 Kieran Sargeant loaned to Lexington SC in USL Championship for 202510:14 Jefferson Valverde loaned to Orense SC in Ecuador for 202511:25 Dynamo sign Jack McGlynn from Philadelphia Union in team's first-ever cash swap18:04 Junior Urso set to join Houston as a free agent20:30 Josh Wolff added to first-team technical staff23:32 Dynamo rumored to acquire academy rights to 16 y/o center back Gavin Wolff from Austin FC26:53 Preseason results from the Dynamo so far 33:30 Season 20 Jersey Unveiling and Season Kickoff Fan Fest are this weekCredits:⬢ Noodle Time is hosted by yours truly⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Andres Naranjo⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ and⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠OSG⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠!⬢ Intro/Outro music by Matt Houston. | Starfox - Armada [Matt Houston Remix]⬢ Support Foxtrot and read the blog on⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Ko-fi.com/DynamicFoxtrot⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠.⬢ Follow the fox on Twitter (⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠@DynamicFoxtrot⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠), Instagram (⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠@dynamicfoxtrot⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠), and Bluesky (⁠⁠⁠⁠@DynamicFoxtrot⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠)⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠.⬢ Subscribe to ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Foxtrot TV⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ on⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠YouTube⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ and⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠GOLZTV⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠!⬢ Thumbnail photo provided by Houston Dynamo FC.

Angie Wong, Miami Republican Exec Committeewoman D17, Florida Delegate, Columnist, Columbia Graduate School of Journalism, fmr Asst Editor South China Morning Post. Homan rounding up illegals in South Florida. Eric Adams new legal problems

THE DEA IS ROUNDING UP BAD HOMBRES And I've got someone on the show today to talk about the massive roundup of drug and human dealing Tren De Aragua gang members at their own exclusive party this weekend. I'm talking to someone from DEA at 2:30 about it.

Sue Kim and Myuriel Von Aspen, Building Productive Partnerships   ROUNDING UP: SEASON 3 | EPISODE 10 In this episode, we examine the practice of building productive student partnerships. We'll talk about ways  educators can cultivate joyful and productive partnerships and the role the educator plays once students are engaged with their partner.  BIOGRAPHIES Sue Kim is an advocate for children's thinking and providing them a voice in learning mathematics. She received her teaching credential and master of education from Biola University in Southern California. She has been an educator for 15 years and has taught and coached across TK–5th grade classrooms including Los Angeles Unified School District and El Segundo Unified School District as well as several other Orange County, California, school districts.  Myuriel von Aspen believes in fostering collaborative partnerships with teachers with the goal of advancing equitable, high-quality learning opportunities for all children. Myuriel earned a master of arts in teaching and a master of business administration from the University of California, Irvine and a bachelor of science in computer science from Florida International University. She currently serves as a math coordinator of the Teaching, Learning, and Instructional Leadership Collaborative. ​ RESOURCES Catalyzing Change in Early Childhood and Elementary Mathematics by National Council of Teachers of Mathematics Purposeful Play by Kristine Mraz, Alison Porcelli, and Cheryl Tyler  Hands Down, Speak Out: Listening and Talking Across Literacy and Math K–5 by Kassia Omohundro Wedekind and Christy Hermann Thompson TRANSCRIPT Mike Wallus: What are the keys to establishing productive student partnerships in an elementary classroom? And how can educators leverage the learning that happens in partnerships for the benefit of the entire class? We'll explore these and other questions with Sue Kim and Myuriel von Aspen from the Orange County Office of Education on this episode of Rounding Up.  Well, hi, Sue and Myuriel. Welcome to the podcast. Myuriel von Aspen: Hi, Mike.  Sue Kim: Thanks for having us. Mike: Thrilled to have you both.  So, I first heard you two talk about the power of student partnerships in a context that involved counting collections. And during that presentation, you all said a few things that I have been thinking about ever since. The first thing that you said was that neuroscience shows that you can't really separate emotions from the way that we learn. And I wonder what do you mean when you say that and why do you think it's important when we're thinking about student partnerships? Myuriel: Yes, absolutely. So, this idea comes directly from neuroscience research, the idea that we cannot build memories without emotions. I'm going to read to you a short quote from the NCTM [National Council of Teachers of Mathematics] publication Catalyzing Change in Early Childhood and Elementary Mathematics that says, “Emerging evidence from neuroscience strongly shows that one cannot separate the learning of mathematics content from children's views and feelings toward mathematics.”  So, to me, what that says is that how children feel has a huge influence on their ability to learn math and also on how they feel about themselves as learners of math. So, depending on how they feel, they might be willing to engage in the content or not. And so, as they're engaging in counting collections and they're enjoying counting and they feel joyful and they're doing this with friends, they will learn better because they enjoy it, and they care about what they're doing and what they're learning. Mike: You know, this is a nice segue to the other thing that has been on my mind since I heard you all talk about this because I remember you said that students don't think about a task like counting collections as work, that they see it as play. And I wonder what you think the ramifications of that are for how we approach student partnership? Sue: Yeah, you know, I've been in so many classrooms across TK through fifth [grade], and when I watch kids count collections, we see joy, we see engagement in these ways. But I've also been thinking about this idea of how play is even defined, in a way, since you asked that question that they think of it as play.  Kristine Mraz, teacher, author, and a consultant, has [coauthored] a book called Purposeful Play. And I remember this was the first time I hear about this reference about Vivian Paley, an American early childhood educator and researcher, stress through her career, the importance of play for children when she discovered in her work that play's actually a very complex activity and that it is indeed hard work. It's the work of kids. It's the work of what children do. That's their life, in a sense. And so, something I've been thinking about is how kids perceive play is different than how adults perceive play. And so, they take it with seriousness. There is a complex, very intentionality behind things that they do and say. And so, when we are in our session, and we reference Megan Franke, she says that when young people are engaging with each other's ideas, what they're able to do is mathematically important. But it's also important because they're learning to learn together. They're learning to hear each other. They're developing social and emotional skills as they try and navigate and negotiate each other's ideas. And I think for kids that this could be considered play, and I think that's so fascinating because it's so meaningful to them. And even in a task like counting, they're doing all these complex things. But as adults we see them, and we're like, “Oh, they're playing.” But they are really thinking deeply about some of these ideas while they're developing these very critical skills that we need to give opportunities for them to develop. Myuriel: I like that idea of leaning into the play that you consider maybe not as serious, but they are. Whether they're playing seriously or not, that you might take that opportunity to make it into a mathematical question or a mathematical reflection. Sue: I totally agree with you. And taking it back to that question that you asked, Mike, about, “How do we approach student partnerships then?” And I think that we need to approach it with this lens of curiosity while we let kids engage in these ways and opportunities of learning to hear each other and develop these social-emotional skills, like we said. And so, when you see kids that we think are “playing” or they're building a tower: How might we enter that space with a lens of curiosity? Because to them, I think it's serious work. We can't just think, “Oh, they're not really in the task” or “They're not doing what they were supposed to do.” But how do we lean into that space with a lens of curiosity as Megan reminded us to do, to see what mathematical things we can tap into? And I think that kids always rise to the occasion. Mike: I love that. So, let's talk about how educators can cultivate joyful and productive student partnerships. I'm going to guess that as is often the case, this starts by examining existing beliefs that I might have and some of my expectations. Sue: Yeah, I think it really begins with your outlook and your identity as a teacher. What's your outlook on what's actually possible for kids in your class? Do you believe that kids as young as 4-year-olds can take on this responsibility of engaging with each other in these intelligent ways? Unless we begin there and we really think and reflect and examine what our beliefs are about that, I think it's hard to go and move beyond that, if that makes sense.  And like what we just talked about, it's being open to the curiosity of what could be the capacity of how kids learn. I've seen enough 4-year-olds in TK classrooms doing these big things. They always blow my mind, blow my expectations, when opportunities are given to them and consistently given to them. And it's a process, right? They're not going to start on day one doing some of these more complex things. But they can learn from one another, and they also learn from you as a teacher because they are really paying attention. They are attending to some of these complex ideas that we put in front of them. Mike: Well, you hit on the question that I was thinking about. Because I remember you saying that part of nurturing partnerships starts with a teacher and perhaps a pair of children at a table. Can you all paint a picture of what that might look like for educators who are listening? Sue: Yeah, so actually in one of the most recent classrooms, I went in, and this teacher allowed me to partner with her in this work. She wanted to be able to observe and do it in a structured way so that she could pick up on some details of noticing the things that kids were doing. And so, she would have a collection out, or they got to choose. She was really good about offering choice to kids, another way to really engage them. And so, they would choose. They would come together. And then she started just taking some anecdotal notes on what she heard kids saying, what she saw them doing, what they had to actually navigate through some of the things, the stuck moments that came up.  From that, we were able to develop, “OK, what are some goals? We noticed Students A and B doing this and speaking in these ways. What might be the next step that we might want to put into a mini lesson or model out or have them actually share with the class what they were working on mathematically?” Whether it was organization, or how they decided they wanted to represent their count, how they counted and things like that.  And so, it was just this really natural process that took place that we were able to really lean into and leverage that kids really responded to because it wasn't someone else's work or a page from a textbook. It was their work, their collection that was meaningful to them and they had a true voice and a stake in that work. Mike: I feel like there have been points in time where my understanding of building groups was almost like an engineering problem, where you needed to model what you wanted kids to do and have them rehearse it so specifically. But I think what sits at the bottom of that approach is more about compliance. And what I loved about what you described, Sue, is a process where you're building on the mathematical assets that kids are showing you during their time together—but also on the social assets that they're showing you. So, in that time when you might be observing a pair or a partnership playing together, working together with something like counting collections, you have a chance to observe the mathematics that's happening. You also have a chance to observe the social assets that you see happening. And you can use that as a way to build for that group, but also to build for the larger group of children. And that just feels really profoundly different than, I think, how I used to think about what it was to build partnerships that were “effective.” Myuriel: You know, Mike, I think it's not only compliance. It's also that control. And what it makes me think about is, when we want to model ourselves what we want students to do, instead of—exactly what you said, looking at what they're doing and bringing that knowledge, those skills, that wisdom that's in the room from the students to show to others so that they feel like their knowledge counts. The teacher is not only the only authority or the only source of knowledge in the room—we bring so much, and we can learn from each other. So, I think it's so much more productive and so effective in developing the identity of students when you are showing something that they're doing to their peers versus you as an adult telling them what to do. Mike: Yeah. Are there any particular resources that you all have found helpful for crafting mini lessons as students are learning about how to become a partnership or to be productive in a partnership? Myuriel: Yes. One book that I love, it's not specific to counting collections, but it does provide opportunities for teachers to create micro-lessons when students are listening and talking to each other. It's Hands Down, Speak Out: Listening and Talking Across Literacy and Math K–5 by Kassia [Omohundro] Wedekind and Christy [Hermann] Thompson. And the reason why I love this book is because it provides, again, these micro-lessons depending on what the teacher is noticing, whether it is that the teacher is noticing that students need support listening to each other or maybe making their ideas clear. Or maybe students need to learn how to ask questions more effectively or even reflect on setting and reflecting on the goals that they have as partners. It does provide ideas for teachers to create those micro-lessons based on what the teacher is noticing. Sue: Yeah, I guess I want to add to that, Mike, as well, the resources that Myuriel said. But also, I think this is something I really learned along the process of walking alongside this teacher, was looking at partnerships through a mathematical lens and then a social lens. And so, the mini lesson could be birthed out of watching kids in one day. It might be a social lens thinking about, “They were kind of stuck because they wanted to choose different collections. What might we do about that?” And that kind of is tied to this problem-solving type of skill and goal that we would want kids to work on. That's definitely something that's going to come up as kids are working in partnerships. These partnerships are not perfect and pristine all the time. I think that's the nature of the job. And just as humans, they're learning how to get along, they're learning how to communicate and navigate and negotiate these things. And I think those are beautiful opportunities for kids and for teachers, then, to really lean into as goals, as mini lessons that can be out of this. And these mini lessons don't have to be long and drawn out. They can be a quick 5-, 10-minute thing. Or you can pause in the middle of counting and kind of spotlight the fact that “Mike and Brent had this problem, but we want to learn from them because they figured out how to solve it. And this is how. Let's listen to what happened.” So, these natural, not only places in a lesson that these opportunities for teaching can pop up, but that these mini lessons come straight from kids and how they are interacting and how they are taking up partnerships, whether it be mathematical or social. Mike: I think you're helping me address something that if I'm transparent about was challenging for me when I was a classroom teacher. I got a little bit nervous about what was happening and sometimes I would shut things down if I perceived partnerships to be, I don't know, overwhelming or maybe even messy. But you're making me think now that part of this work is actually noticing what are the assets that kids have in their social interactions in the way that they're playing together, collaborating together, the mathematics? And I think that's a big shift in my mind from the way that I was thinking about this work before. And I wonder, first of all, is this something that you all notice that teachers sometimes are challenged by? And two, how you talk to someone who's struggling with that question of like, “Oh my gosh, what's happening in my classroom?” Myuriel: Yes, I can totally understand how teachers might get overwhelmed. We hear this from, not only from teachers trying to do the work of counting collections, but even just using tools for students to problem-solve because it does get messy. I like the way Sue keeps emphasizing how it will be messy. When you have rich mathematical learning happening, and you're using tools and collections and you have 30 students having conversations, it definitely will get messy. But I would say that something that teachers can do to mitigate some of that messiness is to think about the logistics ahead of time and be intentional about what you are planning to do. So, some of the things that they may want to think about is: How are students going to access the counting collections? Where are you going to [put] the tools that they're going to be using? Where physically in the classrooms will students get together to have collections so that they have enough room to spread out and record and talk to each other? And just like Sue was mentioning: How do I partner students so that they do have a good experience, and they support each other? So, all of these things that might cost a bit of chaos if you don't think about them, you can actually think about each one of those ahead of time so that you do have a plan for each one of those.  Another thing that teachers may want to consider thinking about is, what do they want to pay attention to when they are facilitating or walking around? There's a lot that they need to pay attention to. Just like Sue mentioned, it is important for them to pay attention to something because you want to bring what's in the room to connect it and have these mini lessons of what students actually need. And also, thinking about after the counting collections: What worked and what didn't? And what changes do I want to make next time when I do this again? Just so that there is a process of improvement every time. Because as Sue had mentioned, it's not going to happen on day one. You are learning as a teacher, and the students are learning. So, everybody in that room is learning to make this a productive and joyful experience. Sue: Yeah, and another thing that I would definitely remind teachers about is that there's actually research out there about how important it is for kids to engage with one another's mathematical ideas. I'm so thankful that people are researching out there doing this work for us. And this goes along with what Myuriel was saying, but the expectations that we put on ourselves as teachers sometimes are too far. We're our biggest critique-ers of the work that we do. And of course we want things to go well, but to make it more low-risk for yourself. I think that when we lower those stakes, we're more prone to let kids take ownership of working together in these ways, to use language and communication that makes sense while doing math and using these cognitive abilities that are still in the process of developing. And I think they need to remember that it takes time to develop, and it's going to get there. And kids are going to learn. Kids are going to do some really big things with their understanding. But giving [yourself] space, the time to learn along with your students, I think is very critical so that you feel like it's manageable. You feel like you can do it again the next day. Mike: Tell me a little bit about how you have seen educators use things like authentic images or even video to help their students make sense of what it means to work in a partnership. What have you seen teachers do? Sue: Yeah. Not to mention how that is one sure way to get kids engaged. I don't know if you've been in a room full of first graders or kindergartners, but if you put a video image up that's them counting and showing how they are thinking about things, they are one-hundred-percent there with you. They love being acknowledged and recognized as being the doers and the sensemakers of mathematics. And it goes into this idea of how we position kids competently, and this is another way that we can do that. But capturing student thinking in photos or a short clip has really been a powerful tool to get kids to engage in each other's ideas in a deeper way. I think it allows teachers and students to pause and slow down and really focus in on the skill of noticing. I think people forget that noticing is a skill you have to teach. And you have to give opportunities for kids to actually do these things so they can see mathematically what's happening within the freeze-frame of this image, of this collection, and how we might ask questions to help facilitate and guide their thinking to think deeply about these ideas. And so, I've seen teachers use them with partners, and they may say, “Hey, here's one way that they were counting. How do you think they counted within the frame of this picture or this photo that we took?” And then kids will have these conversations. They'll engage mathematically what they think, and then they might show the video clip of the students actually counting. And they get to make predictions. They get to navigate the language around what they think. And it's just, again, been a really nice tool that has then branched out into whole-group discussions. So, you can use it with partnerships and engage certain kids in specific ways, but then being able to utilize that and leverage that in whole-group settings has really been powerful to see. Myuriel: I also recently observed a teacher with pictures, showing students different tools that different partners were using and having those discussions about, “Why did this tool work and why didn't this one?” or “What will you have to do if your collection gets bigger?” So, it is a great opportunity to really show from what they're using and having those discussions about what works and what doesn't, and “Why would I use this versus this?” from their own work. Mike: Myuriel, what you made me wonder is if you could apply this same idea of using video or images to help support some of those social goals that we were talking about for students as well. Myuriel: I think that you could. I can just imagine that if you see two students working together and supporting each other or asking some good questions and being curious, you could record them and then show that to the others to ask them what they're noticing. “How are these two students supporting each other in their learning?” Even “How are they being kind to each other when they make a mistake?” So, there is so much power in using video for not just the mathematical skills, but also for the social skills. Sue: Myuriel, when you're talking, you're reminding me about two particular students that we have watched, and we have recorded video around, actually, when they came to a disagreement.  There was this one instance when a couple of students came to a disagreement about what to call the next number of the sequence. And that was a really cool moment because we actually discovered, “Wow, these two peers had enough trust in each other to pause, to listen to both sides.” And then when it came time to actually call the number and the sequence, the other student actually trusted enough and listened to the reasoning of the other student to say, “OK, I'm going to go along with you, and I think that should be what the sequence is.” And it was just a really neat opportunity and—that this teacher actually showed in front of kids just to see what kids would say in response to that particular moment. Myuriel: It was actually one very cute, but very interesting moment when you see that second student who's listening to the other one. And actually at first she kind of argued with him a little bit about, “No, it's not this number.” But the second time around, when she counted, she paused right at that same spot where she had trouble before, and she set the number that he had suggested the earlier time so that you see that she's listening, she's considering someone else's ideas, and she's learning the correct sequence. Yes, that was really amazing to see. Sue: So, it's the sequence of numbers that they're working on, but think about all the social aspects of what is happening and developing, and I think that they're addressing it and that they're having to engage with [it]. It's [a] very complex situation that they're learning a lot of skills around in that very moment. Mike: You know, I wonder how an educator might think about their role once students are actually engaged with a partner. How do you all think about goals, or the role of the teacher, once students are working with a partner? Sue: I think that one of the things we're really thinking about and being more intentional about is: When do we actually interject, or when do we as teachers actually say something? When and how do we make those decisions? And for several years now, I've really taken on this notion that we are facilitators. Yes, we're teachers. But more than anything, we are facilitators of the students in our class, and we want to really give them the opportunity to work through some of these ideas. And we will have set up partnerships based on what we've seen and notes that we took as kids have been working. But it's an ever-innovated process, I think. And I think something that's always going to be on the forefront is that idea: How are we facilitating? How are we deciding when we want to say something or interject, and why? And what is it that we are trying to get kids to think about? Because I think we need to help students realize that they are always in the driver's seat of what they're doing, especially if they're in a partnership. And there are targeted things that we can have them maybe think about when we drop a question based on what we're noticing. Or maybe when they're stuck, and they're in the middle of negotiating something. But I really think that it starts there with us kind of thinking about: What is our role? Is it OK that we step back and we just watch even if they have to problem-solve through something that feels like, “Oh, I don't know if they're going to get through that moment.” But we've got to let them. We've got to give them opportunities to do that without having to rescue them every single time. Myuriel: And you're right, Sue, we've seen it so many times when if you just bite your tongue, 10 seconds later, it's happening, right? They're helping each other, and they get to the idea that you thought you had to bring up to them. But they were able to resolve it. So, if we only allow that time for them to process the idea or to revise their thinking or to allow the other partner to support their partner, it will happen. Sue: Yeah, and I think that doesn't mean that we can't set kids up. I've seen teachers launch the lesson with something a partner did before yesterday, and they will have referred to a protocol or something they're working on. And then as facilitators, we can then go out, and we might already be thinking about, “Oh, I want to be watching these two partnerships today”—having in mind, “OK, this is my target idea for them, my target goal for them.” So, there are definite ways that we can frame and decide who we want to watch and observe, but while in the balance of letting kids do what they're going to do and what the expectation of being surprised. Because kids always surprise us with their brilliance. Mike: Yeah, there's multiple things that came to mind as I was listening to you all talk about this. The first one is how it's possible to inadvertently condition kids to see the teacher coming and look and stop and potentially look for the teacher to say something. We actually do want to avoid that. We want to see their thinking.  The other piece is the difference between, as you said, potentially dropping a question and interjecting, as you said, Myuriel, biting your tongue and letting them persist through—whether it's an idea they're grappling with or a struggle for what to do next—that there's so much information in those moments that we can learn or that might help us think about what's next. It's a challenge, I think, because math culture in the United States is such that we're kind of trained to see something that looks like a mistake. “Let's get in there.” And I hear you giving people permission to say, “Actually, it's OK to step back and watch their thinking and watch them try to make sense of things because there's a big payoff there.” Sue: Absolutely. Yeah.  Myuriel: Yes. And, Mike, I think we as teachers—you feel the need of having to address every single “mistake” per either individual student or per partnership. And sometimes you feel like, “I have 30 students, how can I possibly do that?” And I think that's where the power of doing a share out from what you've observed, bringing everyone together, learning from what was in the room, right? Because just like Sue was saying, it's not that you don't ever set up kids with knowledge of what you've observed, but you bring the power. It's what you're bringing, what's in the room, what you've noticed. But you share it out, or you have students share it out, with everyone so that everyone is moving forward. Mike: I have a follow-up question for you all about goals for partnerships. I'm wondering how you think about the potential for partnerships as a way to help develop language, be it academic or social, for students. Are there particular practices that you imagine educators could take up if language development was one of their goals? Myuriel: I'm so glad you're asking that question because I don't think we can learn math without language. I don't think we can learn anything without language. And I think that working in partnerships provides such an authentic, meaningful way of developing language because students are in conversations with each other. And we know that conversation is one way that ideas develop conversations or even sharing your thinking. Sometimes we notice that as students are sharing their thinking, and they're listening to themselves, they catch themselves making a mistake, and they are able to revise their thinking based on what they are saying. So again, I think it is the perfect opportunity for students to mathematically learn counting sequence or socially learn how to negotiate and make sense of what they're going to represent, when they're counting, or to explain their thinking. And we know, of course, that one of the mathematical practices is justifying, explaining your thinking. So, it's important to provide those opportunities for students to do that in this kind of structural way. I also think that working in partnerships provides this opportunity for teachers to listen and notice if there's any language that students are starting to use that can be shared with others. So again, this idea that you hear it from someone in the room and that's going to help everybody else grow. Or that if students are doing something and you can name it, provide those terms to students. So, for example, just like I mentioned, somebody's explaining their thinking and through that they change their mind. They revised their thinking. Actually sharing that with the whole class and naming it: “Oh, they were revising their thinking” or sharing how they were explaining something with academic language so that others can also use that language as they're explaining their own thinking. So, I think that those are powerful ways to provide opportunities for everyone's academic language or social skills through language to be developed. Sue: Yeah, I think that another big idea that comes out of that language piece is just how kids are learning to make sense of how to be partners, especially our younger students, our younger mathematicians. They're really needing to figure out like, “Oh, what does it mean to take turns to speak about this and how I use my words in this way versus another?” And I think that's another big opportunity for kids to build those skills because we can't just assume that kids come into our classrooms knowing how to talk in these ways, how to address each other, how to engage respectfully, that they can disagree respectfully, even in partnerships. And we want them to have the time and space to be able to develop those skills through language as well. Mike: You know, I think the mental movie that I have for the point in time after children have engaged in any kind of partnership task, be it counting collections or something else, has really shifted. Because I think beforehand the way the movie ended was potentially sharing a student's representation if they had represented something on a piece of paper that showed what they had physically done with their things. And I still think that's valid and important, particularly if that's one of your goals.  But you're making me think a lot more about the potential of images of students at work as they're going through the process or video and how closing, or potentially opening the next time, with that really just kind of expands this idea of what's happening. Being able to look at a set of hands that are on a set of materials or in the process of moving materials or listening to language that's emerging from students in the form of a short video. There's a lot of richness that you could capture, and it's also a little bit more of a diverse way of showing what's going on. And it feels like another way to really position what you're doing—not just the output in the form of the paper representation—but what you're actually doing is valuable, and it's a contribution. And I think that just feels like there's a lot of potential in what you all are describing. Sue: I think you hit the nail on the head. We're trying, and it's hard work. But to be open to these ideas, to these possibilities. And like you said, it's positioning kids so drastically different than how we've been doing it for so many years. And how you're actually inviting kids to be contributors of this work that they are now. They have the knowledge. They are the ones that hold the knowledge in the room. And how we frame kids and what they're doing is I think very critical because kids learn from that, and kids have so many things to offer that we need to really be able to think about how we want to create those opportunities for kids. Myuriel: And, Mike, something that you said also made me think of just like we want to provide those opportunities for students to be creative and to show what they know. What you were talking about, having this new perspective, makes me think about also teachers being creative with how they use counting collections, right? There isn't just the one way. It doesn't mean that at the end of every counting collection, I have to have a share out right at the end and decide at that moment. I could start the day that way. I could start the next session that way. I could use a video. I could use a picture. I could have students share it. So, you can get creative. And I think that's the beauty also, because I think as a teacher, it's not only the students that are learning; you are learning along with them. Mike: That's a great place to stop. This has been an absolutely fabulous conversation. Thank you both so much for joining us. Myuriel: Thank you. Thank you so much for this opportunity. Sue: Thank you. 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. © 2025 The Math Learning Center | www.mathlearningcenter.org  

Happy New Year! Jake and Andrew ring in the New Year by talking a little college football before digging into all the latest Browns news, including Mike Vrabel's status, some roster moves from the team, some performances to highlight from their game against Miami, and some early thoughts on how to evaluate potential offensive changes coming in 2025 for the team. Thank you all for your support in 2024 and we look forward to a great 2025! Join and Support us by subscribing at BrownsFilmBreakdown.com! Learn more about your ad choices. Visit podcastchoices.com/adchoices

I discuss my latest Substack, the rounding up of illegals and the dummies who indent on obstructing justice; a local teachers who is allegedly grooming students and the district that is covering it up; and I cover the lates in jab news and how the final results are in, that frankly we've known of from the start. Substack: https://theamericanclassroom.substack.com/p/molecular-communication Book Websites:  https://www.moneytreepublishing.com PROMO CODE: “AEFM” for 10% OFF https://armreg.co.uk  PROMO CODE: "americaneducationfm" for 15% off all books and products.  (I receive no kickbacks).

Listen to the top News from Australia in Hindi.

Doug Fifer is a 25-year veteran of the Anchorage P.D.  He's seen his share of homicides, suicides, financial scams, and sexual deviants.  In this episode, we learn about the unique challenges of working in law enforcement within a large, sparsely populated, rugged environment such as Alaska.  Few jurisdictions have to deal with 1600-pound grizzlies, towns inaccessible by road, near-perpetual darkness in winter, snowfall measured in feet, and a pandemic of alcoholism.  Doug Fifer will take us along with him to discuss hostage negotiations, homicide investigations, death notifications and more.  He has recently authored "Fifty Shades of True Crime."

It's not much of a show this week, but it's a show nonetheless! Join us as we have an existential crisis about why the news all feels so pointless at the moment, take solace in some nostalgia for kinda good not-songs, and plenty of our usual other antisocial nonsense. Listen, if you must! Has something we said, or failed to say, made you FEEL something? You can tell us all about it by joining the conversation on our Substack or you can send us an email here. Enjoy!Show RundownOpen — Remembering to remember things, especially Thom Brenneman6:36 — Why we're struggling to talk about the news today26:52 — The Billboard Hot 100 Game49:45 — Wrap-up! Reagan, and other chatterRelevant Linkage can be found by visiting https://brainiron.substack.com/, where, if you would like to support this and the other podcasting and blogging endeavors of the Brain Iron dot com media empire, you can also become a paying subscriber.

Thanks for listening to the Long Ball Futebol Podcast!Become a Long Ball Futebol Sócio for just £1 a month → https://www.patreon.com/LongBallFutebolThis week we round up every game from Jornada 3 of the 24/25 Primeira Liga season, including another massive win for Sporting, impressive performances from Porto and Braga, a first win for Arouca, Casa Pia's struggles, and much more!You can get in contact with the show on Twitter & Instagram @LongBallFutebol

The 101st edition of Tennessee 4-H Roundup has been taking place this week on the campus of University of Tennessee at Martin where more than 300 of the state's top 4-H'ers, staff and volunteers have gathered to celebrate the year's accomplishments.

Rounding Up Season 2 | Episode 18 – Counting Collections Guest: Danielle Robinson and Melissa Hedges Mike Wallus: Earlier this season, we released an episode focused on the complex and interconnected set of concepts that students engage with as they learn to count. In this follow-up episode, we're going to examine a powerful routine called “counting collections.” We'll be talking with Danielle Robinson and Dr. Melissa Hedges from the Milwaukee Public Schools about counting collections and the impact that this routine can have on student thinking.  Mike: Well, welcome to the podcast, Danielle and Melissa. I can't tell you how excited I am to talk with y'all about the practice of counting collections.  Danielle Robinson and Melissa Hedges: Thanks for having us. Yes, we're so excited to be here. Mike: I want to start this conversation by acknowledging that the two of you are actually part of a larger team of educators who really took this work on counting collections. You introduced it in the Milwaukee Public Schools. And, Melissa, I think I'll start with you. Can you take a moment to recognize the collaborators who have been a part of this work? Melissa: Absolutely. In addition to Danielle and myself, we are fortunate to work with three other colleagues: Lakesha King, Krista Beal, and Claire Madden. All three are early childhood coaches that actively support this work as well. Mike: So, Danielle, I wonder for some folks if we can help them see this practice more clearly. Can you spend time unpacking, what does counting collections look like in a classroom? If I walked in, what are some of the things that I might see? Danielle: Yeah, I think what's really amazing about counting collections is there might be some different ways that you might see counting collections happening in the classroom. When you walk into a classroom, you might see some students all over. Maybe they're sitting at tables, maybe they're on the carpet. And what they're doing is they're actually counting a baggie of objects. And really their job is to answer this question, this very simple but complicated question of, “How many?” And they get to decide how they want to count. Not only do they get to pick what they want to count, but they also get to pick their strategy of how they actually want to count that collection. They can use different tools. They might be using bowls or plates. They might be using 10-frames. They might be using number paths. You might see kiddos who are counting by ones. Danielle: You might see kids who are making different groupings. At times, you might also see kiddos [who] are in stations, and you might see a small group where a teacher is doing counting collections with a few kiddos. You might see them working with partners. And I think the beautiful piece of this and the unique part of counting collections within Milwaukee Public Schools is that we've been able to actually pair the counting trajectory from Doug Clements and Julie Sarama with counting collections where teachers are able to do an interview with their students, really see where they're at in their counting so that the kids are counting a just right collection for them—something that's not too easy, something that's not too hard, but something that is available for them to really push them in their understanding of counting. So, you're going to see kids counting different sizes. And we always tell the teachers it's a really beautiful moment when you're looking across the classroom and as a teacher, you can actually step back and know that every one of your kids are getting what they need in that moment. Because I think oftentimes, we really don't ever get to feel like that, where we feel like, “Wow, all my kids are getting what they need right now, and I know that I am providing the scaffolds that they need.” Mike: So, I want to ask you a few follow-ups, if I might, Danielle. Danielle: Yeah, of course.  Mike: There's a bit of language that you used initially where I'm paraphrasing. And tell me where I get this wrong. You use the language “simple yet complicated,” I think. Am I hearing that right? Danielle: I did. I did, yeah. Mike: Tell me about that. Danielle: I think it's so interesting because a lot of times when we introduce this idea of counting collections with our teachers, they're like, “Wait a minute, so I'm supposed to give this baggie of a bunch of things to my students, and they just get to go decide how they want to count it?” And we're like, “Yeah, that is absolutely what we're asking you to do.” And they feel nervous because this idea of the kids, they're answering how many, but then there's all these beautiful pieces a part of it. Maybe kids are counting by ones, maybe they're deciding that they want to make groups, maybe they're working with a partner, maybe they're using tools. It's kind of opened up this really big, amazing idea of the simple question of how many. But there's just so many things that can happen with it. Mike: There's two words that kept just flashing in front of my eyes as I was listening to you talk. And the words were access and differentiation. And I think you didn't explicitly say those things, but they really jump out for me in the structure of the task and the way that a teacher could take it up. Can you talk about the way that you think this both creates access and also the places where you see there's possibility for differentiation? Danielle: For sure. I'm thinking about a couple classrooms that I was in this week and thinking about once we've done the counting trajectory interview with our kiddos, you might have little ones who are still really working with counting to 10. So, they have collections that they can choose that are just at that amount of about 10. We might have some kiddos who are really working kind of in that range of 20 to 40. And so, we have collections that children can choose from there. And we have collections all the way up to about 180 in some cases. So, we kind of have this really nice, natural scaffold within there where children are told, “Hey, you can go get this just right color for you.” We have red collections, blue collections, green and yellow. Within that also, the children get to decide how they want to count. Danielle: So, if they are still really working on that verbal count sequence, then we allow them to choose to count by ones. We have tools for them, like number paths to help do that. Maybe we've got our kiddos who are starting to really think about this idea of unitizing and making groups of 10s. So, then what they might do is they might take a 10-frame and they might fill their 10-frame and then actually pour that 10-frame into a bowl, so they know that that bowl now is a collection of 10. And so, it's this really nice idea of helping them really start to unitize and to make different groupings. And I think the other beautiful piece, too, is that you can also partner. Students can work together and actually talk about counting together. And we found that that really supports them, too, of just that collaboration piece, too. Mike: So, you kind of started poking around the question that I was going to ask Melissa.   Danielle and Melissa: ( laugh ) Mike: You said the word “unitizing,” which is the other thing that was really jumping out because I taught kindergarten and first grade for about eight years. And in my head, immediately all of the different trajectories that kids are on when it comes to counting, unitizing, combining … those things start to pop out. But, Melissa, I think what you would say is there is a lot of mathematics that we can build for kids beyond say K–2, and I'm wondering if you could talk a little bit about that. Melissa: Absolutely. So before I jump to our older kids, I'm just going to step back for a moment with our kindergarten, first- and second-graders. And even our younger ones. So, the mathematics that we know that they need to be able to count collections, that idea of cardinality, one-to-one correspondence, organization—Danielle did a beautiful job explaining how the kids are going to grab a bag, figure out how to count, it's up to them—as well as this idea of producing a set, thinking about how many, being able to name how many. The reason why I wanted to go back and touch on those is that we know that as children get older and they move into third, fourth, and fifth grade, those are understandings that they must carry with them. And sometimes those ideas aren't addressed well in our instructional materials. So, the idea of asking a first- and second-grader to learn how to construct a unit of 10 and know that 10 ones is one 10 is key, because when we look at where place value tends to fall apart in our upper grades. My experience has been it's fifth grade, where all of a sudden we're dealing with big numbers, we're moving into decimals, we're thinking about different size units, we've got fractions. There's all kinds of things happening.  Melissa: So, the idea of counting collections in the early elementary grades helps build kids' number sense, provides them with that confidence of magnitude of number. And then as they move into those either larger collections or different ways to count, we can make beautiful connections to larger place values. So, hundreds, thousands, ten thousands. Sometimes those collections will get big. All those early number relationships also build. So, those early number relationships, part-whole reasoning that numbers are composed and decomposed of parts. And then we've just seen lots really, really fun work about additive and multiplicative thinking. So, in a third-, fourth-, fifth-grade classroom, what I used to do is dump a cup full of lima beans in the middle of the table and say, “How many are there?” And there's a bunch there. So, they can count by ones. It's going to take a long time. And then once they start to figure out, “Oh wait, I can group these.” “Well, how many groups of five do you have?” And how we can extend to that from that additive thinking of five plus five plus five plus five to then thinking about and extending it to multiplicative thinking. So, I think the extensions are numerous.  Mike: There's a lot there that you said, and I think I wanted to ask a couple follow-ups. First thing that comes to mind is, we've been interviewing a guest for a different podcast … and this idea that unitizing is kind of a central theme that runs really all the way through elementary mathematics and certainly beyond that. But I really am struck by the way that this idea of unitizing and not only being able to unitize, but I think you can physically touch the units, and you can physically re-unitize when you pour those things into the cup. And it's giving kids a bit more space with the physical materials themselves before you step into something that might be more abstract. I'm wondering if that's something that you see as valuable for kids and maybe how you see that play out? Melissa: Yes, it's a great question. I will always say when we take a look at our standard base 10 blocks, “The person that really understands the construction of those base 10 blocks is likely the person [who] invented them.” They know that one little cube means one, and that all of a sudden these 10 cubes are fused together and we hold it up and we say, “Everybody, this is 10 ones. Repeat, one 10. What we find is that until kids have multiple experiences and opportunities over time to construct units beyond one, they really won't do it with deep understanding. And again, that's where we see it fall apart when they're in the fourth and fifth grade. And they're struggling just to kind of understand quantity and magnitude. So, the idea and the intentionality behind counting collections and the idea of unitizing is to give kids those opportunities that to be quite honest—and no disrespect to the hardworking curriculum writers out there—it is a tricky, tricky, tricky idea to develop in children through paper and pencil and workbook pages. Melissa: I think we have found over time that it's the importance of going, grabbing, counting, figuring it out. So, if my collection is bears, does that collection of 10 bears look the same as 10 little sharks look the same as 10 spiders? So, what is this idea of 10? And that they do it over and over and over and over again. And once they crack the code—that's the way I look at it—once our first- and second-graders crack the code of counting collections, they're like, “Oh, this is not hard at all.” And then they start to play with larger units. So, then they'll go, “Oh, wait, I can combine two groups of 10. I just found out that's 20. Can I make more 20s?” So, then we're thinking about counting not just by ones, not just by 10s, but by larger units. And I think that we've seen that pay off in so many tremendous ways. And certainly on the affective side, when kids understand what's happening, there's just this sense of joy and excitement and interest in the work that they do, and I actually think they see themselves learning. Mike: Danielle, do you want to jump in here?  Danielle: I think to echo that, I just recently was speaking with some teachers. And the principal was finally able to come and actually see counting collections happening. And what was so amazing is these were K–5 kiddos, 5-year-olds who were teaching the principal about what they were doing. This was that example where we want people to come in, and the idea is what are you learning? How do you know you've learned it, thinking about that work of Hattie? And these 5-year-olds were telling him exactly what they were learning and how they were learning it and talking about their strategies. And I just felt so proud of the K–5 teacher who shared that with me because her principal was blown away and was seeing just the beauty that comes from this routine. Mike: We did an episode earlier this year on place value, and the speaker did a really nice job of unpacking the ideas around it. I think what strikes me, and at this point I might be sounding a bit like a broken record, is the extent to which this practice makes place value feel real. These abstract ideas around unitizing. And I think, Melissa, I'm going back to something you said earlier where you're like, “The ability to do this in an abstract space where you potentially are relying on paper and pencil or even drawing, that's challenging.” Whereas this puts it in kids' hands, and you physically re-unitize something, which is such a massive deal. This idea that one 10 and 10 ones have the same value even though we're looking at them differently, simultaneously. That's such a big deal for kids, and it just really stands out for me as I hear you all talk. Melissa: I had the pleasure of working with a group of first-grade teachers the other day, and we were looking at student work for a simple task that the kids were asked to do. I think it was 24 plus seven, and so it was just a very quick PLC. Look at this work. Let's think about what they're doing. And many of the children had drawn what the teachers referred to as sticks and circles or sticks and dots. And I said, “Well, what do those sticks and dots mean?” Right? “Well, of course the stick is the 10 and the dot is the one.” And I said, “There's lots of this happening,” I said, “Let's pause for a minute and think, ‘To what degree do you think your children understand that that line means 10 and that dot means one? And that there's some kind of a connection, meaningful connection for them just in that drawing.'” It got kind of quiet, and they're like, “Well, yep, you're right. You're right. They probably don't understand what that is.” And then one of the teachers very beautifully said, “This is where I see counting collections helping.” It was fantastic. Mike: Danielle, I want to shift and ask you a little bit about representation. Just talk a bit about the role of representing the collection once the counting process and that work has happened. What do you all ask kids to do in terms of representation and can you talk a little bit about the value of that? Danielle: Right, absolutely. I think one thing that as we continue to go through in thinking about this routine and the importance of really helping our students make sense and count meaningfully, I think we will always go back to our math teaching framework that's been laid out for us through “Taking Action,” “Principles to Action,” “Catalyzing Change.” And really thinking about the power of using multiple representations. And how, just like you said, we want our students to be able to be physically unitizing, so we have that aspect of working with our actual collections. And then how do we help our students understand that “You have counted your collection. Now what I want you to do is, I want you to actually visually represent this. I want you to draw how you counted.” And so, what we talk about with the kids is, “Hey, how you have counted. If you have counted by ones, I should be able to see that on your paper. I should be able to look at your paper, not see your collection and know exactly how you counted. If you counted by tens, I should be able to see, ‘Oh my gosh, look, that's their bowl. I see their bowls, I see their plates, I see their tens inside of there.'”  Danielle: And to really help them make those connections moving back and forth between those representations. And I think that's also that piece, too, for them that then they can really hang their hat on. “This is how I counted. I can draw a picture of this. I can talk about my strategy. I can share with my friends in my classroom.” And then that's how we like to close with our counting collections routine is really going through and picking a piece of student work and really highlighting a student's particular strategy. Or even just highlighting several and being like, “Look at all this work they did today. Look at all of this mathematical thinking.” So, I think it's a really important and powerful piece, especially with our first- and second-graders, too. We really bring in this idea of equations, too. So, this idea of, “If I've counted 73, and I've got my seven groups of 10, I should have 10 plus 10 plus 10, right? All the way to 70. And then adding my three.” So, I think it's just a continuous idea of having our kids really developing that strong understanding of meaningful counting, diving into place value. Mike: I'm really struck by the way that you described the protocol where you said you're asking kids to really clearly make sure that what they're doing aligns with their drawing. The other piece about that is it feels like one, that sets kids up to be able to share their thinking in a way where they've got a scaffold that they've created for themself. The other thing that it really makes me think about is how if I'm a teacher and I'm looking at student work, I can really use that to position that student's idea as valuable. Or position that student's thinking as something that's important for other people to notice or attend to. So, you could use this to really raise a student's ideas status or raise the student status as well. Does that actually play out in a reality? Danielle: It does actually. So, a couple of times what I will do is I will go into a classroom. And oftentimes it can be kind of a parent for which students may just not have the strongest mathematical identity or may not feel that they have a lot of math agency in the space. And so, one thing that I will really intentionally do and work with the teacher to do is, “You know what? We are going to share that little one's work today. We're going to share that work because this is an opportunity to really position that child as a mathematician and to position that child as someone who has something to offer. And the fact that they were able to do this really hard work.” So, that is something that is very near and dear to us to really help our teachers think of these different ways to ensure that this is a routine that is for all of our children, for each and every child that is in that space. So, that is absolutely something that we find power in and seek to help our teachers find as well. Mike: Well, I would love for each of you to just weigh in on this next question. What has really come to mind is how different this experience of mathematics is from what a lot of adults and unfortunately what a lot of kids might experience in elementary school. I'm wondering if both of you would talk a bit about what does this look like in classrooms? How does this impact the lived experience of kids and their math identities? Can you just talk a little bit about that? Melissa: I can start. This is Melissa. So, we have four beliefs on our little math team that we anchor our work around every single day. And we believe that mathematics should be humanizing, healing, liberating and joyful. And so, we talk a lot about when you walk into a classroom, how do you know that mathematics instruction is humanizing, which means our children are placed at the center of this work? It's liberating. They see themselves in it. They're able to do it. It's healing. Healing for the teacher as well as for the student. And healing in that the student sees themselves as capable and able to do this, and then joyful that it's just fun and interesting and engaging. I think, over time, what we've seen is it helps us see those four beliefs come to life in every single classroom that's doing it. When that activity is underway and children are engaged and interested, there's a beautiful hum that settles over the room. And sometimes you have to remind the teacher step back, take a look at what is happening. Melissa: Those guys are all engaged. They're all interested. They're all doing work that matters to them because it's their work, it's their creation. It's not a workbook page, it's not a fill in the blank. It's not a do what I do. It's, you know what? “We have faith in you. We believe that you can do this,” and they show us time and time again that they can.  Danielle: I'll continue to echo that. Where for Milwaukee Public Schools and in the work that we are seeking to do is really creating these really transformative math spaces for, in particular, our Black and brown children. And really just making sure that they are seeing themselves as mathematicians, that they see themselves within this work, and that they are able to share their thinking and have their brilliance on display. And also, to work through the mathematical processes, too, right? This routine allows you to make mistakes and try a new strategy.  Danielle: I had this one little guy a couple months ago, he was working in a pretty large collection, and I walked by him and he was making groups of two, and I was like, “Oh, what are you working on?” And he's like, “I'm making groups of two.” And I thought to myself, I was like, “Oh boy, that's going to take him a long time” cause they had a really big collection. And I kind of came back around and he had changed it and was making groups of 10. So, it really creates a space where they start to calibrate and they are able to engage in that agency for themselves. I think the last piece I'd like to add is to really come to it from the teacher side as well … is that what Melissa spoke about was those four beliefs. And I think what we've also found is that county collections has been really healing for our teachers, too. We've had teachers who have actually told us that this helped me stay in teaching. I found a passion for mathematics again that I thought I'd lost. And I think that's another piece that really keeps us going is seeing not only is this transformative for our kids, cause they deserve the best, but it's also been really transformative for our teachers as well to see that they can teach math in a different way.  Mike: Absolutely, and I think you really got to this next transition point that I had in mind when I was thinking about this podcast, which is, listening to the two of you, it's clear that this is an experience that can be transformative mathematically and in terms of what a child or even a teacher's lived experience with mathematics is. Can you talk a little bit about what might be some very first steps that educators might take to get started with this? Danielle: Absolutely. I think one thing, as Melissa and I were kind of thinking about this, is someone who is like, “Oh my gosh, I really want to try this.” I think the first piece is to really take stock of your kiddos. If you're interested in diving into the research of Clements and Sarama and working with the county trajectory, we would love for you to Google that and go to learningtrajectories.org. But I think the other piece is to even just do a short little interview with your kids. Ask each of your little ones, “Count as high as you can for me and jot down what you're noticing.” Give them a collection of 10 of something. It could be counters, it could be pennies. See how they count that group of 10. Are they able to have that one-to-one? Do they have that verbal count sequence? Do they have that cardinality? Can they tell you that there is 10 if you ask them again, “How many?”? Danielle: If they can do that, then go ahead and give them 31. Give them 31 of something. Have them count and kind of just see the range of kiddos that you have and really see where is that little challenge I might want to give them. I think another really nice piece is once you dive into this work, you are never going to look at the dollar section different. You are always just start gathering things like pattern blocks. I started with noodles. That is how I started counting collections in my classroom. I used a bunch of erasers that I left over from my prize box. I use noodles, I use beads, bobby pins, rocks, twigs. I mean, start kind of just collecting. It doesn't have to be something that you spend your money on. This can be something that you already use, things that you have. I think that's one way that you can kind of get started. Then also, procedures, procedures, procedures, like go slow to go fast. Once you've got your collections, really teach your kids how to respect those collections. Anchor charts are huge. We always say, when I start this with 4-year-olds, our first lesson is, “This is how we open the bag today. This is how we take our collections out.” So, we always recommend go slow to go fast, really help the kids understand how to take care of the collections, and then they'll fly from there.  Mike: So, Melissa, I think this is part two of that question, which is, when you think about the kinds of things that helped you start this work and sustain this work in the Milwaukee Public Schools, do you have any recommendations that you think might help other folks? Melissa: Yeah. My first entry point into learning about counting collections other than through an incredibly valued colleague [who] learned about it at a conference, was to venture into the TED. I think it's TED, the teacher resource site, and that was where I found some initial resources around how do we do this? We were actually getting ready to teach a course that at the time Danielle was going to be a student in, and we knew that we wanted to do this thing called counting collection. So, it's like, “Well, let's get our act together on this.” So, we spent a lot of time looking at that. There's some lovely resources in there. And since the explosion of the importance of early mathematics has happened in American mathematical culture, which I think is fantastic, wonderful sites have come up. One of our favorites that we were talking about is Dreme. D-R-E-M-E, the Dreme website. Fantastic resources. Melissa: The other one Danielle mentioned earlier, it's just learningtrajectories.org. That's the Clements and Sarama research, which, 15 years ago, we were charged as math educators to figure out how to get that into the hands of teachers, and so that's one of the ways that they've done that. A couple of books that come to mind is the [“Young Children's Mathematics: Cognitively Guided Instruction in Early Childhood Education”]. Fantastic. If you don't have it and you're a preschool teacher and you're interested in math, get it. And then of course, the “Choral Counting & Counting Collections” book by Franke, Kazemi, Turrou. Yeah, so I think those are some of the big ones. If you want just kind of snippets of where to go, go to the Dreme, D-R-E-M-E, and you'll get some lovely, lovely hits. There's some very nice videos. Yeah, just watch a kid count ( laughs ). Mike: I think that's a great place to stop. I can't thank you two enough for joining us. It has really been a pleasure talking with both of you. Danielle: Thank you so much.  Melissa: Thanks for your interest in our work. We really appreciate it. Mike: With the close of this episode, we are at the end of season two for Rounding Up, and I want to just thank everyone who's been listening for your support, for the ways that you're taking these ideas up in your own classrooms and schools. We'll be taking the summer off to connect with new speakers, and we'll be back with season three this fall. In the meantime, if you have topics or ideas that you'd like for us to talk about, let us know. You can reach out to us at mikew@mathlearningcenter.org. What are some things you'd like us to talk about in the coming year? Have a great summer. We'll see you all in the fall.  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 2 | Episode 16 – Strengthening Tasks Through Student Talk Guests: Dr. Amber Candela and Dr. Melissa Boston Mike Wallus: One of the goals I had in mind when we first began recording Rounding Up was to bring to life the best practices that we aspire to in math education and to offer entry points so that educators would feel comfortable trying them out in their classrooms. Today, we're talking with Drs. Amber Candela and Melissa Boston about powerful but practical strategies for supporting student talk in the elementary math classroom.  Welcome to the podcast, Amber and Melissa. We're really excited to be talking with you today. Amber Candela: Thank you for having us.  Melissa Boston: Yes, thank you. Mike: So we've done previous episodes on the importance of offering kids rich tasks, but one of the things that you two would likely argue is that rich tasks are necessary, but they're not necessarily sufficient, and that talk is actually what makes the learning experience really blossom. Is that a fair representation of where you all are at? Melissa: Yes. I think that sums it up very well. In our work, which we've built on great ideas from Smith and Stein, about tasks, and the importance of cognitively challenging tasks and work on the importance of talk in the classroom. Historically, it was often referred to as “talk moves.” We've taken up the term “discourse actions” to think about how do the actions a teacher takes around asking questions and positioning students in the classroom—and particularly these talk moves or discourse actions that we've named “linking” and “press”—how those support student learning while students are engaging with a challenging task. Mike: So I wonder if we could take each of the practices separately and talk through them and then talk a little bit about how they work in tandem. And Melissa, I'm wondering if you could start unpacking this whole practice of linking. How would you describe linking and the purpose it plays for someone who, the term is new for them? Melissa: I think as mathematics teachers, when we hear linking, we immediately think about the mathematics and linking representations or linking strategies. But we're using it very specifically here as a discourse action to refer to how a teacher links student talk in the classroom and the explicit moves a teacher makes to link students' ideas.  Sometimes a linking move is signaled by the teacher using a student's name, so referring to a strategy or an idea that a student might've offered. Sometimes linking might happen if a teacher revoices a student's idea and puts it back out there for the class to consider. The idea is in the way that we're using linking, that it's links within the learning community, so links between people in the classroom and the ideas offered by those people, of course. But the important thing here that we're looking for is how the links between people are established in the verbal, the explicit talk moves or discourse actions that the teacher's making. Mike: What might that sound like? Melissa: So that might sound like, “Oh, I noticed that Amber used a table. Amber, tell us how you used a table.” And then after Amber would explain her table, I might say, “Mike, can you tell me what this line of Amber's table means?” or “How is her table different from the table you created?” Mike: You're making me think about those two aspects, Melissa, this idea that there's mathematical value for the class, but there's also this connectivity that happens when you're doing linking. And I wonder how you think about the value that that has in a classroom.  Melissa: We definitely have talked about that in our work as well. I'm thinking about how a teacher can elevate a student's status in mathematics by using their name or using their idea, just marking or identifying something that the student said is mathematically important that's worthy of the class considering further. Creating these opportunities for student-to-student talk by asking students to compare their strategies or if they have something to add on to what another student said. Sometimes just asking them to repeat what another student said so that there's a different accountability for listening to your peers. If you can count on the teacher to revoice everything, you could tune out what your peers are saying, but if you might be asked to restate what one of your classmates had just said, now there's a bit more of an investment in really listening and understanding and making sense. Mike: Yeah, I really appreciate this idea that there's a way in which that conversation can elevate a student's ideas, but also to raise a student's status by naming their idea and positioning it as important. Melissa: I have a good example from a high school classroom where a student [...] was able to solve the contextual problem about systems of equations, so two equations, and it was important for the story when the two equations or the two lines intersected. And so one student was able to do that very symbolically. They created a graph, they solved the system of equations where another student said, “Oh, I see what you did. You found the difference in the cost per minute, and you also found the difference in the starting point, and then one had to catch up to the other.”  And so the way that the teacher kind of positioned those two strategies, one had used a sensemaking approach based really in the context. The other had used their knowledge of algebra. And by positioning them together, it was actually the student who had used the algebra had higher academic status, but the student who had reasoned through it had made this breakthrough that was really the aha moment for the class. Mike: That is super cool.  Amber, can we shift to press and ask you to talk a little bit about what press looks like? Amber: Absolutely. So how Melissa was talking about linking is holding students accountable to the community; press is more around holding students accountable to the mathematics.  And so the questions the teacher is going to ask is going to be more related specifically to the mathematics. So, “Can you explain your reasoning?” “How did you get that answer?” “What does this x mean?” “What does that intersection point mean?” And so the questions are more targeted at keeping the math conversation in the public space longer. Mike: I thought it was really helpful to just hear the example that Melissa shared. I'm wondering if there's an example that comes to mind that might shed some light on this. Amber: So when I'm in elementary classrooms and teachers are asking their kids about different problems, and kids will be like, “I got 2.” OK, “How did you get 2?” “What operation did you use?” “Why did you use addition when you could have used something else?”  So it's really pressing at the, “Yes, you got the answer, but how did you get the answer?” “How does it make sense to you?”, so that you're making the kids rather than the teacher justify the mathematics that's involved. And they're the ones validating their answers and saying, “Yes, this is why I did this because…” Mike: I think there was a point when I was listening to the two of you speak about this where, and forgive me if I paraphrase this a little bit, but you had an example where a teacher was interacting with a student and the student said something to the effect of, “I get it” or “I understand.” And the teacher came back and she said, “And what do you understand?” And it was really interesting because it threw the justification back to the student. Amber: Right. Really what the linking and press does, it keeps the math actionable longer to all of the peers in the room. So it's having this discussion out loud publicly. So if you didn't get the problem fully all the way, you can hear your peers through the press moves, talk about the mathematics, and then you can use the linking moves to think through, “Well, maybe if Mike didn't understand, if he revoices Melissa's comment, he has the opportunity to practice this mathematics speaking it.” And then you might be able to take that and be like, “Oh, wait, I think I know how to finish solving the problem now.” Mike: I think the part that I want to pull back and linger on a little bit is [that] part of the purpose of press is to keep the conversation about the mathematics in the space longer for kids to be able to have access to those ideas. I want y'all to unpack that just a little bit. Amber: Having linking and press at the end is holding the conversation longer in the classroom. And so the teacher is using the press moves to get at the mathematics so the kids can access it more. And then by linking, you're bringing in the community to that space and inviting them to add: “What do you agree [with]?” “Do you disagree?” “Can you revoice what someone said?” “Do you have any questions about what's happening?” Melissa: So when we talk about discourse actions, the initial discourse action would be the questions that the teacher asks. So there's a good task to start with. Students have worked on this task and produced some solution strategies. Now we're ready to discuss them. The teacher asks some questions so that students start to present or share their work and then it's after students' response [that] linking and press come in as these follow-up moves to do what Amber said: to have the mathematics stay in the public space longer, to pull more kids into the public space longer.  So we're hoping that by spending more time on the mathematics, and having more kids access the mathematics, that we're bringing more kids along for the ride with whatever mathematics it is that we're learning. Mike: You're putting language to something that I don't know that I had before, which is this idea that the longer we can keep the conversation about the ideas publicly bouncing around—there are some kids who may need to hear an idea or a strategy or a concept articulated in multiple different ways to piece together their understanding. Amber: And like Melissa was saying earlier, the thing that's great about linking is oftentimes in a classroom space, teachers ask a question, kids answer, the teacher moves on. The engagement does drop. But by keeping the conversation going longer, the linking piece of it, you might get called on to revoice, so you need to be actively paying attention to your peers because it's on the kids now. The math authority has been shared, so the kids are the ones also making sense of what's happening. But it's on me to listen to my peers because if I disagree, there's an expectation that I'll say that. Or if I agree or I might want to add on to what someone else is saying.  So oftentimes I feel like this pattern of teacher-student-teacher-student-teacher-student happens, and then what can start to happen is teacher-student-student-student-teacher. And so it kind of creates this space where it's not just back and forth, it kind of popcorns more around with the kids. Mike: You are starting to touch on something that I did want to talk about, though, because I think when I came into this conversation, what was in my head is, like, how this supports kids in terms of their mathematical thinking. And I think where you two have started to go is: What happens to kids who are in a classroom where link and press are a common practice? And what happens to classrooms where you see this being enacted on a consistent basis? What does it mean for kids? What changes about their mathematical learning experience? Melissa: You know, we observe a lot of classrooms, and it's really interesting when you see even primary grade students give an answer and immediately say, you know, “I think it's 5 because …,” and they provide their justification just as naturally as they provide their answer or they're listening to their peers and they're very eager to say, “I agree with you; I disagree with you, and here's why” or “I did something similar” or “Here's how my diagram is slightly different.”  So to hear children and students taking that up is really great. And it just—a big shift in the amount of time that you hear the teacher talking versus the amount of time you hear children talking and what you're able to take away as the teacher or the educator formatively about what they know and understand based on what you're hearing them say. And so [in] classrooms where this has become the norm, you see fewer instances where the teacher has to use linking and press because students are picking this up naturally. Mike: As we were sitting here and I was listening to y'all talk, Amber, the thing that I wanted to come back to is [that] I started reflecting on my own practice and how often, even if I was orchestrating or trying to sequence, it was teacher-student-teacher-student-teacher-student. It bounced back to me, and I'm really kind of intrigued by this idea, teacher-student-student-student-teacher—that the discourse, it's moving from a back and forth between one teacher, one student, rinse and repeat, and more students actually taking up the discourse. Am I getting that right? Amber: Yes. And I think really the thought is we always want to talk about the mathematics, but we also have to have something for the community. And that's why the linking is there because we also need to hold kids accountable to the community that they're in as much as we need to hold them accountable to the mathematics. Mike: So, Amber, I want to think about what does it look like to take this practice up? If you were going to give an educator a little nudge or maybe even just a starting point where teachers could take up linking and press, what might that look like? If you imagined kind of that first nudge or that first starting point that starts to build this practice? Amber: We have some checklists with sentence stems in [them], and I think it's taking those sentence stems and thinking about when I ask questions like, “How did you get that?” and “How do you know this about that answer?”, that's when you're asking about the mathematics. And then when you start to ask, “Do you agree with what so-and-so said? Can you revoice what they said in your own words?”, that's holding kids accountable to the community and just really thinking about the purpose of asking this question. Do I want to know about the math or do I want to build the conversation between the students? And then once you realize what you want that to be, you have the stem for the question that you want to ask. Mike: Same question, Melissa. Melissa: I think if you have the teacher who is using good tasks and asking those good initial questions that encourage thinking, reasoning, explanations, even starting by having them try out, once a student gives you a response, asking, “How do you know?” or “How did you get that?” and listening to what the student has to say. And then as the next follow-up, thinking about that linking move coming after that. So even a very formulaic approach where a student gives a response, you use a press move, hear what the student has to say, and then maybe put it back out to the class with a linking move. You know, “Would someone like to repeat what Amber just said?” or “Can someone restate that in their own words?” or whatever the linking move might be. Mike: So if these two practices are new to someone who's listening, are there any particular resources or recommendations that you'd share with someone who wants to keep learning? Amber: We absolutely have resources. We wrote an article for the NCTM's MTLT [Mathematics Teacher: Learning and Teaching PK-12] called “Discourse Actions to Promote Student Access .” And there are some vignettes in there that you can read through and then there [are] checklists with sentence stems for each of the linking and press moves. Melissa: Also, along with that article, we've used a lot of the resources from NCTM's Principles to Actions [Professional Learning] Toolkit.   that's online, and some of the resources are free and accessible to everyone. Amber: And if you wanted to dig in a bit more, we do have a book called Making Sense of Mathematics to Inform Instructional Quality. And that goes in-depth with all of our rubrics and has other scenarios and videos around the linking and press moves along with other parts of the rubrics that we were talking about earlier. Mike: That's awesome. We will link all of that in our show notes.  Thank you both so much for joining us. It was a real pleasure talking with you. Amber: Thanks for having us.  Melissa: Thank 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 References and Resources: NCTM: https://pubs.nctm.org/view/journals/mtlt/113/4/article-p266.xml#:~:text=Discourse%20actions%20provide%20access%20to,up%20on%20contributions%20from%20students ERIC: https://eric.ed.gov/?id=EJ1275372 https://www.nctm.org/PtAToolkit/ https://www.nctm.org/uploadedFiles/Conferences_and_Professional_Development/Annual_Meetings/LosAngeles2022/Campaigns/12-21_PtA_Toolkit.pdf?utm_source=nctm&utm_medium=web&utm_campaign=LA2022&utm_content=PtA+Toolkit

Bryony and Michael round up the eleventh season of Cleaning Up this week. They explore the themes running through the episodes, from theories of change to innovation, and discuss the things that surprised them, the moments they liked (or didn't) and reasons for optimism for the transition.  Links: Ep149: Material World - Ed Conway: https://www.cleaningup.live/material-world-ep149-ed-conway/ Ep150: Selling Sustainability - Solitaire Townsend: https://www.cleaningup.live/selling-sustainability-ep150-solitaire-townsend/Ep151: Redesigning Mining - Mark Cutifani: https://www.cleaningup.live/redesigning-mining-ep151-mark-cutifani/ Ep152: Can We Have a Habitable Planet? - David Wallace-Wells: https://www.cleaningup.live/can-we-have-an-habitable-planet-ep152-david-wallace-wells/ Ep153: Shedding Light on Energy's Dirty Secrets - Lauri Myllyvirta: https://www.cleaningup.live/shedding-light-on-energys-dirty-secrets-ep153-lauri-myllyvirta/ Ep154: Green Heat (And Cooling) Under Our Feet - Tamsin Lishman: https://www.cleaningup.live/green-heat-and-cooling-under-our-feet-ep154-tamsin-lishman/ Ep155: Extreme Electrochemistry - Prof. Donald Sadoway: https://www.cleaningup.live/extreme-electrochemistry-for-a-sustainable-future-ep155-prof-donald-sadoway/ Ep156: A Magnificent Woman And Her Flying Machines - Bonny Simi: https://www.cleaningup.live/a-magnificent-woman-and-her-flying-machines-ep156-bonny-simi/ A11: The Five Horsemen of the Transition: https://www.cleaningup.live/audioblog-11-net-zero-will-be-harder-than-you-think-and-easier-part-i-harder-1/ A12: The Five Superheroes of the Transition: https://www.cleaningup.live/audioblog-12-net-zero-will-be-harder-than-you-think-and-easier-part-ii-easier/Ep157: The Methane Hunters - Sebastien Biraud & Sharon Wilson: https://www.cleaningup.live/the-methane-hunters-ep157-dr-sebastien-biraud-sharon-wilson/Ep 158: Absolutely Electrifying - Saul Griffith: https://www.cleaningup.live/absolutely-electrifying-ep158-saul-griffith/

Ricky Williams joins for a conversation about how football made his uncomfortable and Elon Musk's astrological chart. Then, the polls! Learn more about your ad choices. Visit megaphone.fm/adchoices