Podcasts about Mathematics

1144. This week, we look at the origin of the letter X as the variable for the unknown in algebra. Then, we look at the phrase "how come," explaining why it's more informal than "why" and how its grammar subtly differs from other question words.That X segment was written by Peter Schumer, Professor of Mathematics and Natural Philosophy at Middlebury College, and it originally appeared on The Conversation and appears here through a Creative Commons license.Links to Get One Month Free of the Grammar Girl Patreon (different links for different levels)Order of the Snail ($1/month level): https://www.patreon.com/grammargirl/redeem/687E4Order of the Aardvark ($5/month level): https://www.patreon.com/grammargirl/redeem/07205Keeper of the Commas ($10/month level): https://www.patreon.com/grammargirl/redeem/50A0BGuardian of the Grammary ($25/month level): https://www.patreon.com/grammargirl/redeem/949F7

The Artifact Research Foundation conducts archaeological, metrological, and historical research to explore the technological capabilities of prehistoric human cultures.​Human evolution is long and mysterious.  Today, we know very little about our ancient ancestors, save for stories passed down through time.  Physical remains of archaic human civilization may seem elusive, yet modern forensic methods can uncover more than we ever thought possible.​We approach forensic archaeology from a multi-disciplinary perspective.  The world's biggest story is also the world's biggest mystery.  To unlock it requires a different approach.  Our researchers come from diverse fields such as Mathematics, Physics, Engineering, Manufacturing, Geology, Computer Science, History, Art, and Literature.Adam YoungFounder and ResearcherAdam is an independent researcher with a background in mathematical statistics. Over the past decade, he has researched ancient artifacts throughout the world, most notably in Egypt. He was the first researcher to apply modern Metrology to analyze predynastic stone vessels in a controlled setting. With the help of other dedicated professionals, he founded the Artifact Research Foundation to study advanced machining in ancient Egypt and elsewhere. Members of the foundation have diverse backgrounds, but are united in a common purpose:  to analyze, document, and publish results to help further our understanding of ancient cultures.https://www.artifactfoundation.org/Become a supporter of this podcast: https://www.spreaker.com/podcast/earth-ancients--2790919/support.

Indigenous math isn't just about numbers and equations, it involves culture, spirituality and more. Math professor Edward Doolittle, a Mohawk from Six Nations in Ontario, sees math as something embedded in Creation itself. In his Hagey Lecture at the University of Waterloo, he describes Indigenous mathematics as being grounded in cognition, emotion, the physical world and community. Indigenizing math, Doolittle hopes, will make it more approachable and meaningful to Indigenous students — show them how entwined it is with everyday life and something much bigger than ourselves.

GB2RS News Sunday, the 21st of December 2025 The news headlines: A British Science Week opportunity not to be missed Could you be the new RSGB Honorary Skills and Career Development Officer? Challenge yourself with the RSGB Construction Competition The RSGB is giving away 400 FM radio receiver kits and Morse code tutor kits as part of its British Science Week 2026 activities. The kits are available for school, university, Scout, Girlguiding, and Cadet groups, as well as other youth-related Science, Technology, Engineering, and Mathematics groups. The project is being delivered thanks to a partnership between the RSGB Outreach Team, the Radio Communications Foundation and the RSGB Legacy Fund. To get involved, simply complete a form available at rsgb.org/bsw. If you need support, the RSGB can put you in touch with local radio amateurs who can assist. In exchange for the free kits, you'll need to send a brief report and photos that the Society can share afterwards to celebrate the activity and inspire other groups to try amateur radio. Don't miss out on this opportunity to share amateur radio with the next generation. The RSGB is looking for a volunteer Honorary Skills and Career Development Officer. One of the main responsibilities will be to build a team to engage with early-career engineers, as well as those making a career transition, in order to encourage them to use amateur radio to develop their skills and knowledge. As part of this engagement, the Society would like the new team to design and deliver learning material and courses at a level both just beyond and significantly beyond the Full Licence. Go to rsgb.org/volunteers  for the full role description. Keep yourself busy over the Christmas holidays by getting involved with the RSGB Construction Competition. There are seven categories to enter, including ‘Beginners' and ‘Software', which is for designs that recognise the importance of software technology to all aspects of amateur radio. A £150 cash prize will be awarded to the winner of each category, with a £50 cash prize for the runner-up. Find out more about the other categories and details of how to enter at rsgb.org/construction-competition The RSGB is releasing more presentations from its recent Convention. The lectures range in topics from Polar modulation to engaging young people with amateur radio. Four further presentations will be released over the festive season. To make sure you are the first to receive notifications when they're available, click the subscribe button on the Society's YouTube channel at youtube.com/thersgb  Young operators continue to host the special callsign GB25YOTA for Youngsters on the Air Month. Cambridge University Wireless Society is active today, Sunday the 21st of December and then tomorrow, Monday the 22nd of December, Jack, M7OFM, will be operating under the supervision of Pete, M0OFM. Jack will also be on the air on Christmas Day between 10 am and 12 pm, so ensure you listen out and make a seasonal QSO with him. View the operating times, bands and modes at rsgb.org/yota-month The RSGB would like to thank Dr Harry Squance, GI4JTF, who has retired after volunteering for 25 years as a QSL Bureau sub-manager. Most recently, Harry was the GI/MI/2I QSL sub-manager, and those callsigns will now be covered by Lindsay Pennell, GI3KME. All stamped addressed envelopes and any outstanding QSL cards will be transferred to Lindsay, but RSGB members in Northern Ireland who collect cards should, in future, send stamped addressed envelopes directly to Lindsay. The list of QSL Sub-managers at rsgb.org/qsl  has been updated to reflect the changes. On the 1st of December 1924, the 200kW Alexanderson alternator, with the callsign SAQ, was put into commercial operation with telegram traffic from Sweden to the United States. 101 years later, it is the only remaining electro-mechanical transmitter from this era and is still in running condition. At 0800UTC on Christmas Eve, the transmitter is scheduled to broadcast its traditional Christmas message using CW on 17.2kHz. Find out more by visiting tinyurl.com/SAQ25 Please send details of all your news and events to radcom@rsgb.org.uk. The deadline for submissions for the GB2RS News on Sunday, the 28th of December, is 10 am on Tuesday, the 23rd of December. Please note there will be no GB2RS broadcast on Sunday, the 4th of January 2026, but many newsreaders will be holding informal nets in their usual broadcasting slots. And now for details of rallies and events Sparkford Radio Rally is due to take place on Sunday, the 28th of December at Davis Hall, Howell Hill, West Camel, near Yeovil, BA22 7QX. The doors will be open from 9.30 am, and admission will cost £2. Refreshments and free parking will be available on site. For more details, contact Luke on 07870 168 197 or email luke@mymixradio.co.uk On the 25th of January 2026, Lincoln Short Wave Club Winter Radio Rally will be held at Festival Hall, Caistor Road, Market Rasen, LN8 3HT. This is an indoor event with ample free parking. The doors will be open from 10 am, and admission is £3. Tables cost £10. To book tables, or for more information, contact Steve, M5ZZZ on 0777 7699 069 or email m5zzz@outlook.com Now the Special Event news The Rugby Amateur Transmitting Society will be using special callsign GB100GBR from the 1st to the 4th of January to celebrate the centenary of the first CW transmissions from the GBR transmitter at Rugby Radio Station. Operators will begin transmitting from the historic site at 1200UTC on the 1st of January, the same time as the original station 100 years earlier in 1926. Listen for activity on the HF bands using CW, FT8 and SSB. More information about the station is available at QRZ.com Simeon, M0VOB in Bradford, West Yorkshire, is running special event callsign GB54NTA until Monday, the 5th of January. The station is active on the HF, 2m and 70cm bands. Recently, the station was worked on the 40m band using FT8. All QSOs will be logged and confirmed via QRZ.com Now the DX news Roland, F8EN, is active as TR8CR from Gabon until the 25th of December. He operates CW only. QSL via F6AJA. For more information, visit QRZ.com George, VU2DGR, is using the AT44I callsign from Bharati Research Station until the 31st of December. He is a member of the 44th Indian Scientific Expedition to Antarctica. The station is often worked using FT8 on the 20m band. QSL via George's home call. Now the contest news On Friday, the 26th of December, the DARC Christmas Contest runs from 0830 to 1100 UTC. Using CW and SSB on the 80 and 40m bands, the exchange is signal report and serial number. The Worked All Britain Christmas Party starts on Friday, the 26th of December and ends on Tuesday, the 6th of January 2026. Using all modes on all bands, the exchange is your Worked All Britain book number. On Saturday, the 27th of December, the RSGB 50MHz Christmas Contest runs from 1500 to 1700 UTC. Using all modes on the 6m band, the exchange is signal report, serial number and locator. The Stew Perry Topband Challenge starts at 1500UTC on Saturday, the 27th of December and ends at 1500 UTC on Sunday, the 28th of December. Using CW on the 160m band, the exchange is your four-character locator. On Sunday, the 28th of December, the RSGB 70MHz Christmas Contest runs from 1500 to 1700 UTC. Using all modes on the 4m band, the exchange is signal report, serial number and locator. Now the radio propagation report, compiled by G0KYA, G3YLA and G4BAO on Thursday the 18th of December 2025 Last week, we suffered from the double whammy of a reduced solar flux index and an increased Kp index. The solar flux index went down to 119 by Thursday, the 18th, with the sunspots looking pretty spartan when compared with just a week or so ago. Unfortunately, a coronal hole contributed to a fast solar wind with a south-pointing interplanetary magnetic field or Bz. The net result was a Kp index of 5 and a minor G1 geomagnetic storm. Nevertheless, the maximum usable frequencies, or MUFs, over a 3,000km path mostly remained above 28MHz, at least during daylight hours, and there was DX to be worked. As it's Christmas, let's focus on special calls for the season. YR0XMAS in Romania has been worked on the 20m band using CW and will be active until the end of the month. A little further afield is the 12 Days of Christmas event in the US. It runs until Christmas Day with 12 three-letter callsigns in the W2 and K2 series. You only have to work one to get a certificate, so it should be possible for most amateurs. If you are lucky enough to work all 12, plus a bonus station in Puerto Rico, you can get a special ‘Clean Sweep Plus' endorsement. W2S has already been spotted in the UK, and more details are available by Googling ‘12 days of Christmas ham radio'. Next week, we have another large coronal hole to contend with, which NOAA predicts may push the Kp index to 5 between the 22nd and 26th of December. The good news is that the solar flux index may increase over the same period, perhaps up to 180 by the 28th of December. Make the most of the low bands as we hit the winter solstice, with its long periods of darkness. And certainly check 14 to 28MHz during daylight hours. And now the VHF and up propagation news from G3YLA and G4BAO The tail end of the previous week ended on a dramatically mild, wet and windy note, with heavy rain and gales in places. It might be good for the earth, but little else springs to mind other than some chance rain scatter for the GHz folk. The main feature of this Christmas propagation report is that we have a major change becoming established after this weekend. This change takes the form of swapping out the mild Atlantic pattern for a blocked, cold easterly flow with high pressure parked to the north of the British Isles near the Faroe Islands. If this takes place as suggested by some of the models, then a much colder easterly wind will remain with us for much of the Christmas week. The strength of the high means that the flow is only likely to produce shallow cloud, barely enough for an isolated wintry flurry on the east coast of England.  Lighter winds over northern Britain, closer to the high, will possibly allow some tropo, but it is not convincing in view of the shallow dry layer below the inversion. It will mean some sharp frosts are possible where skies clear. Long dark winter nights are potentially good for seeing meteors, and it is worth mentioning two showers this time. The first is the Ursids, which peak around the 22nd and 23rd of December. The second shower to be aware of is the Quadrantids, which peaks on the 3rd and 4th of January. This is a much larger shower than the Ursids, so maybe the one to focus on for radio activity. Aurora remains on the list, especially in view of the large coronal hole recently. As ever, keep an eye on the Kp index for high values, but it is even better to note conditions on the LF bands for signs of ‘watery' sounding signals. The Sporadic-E folklore often speaks of isolated mid-winter events, and, in view of the two meteor showers adding fuel and there being some useful jet streams, it is certainly worth mentioning. Using the jet stream over the Pyrenees for paths to Spain early this week is a good place to start. For EME operators, Moon declination is rising again, and path losses are decreasing. We are past apogee for the month, the point where the Moon is farthest from the Earth. 144MHz sky noise is also reducing again after reaching a peak yesterday, the 20th of December. And that's all from the propagation team this week.

Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning ROUNDING UP: SEASON 4 | EPISODE 8 Algebraic reasoning is defined as the ability to use symbols, variables, and mathematical operations to represent and solve problems. This type of reasoning is crucial for a range of disciplines.  In this episode, we're talking with Janet Walkoe and Margaret Walton about the seeds of algebraic reasoning found in our students' lived experiences and the ways we can draw on them to support student learning.  BIOGRAPHIES Margaret Walton joined Towson University's Department of Mathematics in 2024. She teaches mathematics methods courses to undergraduate preservice teachers and courses about teacher professional development to education graduate students. Her research interests include teacher educator learning and professional development, teacher learning and professional development, and facilitator and teacher noticing. Janet Walkoe is an associate professor in the College of Education at the University of Maryland. Janet's research interests include teacher noticing and teacher responsiveness in the mathematics classroom. She is interested in how teachers attend to and make sense of student thinking and other student resources, including but not limited to student dispositions and students' ways of communicating mathematics. RESOURCES "Seeds of Algebraic Thinking: a Knowledge in Pieces Perspective on the Development of Algebraic Thinking" "Seeds of Algebraic Thinking: Towards a Research Agenda" NOTICE Lab  "Leveraging Early Algebraic Experiences"  TRANSCRIPT Mike Wallus: Hello, Janet and Margaret, thank you so much for joining us. I'm really excited to talk with you both about the seeds of algebraic thinking. Janet Walkoe: Thanks for having us. We're excited to be here.  Margaret Walton: Yeah, thanks so much. Mike: So for listeners, without prayer knowledge, I'm wondering how you would describe the seeds of algebraic thinking. Janet: OK. For a little context, more than a decade ago, my good friend and colleague, [Mariana] Levin—she's at Western Michigan University—she and I used to talk about all of the algebraic thinking we saw our children doing when they were toddlers—this is maybe 10 or more years ago—in their play, and just watching them act in the world. And we started keeping a list of these things we saw. And it grew and grew, and finally we decided to write about this in our 2020 FLM article ["Seeds of Algebraic Thinking: Towards a Research Agenda" in For the Learning of Mathematics] that introduced the seeds of algebraic thinking idea. Since they were still toddlers, they weren't actually expressing full algebraic conceptions, but they were displaying bits of algebraic thinking that we called "seeds." And so this idea, these small conceptual resources, grows out of the knowledge and pieces perspective on learning that came out of Berkeley in the nineties, led by Andy diSessa. And generally that's the perspective that knowledge is made up of small cognitive bits rather than larger concepts. So if we're thinking of addition, rather than thinking of it as leveled, maybe at the first level there's knowing how to count and add two groups of numbers. And then maybe at another level we add two negative numbers, and then at another level we could add positives and negatives. So that might be a stage-based way of thinking about it.  And instead, if we think about this in terms of little bits of resources that students bring, the idea of combining bunches of things—the idea of like entities or nonlike entities, opposites, positives and negatives, the idea of opposites canceling—all those kinds of things and other such resources to think about addition. It's that perspective that we're going with. And it's not like we master one level and move on to the next. It's more that these pieces are here, available to us. We come to a situation with these resources and call upon them and connect them as it comes up in the context. Mike: I think that feels really intuitive, particularly for anyone who's taught young children. That really brings me back to the days when I was teaching kindergartners and first graders.  I want to ask you about something else. You all mentioned several things like this notion of "do, undo" or "closing in" or the idea of "in-betweenness" while we were preparing for this interview. And I'm wondering if you could describe what these things mean in some detail for our audience, and then maybe connect them back with this notion of the seeds of algebraic thinking. Margaret: Yeah, sure. So we would say that these are different seeds of algebraic thinking that kids might activate as they learn math and then also learn more formal algebra. So the first seed, the doing and undoing that you mentioned, is really completing some sort of action or process and then reversing it.  So an example might be when a toddler stacks blocks or cups. I have lots of nieces and nephews or friends' kids who I've seen do this often—all the time, really—when they'll maybe make towers of blocks, stack them up one by one and then sort of unstack them, right? So later this experience might apply to learning about functions, for example, as students plug in values as inputs, that's kind of the doing part, but also solve functions at certain outputs to find the input. So that's kind of one example there.  And then you also talked about closing in and in-betweenness, which might both be related to intervals. So closing in is a seed where it's sort of related to getting closer and closer to a desired value. And then in formal algebra, and maybe math leading up to formal algebra, the seed might be activated when students work with inequalities maybe, or maybe ordering fractions.  And then the last seed that you mentioned there, in-betweenness, is the idea of being between two things. For example, kids might have experiences with the story of Goldilocks and the Three Bears, and the porridge being too hot, too cold, or just right. So that "just right" is in-between. So these seats might relate to inequalities and the idea that solutions of math problems might be a range of values and not just one. Mike: So part of what's so exciting about this conversation is that the seeds of algebraic thinking really can emerge from children's lived experience, meaning kids are coming with informal prior knowledge that we can access. And I'm wondering if you can describe some examples of children's play, or even everyday tasks, that cultivate these seeds of algebraic thinking. Janet: That's great. So when I think back to the early days when we were thinking about these ideas, one example stands out in my head. I was going to the grocery store with my daughter who was about three at the time, and she just did not like the grocery store at all. And when we were in the car, I told her, "Oh, don't worry, we're just going in for a short bit of time, just a second." And she sat in the back and said, "Oh, like the capital letter A." I remember being blown away thinking about all that came together for her to think about that image, just the relationship between time and distance, the amount of time highlighting the instantaneous nature of the time we'd actually be in the store, all kinds of things.  And I think in terms of play examples, there were so many. When she was little, she was gifted a play doctor kit. So it was a plastic kit that had a stethoscope and a blood pressure monitor, all these old-school tools. And she would play doctor with her stuffed animals. And she knew that any one of her stuffed animals could be the patient, but it probably wouldn't be a cup. So she had this idea that these could be candidates for patients, and it was this—but only certain things. We refer to this concept as "replacement," and it's this idea that you can replace whatever this blank box is with any number of things, but maybe those things are limited and maybe that idea comes into play when thinking about variables in formal algebra. Margaret: A couple of other examples just from the seeds that you asked about in the previous question. One might be if you're talking about closing in, games like when kids play things like "you're getting warmer" or "you're getting colder" when they're trying to find a hidden object or you're closing in when tuning an instrument, maybe like a guitar or a violin.  And then for in-betweeness, we talked about Goldilocks, but it could be something as simple as, "I'm sitting in between my two parents" or measuring different heights and there's someone who's very tall and someone who's very short, but then there are a bunch of people who also fall in between. So those are some other examples. Mike: You're making me wonder about some of these ideas, these concepts, these habits of mind that these seeds grow into during children's elementary learning experiences. Can we talk about that a bit? Janet: Sure. Thank you for that question.  So we think of seeds as a little more general. So rather than a particular seed growing into something or being destined for something, it's more that a seed becomes activated more in a particular context and connections with other seeds get strengthened. So for example, the idea of like or nonlike terms with the positive and negative numbers. Like or nonlike or opposites can come up in so many different contexts. And that's one seed that gets evoked when thinking potentially when thinking about addition. So rather than a seed being planted and growing into things, it's more like there are these seeds, these resources that children collect as they act on the world and experience things. And in particular contexts, certain seeds are evoked and then connected. And then in other contexts, as the context becomes more familiar, maybe they're evoked more often and connected more strongly. And then that becomes something that's connected with that context. And that's how we see children learning as they become more expert in a particular context or situation. Mike: So in some ways it feels almost more like a neural network of sorts. Like the more that these connections are activated, the stronger the connection becomes. Is that a better analogy than this notion of seeds growing? It's more so that there are connections that are made and deepened, for lack of a better way of saying it? Janet: Mm-hmm. And pruned in certain circumstances. We actually struggled a bit with the name because we thought seeds might evoke this, "Here's a seed, it's this particular seed, it grows into this particular concept." But then we really struggled with other neurons of algebraic thinking. So we tossed around some other potential ideas in it to kind of evoke that image a little better. But yes, that's exactly how I would think about it. Mike: I mean, just to digress a little bit, I think it's an interesting question for you all as you're trying to describe this relationship, because in some respects it does resemble seeds—meaning that the beginnings of this set of ideas are coming out of lived experiences that children have early in their lives. And then those things are connected and deepened—or, as you said, pruned. So it kind of has features of this notion of a seed, but it also has features of a network that is interconnected, which I suspect is probably why it's fairly hard to name that. Janet: Mm-hmm. And it does have—so if you look at, for example, the replacement seed, my daughter playing doctor with her stuffed animals, the replacement seed there. But you can imagine that that seed, it's domain agnostic, so it can come out in grammar. For instance, the ad-libs, a noun goes here, and so it can be any different noun. It's the same idea, different context. And you can see the thread among contexts, even though it's not meaning the same thing or not used in the same way necessarily. Mike: It strikes me that understanding the seeds of algebraic thinking is really a powerful tool for educators. They could, for example, use it as a lens when they're planning instruction or interpreting student reasoning. Can you talk about this, Margaret and Janet? Margaret: Yeah, sure, definitely. So we've seen that teachers who take a seeds lens can be really curious about where student ideas come from. So, for example, when a student talks about a math solution, maybe instead of judging whether the answer is right or wrong, a teacher might actually be more curious about how the student came to that idea. In some of our work, we've seen teachers who have a seeds perspective can look for pieces of a student answer that are productive instead of taking an entire answer as right or wrong. So we think that seeds can really help educators intentionally look for student assets and off of them. And for us, that's students' informal and lived experiences. Janet: And kind of going along with that, one of the things we really emphasize in our methods courses, and is emphasized in teacher education in general, is this idea of excavating for student ideas and looking at what's good about what the student says and reframing what a student says, not as a misconception, but reframing it as what's positive about this idea. And we think that having this mindset will help teachers do that. Just knowing that these are things students bring to the situation, these potentially productive resources they have. Is it productive in this case? Maybe. If it's not, what could make it more productive? So having teachers look for these kinds of things we found as helpful in classrooms. Mike: I'm going to ask a question right now that I think is perhaps a little bit challenging, but I suspect it might be what people who are listening are wondering, which is: Are there any generalizable instructional moves that might support formal or informal algebraic thinking that you'd like to see elementary teachers integrate into their classroom practice? Margaret: Yeah, I mean, I think, honestly, it's: Listen carefully to kids' ideas with an open mind. So as you listen to what kids are saying, really thinking about why they're saying what they're saying, maybe where that thinking comes from and how you can leverage it in productive ways. Mike: So I want to go back to the analogy of seeds. And I also want to think about this knowing what you said earlier about the fact that some of the analogy about seeds coming early in a child's life or emerging from their lived experiences, that's an important part of thinking about it. But there's also this notion that time and experiences allow some connections to be made and to grow or to be pruned.  What I'm thinking about is the gardener. The challenge in education is that the gardener who is working with students in the form of the teacher and they do some cultivation, they might not necessarily be able to kind of see the horizon, see where some of this is going, see what's happening. So if we have a gardener who's cultivating or drawing on some of the seeds of algebraic thinking in their early childhood students and their elementary students, what do you think the impact of trying to draw on the seeds or make those connections can be for children and students in the long run? Janet: I think [there are] a couple of important points there. And first, one is early on in a child's life. Because experiences breed seeds or because seeds come out of experiences, the more experiences children can have, the better. So for example, if you're in early grades, and you can read a book to a child, they can listen to it, but what else can they do? They could maybe play with toys and act it out. If there's an activity in the book, they could pretend or really do the activity. Maybe it's baking something or maybe it's playing a game. And I think this is advocated in literature on play and early childhood experiences, including Montessori experiences. But the more and varied experiences children can have, the more seeds they'll gain in different experiences.  And one thing a teacher can do early on and throughout is look at connections. Look at, "Oh, we did this thing here. Where might it come out here?" If a teacher can identify an important seed, for instance, they can work to strengthen it in different contexts as well. So giving children experiences and then looking for ways to strengthen key ideas through experiences. Mike: One of the challenges of hosting a podcast is that we've got about 20 to 25 minutes to discuss some really big ideas and some powerful practices. And this is one of those times where I really feel that. And I'm wondering, if we have listeners who wanted to continue learning about the ways that they can cultivate the seeds of algebraic thinking, are there particular resources or bodies of research that you would recommend? Janet: So from our particular lab we have a website, and it's notice-lab.com, and that's continuing to be built out. The project is funded by NSF [the National Science Foundation], and we're continuing to add resources. We have links to articles. We have links to ways teachers and parents can use seeds. We have links to professional development for teachers. And those will keep getting built out over time.  Margaret, do you want to talk about the article? Margaret: Sure, yeah. Janet and I actually just had an article recently come out in Mathematics Teacher: Learning and Teaching from NCTM [National Council of Teachers of Mathematics]. And it's [in] Issue 5, and it's called "Leveraging Early Algebraic Experiences." So that's definitely another place to check out.  And Janet, anything else you want to mention? Janet: I think the website has a lot of resources as well. Mike: So I've read the article and I would encourage anyone to take a look at it. We'll add a link to the article and also a link to the website in the show notes for people who are listening who want to check those things out.  I think this is probably a great place to stop. But I want to thank you both so much for joining us. Janet and Margaret, it's really been a pleasure talking with both of you. Janet: Thank you so much, Mike. It's been a pleasure.  Margaret: You too. Thanks so much 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  

Jim Elvidge is an independent researcher and author whose work challenges conventional cosmology by proposing that the universe itself may be a computational system. In The Universe — Solved, Elvidge presents a bold framework suggesting that reality is not fundamentally physical, but information-based, governed by mathematical rules similar to those underlying digital computation. Drawing on concepts from physics, information theory, and philosophy, he explores how space, time, energy, and consciousness may emerge from a deeper informational substrate. Elvidge's ideas invite a radical rethinking of existence—one that blurs the line between science and metaphysics and raises profound questions about the nature of reality and humanity's place within it.Become a supporter of this podcast: https://www.spreaker.com/podcast/the-x-zone-radio-tv-show--1078348/support.Please note that all XZBN radio and/or television shows are Copyright © REL-MAR McConnell Meda Company, Niagara, Ontario, Canada – www.rel-mar.com. For more Episodes of this show and all shows produced, broadcasted and syndicated from REL-MAR McConell Media Company and The 'X' Zone Broadcast Network and the 'X' Zone TV Channell, visit www.xzbn.net. For programming, distribution, and syndication inquiries, email programming@xzbn.net.We are proud to announce the we have launched TWATNews.com, launched in August 2025.TWATNews.com is an independent online news platform dedicated to uncovering the truth about Donald Trump and his ongoing influence in politics, business, and society. Unlike mainstream outlets that often sanitize, soften, or ignore stories that challenge Trump and his allies, TWATNews digs deeper to deliver hard-hitting articles, investigative features, and sharp commentary that mainstream media won't touch.These are stories and articles that you will not read anywhere else.Our mission is simple: to expose corruption, lies, and authoritarian tendencies while giving voice to the perspectives and evidence that are often marginalized or buried by corporate-controlled media

This episode of Room to Grow, Curtis and Joanie reflect back on 2025 and all that they learned during the year. A significant number of 2025 episodes of Room to Grow were focused on the Mathematics Teaching Practices from NCTM's Principles to Actions, celebrating the 10th anniversary of its publication. Curtis and Joanie highlighted how these practices have survived the test of time, and continue to reflect good teaching in mathematics. Additionally, our hosts preview what new topics they are hoping to learn and explore podcast episodes about in 2026.  Additional referenced content includes:·       NTCM's Principles to Actions and Taking Action books·       Pam Harris' website and book·       Julianne Foxworthy Gonzalez, Ph.D. in Mathematics Education. Math guidelines for supporting multi-language learners (MLLs). All of us at Room to Grow wish you a peaceful holiday season! Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.   

In the 1800s, it seemed like mathematics was a solved problem. The paradoxes in the field were resolved, and even areas like advanced calculus could be taught consistently and reliably at any school. It was clearly understandable in a way that abstract fields like philosophy weren’t, and it was on its way to solving humanity’s problems. Mathematical work on electromagnetism made modern electrical engineering and power systems possible. New research in algebra created the logical basis for future computer science and digital circuits. But then new problems appeared. In the early 20th century, mathematicians made discoveries that showed them enough to know how little they really knew. Bertrand Russell showed that at its edges, math fell apart. It couldn’t fully define itself on its own terms without becoming logically inconsistent. He gave the analogy of a small-town barber who shaves everyone who doesn't shave himself; the question is, who shaves the barber—if he shaves himself, he breaks the rule, but if he doesn't shave himself, he must, by the rule, shave himself? In today’s episode, I’m speaking to Jason Bardi, author of The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics and we explore the story of three competing efforts by mathematicians to resolve this crisis. What do you do if math, the most logical of all sciences, becomes illogical at a certain point? Bertrand Russell thought the problem could be solved with even more logic, we just hadn’t tried hard enough. David Hilbert thought redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition—and that math is not based on logic but rather logic is based on math. Set against the backdrop of one of the most turbulent periods of European history (from the late 19th century through World War I, the 1920s, the Great Depression, and the early days of World War II), we look at what happens when rock-solid truths don’t seem so rock solid anymore.See omnystudio.com/listener for privacy information.

SummaryIn this episode, Shannon Valenzuela and Peter Ulrickson explore the significance of the Quadrivium in education and Dr. Ulrickson's unique presentation of teaching these arts in his books A Brief Quadrivium and the accompanying teacher's guide. They discuss the interconnectedness of mathematics and the arts and highlight the unique perspectives offered by each discipline. They explore the importance of modeling, proof, and observation and the role of rhetoric and logic in mathematics. The conversation also addresses the sensory engagement in learning and the value of teaching mathematics classically.Topics Covered:The importance of proof and the power of modelingThe arts of the Quadrivium and their perspectives on cosmic orderThe role of rhetoric and logic in the study of mathematicsEngaging the senses in the experience of learning mathematicsThe transformation of students' perceptions of mathematics through an encounter with the QuadriviumToday's Guest:Peter Ulrickson is a professor of mathematics at the Catholic University of America. In addition to his work on the quadrivium, he publishes original research in various areas of modern mathematics. Professor Ulrickson received his Ph.D. from the University of Notre Dame.For more information about the books: briefquadrivium.comTimestamps:00:00 Introduction03:28 Introduction to A Brief Quadrivium04:07 Exploring Music and Astronomy in the Quadrivium10:01 Proof and Modeling in Mathematics13:09 Developing the Sense for Order20:45 Engaging the Senses in Mathematical Inquiry26:51 The Ordering of the Quadrivial Arts30:48 Exploring the Teacher's GuideResources Mentioned in Today's Episode:Peter Ulrickson, A Brief Quadrivium (publisher, Amazon) and Teaching the Quadrivium (publisher, Amazon)"The Quadrivium and the Stakes for Ordering the Mathematical Arts" by Lesley-Anne Dyer WilliamsUniversity of Dallas Links:Classical Education Master's Program at the University of Dallas: udallas.edu/classical-edSt. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/Support the showIf you enjoyed the show, please leave a rating and review — it helps others find us!

In 1961, a young couple boarded a ship to Vienna with nothing but faith, a suitcase, and an “impossible dream”—to bring the Word of God into the most spiritually restricted places on earth. What began with handwritten Scripture, smuggled Bibles, and hidden church meetings has become a sweeping movement of Gospel transformation across Eastern Europe and beyond.The Impossible Dream takes you deep into the heart of that mission, sharing firsthand accounts of courage, smuggling, sacrifice, and the miraculous power of Scripture. Through riveting stories witness how God's Word made its way past secret police, prison walls, and warzones—straight into the hearts of those who needed it most Dirk Smith Vice President Dirk Smith joined Eastern European Mission following his highly successful tenure as a development officer with his alma mater, Harding University. An accomplished manager, he earned experience in business development with an eye for revenue building through positions with firms like Jackson & Coker in Dallas, Texas, and T. Williams Consulting serving clients in Pennsylvania, New Jersey and New York. He has a bachelor's degree in Mathematics and an MBA with a focus on Organizational Development and Ethics. At EEM, Dirk oversees fundraising and marketing efforts as well as assists with U.S. operations. He is an experienced presenter and storyteller and loves sharing the stories of what God is doing through the ministry of EEM.WebsiteInstagramAmazon

Watch the Q&A session here: https://youtu.be/Lv5h-Pp1r6sLooking at the plant world, one discovers beautiful and fascinating structures in the shape and arrangement of leaves, stems and roots. Some are simple and symmetric, other features are arranged in elegant Fibonacci spirals, yet others exhibit fractal-like patterns. How are these structures created with such regularity and reproducibility? Such arrangements often follow simple rules that we can fully understand mathematically.This lecture was recorded by Alain Goriely on 11th November 2025 at Barnard's Inn Hall, London.Professor Alain Goriely FRS is Gresham Professor of Geometry.He is also a mathematician known for dynamical systems, mathematical biology, and mechanics. He developed the mathematical theory of biological growth and is Director of the Oxford Centre for Industrial and Applied Mathematics. His work spans plant tendrils, seashells, umbilical cords, brain modelling, and applied mathematics outreach.The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/watch-now/shape-plantsGresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/Website:  https://gresham.ac.ukTwitter:  https://twitter.com/greshamcollegeFacebook: https://facebook.com/greshamcollegeInstagram: https://instagram.com/greshamcollegeSupport the show

Обновление моего старенького трека, впервые увидевшего свет в 2016 году.

Title: “Not An Empty Visit” Part 3 Text: 1 Thessalonians 2:13-16 FCF: We often struggle identifying true faith in contrast to non-saving faith. Prop: Because only true faith saves, we must ensure we have received Jesus Christ in true faith. Scripture Intro: [Slide 1] Turn in your bible to 1 Thessalonians chapter 2. In a moment we'll read from the Legacy Standard Bible starting in verse 1. You can follow along in the pew bible or in whatever version you prefer. Today we will conclude the thought that Paul began with in chapter 2. However, keen observers might have noticed that there is a significant amount of overlap between chapter 1 and what we've discussed in chapter 2 so far. Indeed, if you took it upon yourself to set the two chapters side by side and drew lines or highlighted with different colors themes that are saying the same things with different words – you could illustrate this quite clearly. I won't impose that upon you – but if you are up for the challenge, I'm sure it would be profitable to you. Chapter 2 has largely been put to the Thessalonians in order to prove to them that the mission to their city was one that proved to be fruitless. Paul began by stating that they know it was not in vain because it was God's Gospel at work. He continued by saying that they know it was not in vain because they conducted themselves like a family. Today, Paul will conclude his assurance to them, in that they know it was not in vain because it rendered familiar results both positively and negatively. Please stand with me to give honor to and to focus on the Word of God as it is read. Invocation: Holy Father, You have revealed Yourself to us Your people through the Word, our Lord Jesus Christ. He has come to us, as God With Us. He has come to us to save us from sin, death, hell, the devil, and the kingdom of darkness. You have freed us from the tyranny of our own wisdom and enabled us to believe in You the giver of life. God give us eyes to behold the truth of Your word this morning as we see what makes true faith and what awaits us if we are without it. May we take the words of hope and warning today in faith, and may it have the effect upon us You desire. We pray this in Jesus' name – Amen. Transition: [Slide 2] “Faith that saves has one distinguishing quality; saving faith is a faith that produces obedience, it is a faith that brings about a way of life.” Billy Graham “A man at his wit's end is not at his faith's end.” Matthew Henry “The function of faith is to turn God's promises into facts.” J. Oswald Chambers Let these thoughts wash over you as we embark on the truth of the passage this morning. I.) True faith produces belief in God's Word and suffering for Christ, so we must ensure we have received Jesus Christ in true faith. (13-14) a. [Slide 3] 13 - And for this reason we also thank God without ceasing that when you received the word of God which you heard from us, you accepted it not as the word of men, but for what it really is, the word of God, which also is at work in you who believe. i. It takes two sides to make a visit profitable. ii. Paul has, in the first twelve verses, explained how he and his companions did their part to produce a successful and fruitful mission among them. iii. They took God's gospel and gave it to them without unseemly methods or greedy motives. iv. They adopted them as family and loved them accordingly. They cared for them like parents, both supplying what they needed to grow and thrive and teaching them to live a life worthy of God's Kingdom. v. But all of this would have been for nothing if the message was ineffective to produce any kind of spiritual change in them. vi. In fact, without God's empowering the message of His gospel, the Thessalonians would never have heard it as His Word. vii. So Paul gives thanks once again, without ceasing, to God, that the Thessalonians responded to the message the way they did. viii. Going back to chapter 1 verse 4-5, we see that Paul expresses similar thoughts. ix. He is thanking God because he is confident that the Thessalonian believers were elect of God. x. Why? xi. Primarily because of how the gospel came to them. xii. Not in word only (ie words of men only) but in the power of the Holy Spirit and with full conviction. xiii. Paul's thanksgiving here is expressed in more detail. xiv. What does it mean that the gospel came in power, in the Spirit, and with full conviction? xv. It means they responded in true faith. Well, how do they know they have true faith? There are two examples in this text. xvi. First, that they believed the content of the message as though it were from God and second, that they received the power of the message. 1. The content of the message, if received in true faith, must be from God. a. The evangelists were demonstrating holy, righteous, and blameless lifestyles and exhorting, encouraging and insisting that the Thessalonians do the same. b. All of this is couched in the idea that a Kingdom is coming where Christ reigns over all, and demands purest devotion and worship. c. The same Lord who died to save them from their sins, will one day return to judge the living and the dead. He will restore His people and make them to rule with Him in that Kingdom. d. If someone receives this in true faith – they must conclude it is from God. e. Paul reveals in a later letter that the Word of God is hidden from those who are without God's Spirit. God's Spirit must do a work in an unbeliever in order to enable them to understand and believe what the Word of God teaches. f. So, we say that faith comes by hearing and hearing by the Word of God… which is true. But hearing the Word of God to the point of understanding that it is from God and even what that message means – all comes through the power of the Holy Spirit. g. We call this step in the salvation process – regeneration. And although the bible does not explicitly teach that it precedes faith, the scriptures clearly teach that God must do something to enable a person to believe the gospel of Jesus Christ. And He must do this to bring them out of their spiritually dead state. Since this is what regeneration is, it is safe for us to conclude that it must precede faith. h. Paul alludes to this here – in that the Thessalonians did not perceive this as a message from men – but they took what the evangelists said as the very words of God. A conclusion they could not have arrived at without the power of the Holy Spirit – which Paul said in chapter 1, did happen when the gospel came to them. 2. The second way we know they responded in true faith, is by the powerful result of that message being received. a. To those who truly believe, the Word of God produces an effect. b. We should expect the Word of God, preached, taught, read, heard, studied, mediated on, memorized, and illustrated to have a powerful effect upon those who are truly God's people. c. Warnings about sin and falling away, and pursuing righteousness, and loving God and others – should have a distinct influence over the hearts of those who are God's people. d. It is a predictable outcome that if absent calls into question the very legitimacy of our faith. xvii. So how specifically were the Thessalonians powerfully affected by the Word they received from God? b. [Slide 4] 14 - For you, brothers, became imitators of the churches of God in Christ Jesus that are in Judea, for you also suffered the same things at the hands of your own countrymen, even as they did from the Jews, i. Paul calls out their suffering in the same way that the first members of the church suffered. ii. In fact, he uses the word – imitate again. iii. This also goes back to chapter 1 verse 6. iv. They became imitators of Christ and the evangelists by receiving the word with affliction. v. Paul again denotes that Christians are the same no matter where they are. Whether in Judea or Macedonia. They are also the same no matter WHEN they are. Whether at Pentecost in the formation of the church or now. vi. There are general markers that are common among all those who receive true faith. vii. In this example, Paul points to how on the day of Pentecost, believers on Christ suffered great persecution at the hands of fellow countrymen who rejected the gospel. viii. In a similar way, the Thessalonians are being treated quite poorly by their neighbors, family, friends, and others in the city who rejected the gospel message. ix. Being persecuted by unbelievers who are among those closest to you is one way that the legitimacy of your faith is demonstrated. c. [Slide 5] Summary of the Point: Paul's primary point in this chapter so far has been to verify that the mission they had among the Thessalonians only a few months previous, was not an empty and fruitless mission. Countering the claims of their fellow residents of Thessalonica, Paul knows it wasn't fruitless because they spoke God's gospel with confidence and for His approval. He also knows it wasn't fruitless because they felt a familial connection to the Thessalonians. And finally, they know it wasn't a fruitless mission because it produced predictable results in the city. The first result is regarding those who received the gospel message. Because they received this message in true faith, they were convinced it was a message from God and were changed by this message to the extent that they endured suffering for Christ's name. True faith produces belief in God's Word and a willingness, and even a joy to endure suffering for Christ's sake. This would be very encouraging to the Thessalonians, to know that these seasoned believers were confident in their faith. But our application must cautiously approach this. We must begin rather with a need for us to make sure that we have received true faith in Jesus Christ. Then and only then can we be assured and take comfort in the apostle's words. Transition: [Slide 6 (blank)] But what other predictable result comes when the gospel of Jesus Christ is truly received by a group of people? In what else does Paul draw confidence that the Thessalonian mission was not fruitless? II.) Without true faith it is impossible to please God or be at peace with Him or mankind, so we must ensure we have received Jesus Christ in true faith. (15-16) a. [Slide 7] 15 - who both killed the Lord Jesus and the prophets, i. Paul now embarks upon what seems like a rabbit trail. ii. He seeks to expand upon the behavior of the Jewish people who have so opposed the gospel message and have had a history of opposing God's word in general. iii. Here he says that these same Jews who persecuted their own countrymen for believing on Jesus, are the ones who killed the Lord Jesus and their own prophets. iv. Paul again uses familial or collective language. Obviously, the same people who killed Jesus could not be the ones who killed all the prophets down through their history. And most likely they are not the same ones who drove Paul or the apostles out of Judea. v. Instead, Paul refers to a branch of Israel that has been cut off. vi. Paul is not being antisemitic here. He is merely pointing out a group of people who although having the racial privilege of being God's portion, have continued to reject Him as their King and Lord. vii. They are following in an unfortunate history of the Jewish people who strayed from Yahweh both in worship and in conduct to kill their own prophets and those God has sent to speak the truth to them. viii. The crown jewel in this ungodly behavior is, of course, the murder of their own Messiah and God – Jesus of Nazareth. ix. They continued their work of unbelief with Paul and his companions. b. [Slide 8] and drove us out, i. This could be referring to several instances where the Jews drove Paul or Christ's other servants out of certain places. ii. The “us” here could simply refer to Jewish believers, or may even refer to the evangelists themselves. iii. In any case – he points to the majority opposition of the Jewish people to receive their own Messiah or any who preach in His name. c. [Slide 9] and do not please God, i. Since Jesus is God's Messiah, His Servant, the Son of Man that the Ancient of Days will lift up to occupy the same throne as Yahweh… ii. You cannot oppose Christ or Christ's followers without also opposing God. iii. It is impossible for any to please God without first believing on Jesus Christ. iv. All the effort put in keeping the law, even if it were successful, would fail to please God if the person did not put their faith in Christ alone. v. And so, these Jews, in spite of being God's portion and part of Abraham's line, cannot please God and oppose His Son or His Son's Bride, at the same time. vi. But not only are they opposed to God… d. [Slide 10] and are hostile to all men, i. In opposing Christ, the Savior of the world, it is also impossible to love others. ii. To reject Christ is to render yourself unable to truly love other human beings. iii. Why? iv. Because Christ is the hope of the nations. Christ is the King of Kings. Christ is the Bright and Morning Star. Christ is the Lord of Light. v. As Psalm 2 says, we must kiss the Son lest He be angry. vi. All nations must bow to His rule. All nations have hope only in His rule. vii. All nations who do not hope in Him, will cease to exist. viii. And so, to oppose Christ is to oppose the only hope the nations have. ix. The most hateful thing you can do to humanity is to reject His Messiah and harm His Son's Bride. x. Our culture says the most loving thing you can do is to be tolerant and accepting to all faiths. xi. The truth could not be more opposed to this thought. xii. The exclusivity of Christ as Savior and Lord of all, is the way we establish peace with all men. Peace only comes by the Exclusive rule of Christ alone. xiii. Next, Paul specifically calls out in what way the Jews were hostile to all men… e. [Slide 11] 16 - hindering us from speaking to the Gentiles so that they may be saved; i. To hinder the gospel message from going out to the nations is to hate the nations. ii. To stop the message of Christ crucified for sinners is to hate sinners and desire their eternal judgment. iii. The salvation of every man's soul rests in the work of Christ, alone. iv. And to prevent this message from going to all men – is to hate all men. v. No, telling people they are sinners and they need a Savior is not hateful, or unkind. It is the most loving thing we could do. But do you know what is truly hateful and hostile? Doing what you can to prevent others hearing the exclusive gospel of Jesus Christ. vi. Suggesting there are many paths to God through many religions, is the most hateful and hostile thing you could ever tell someone. vii. Since the Jews have opposed God, and man in this way… what is the result? f. [Slide 12] with the result that they always fill up the measure of their sins. i. Their sins have come to completion. ii. There is a call back here to the ban God put on the Canaanite nations before Israel entered into the promised land. iii. God speaks of the sins of the people who lived in the land as filling up a cup. Or coming to completion. iv. Jesus spoke to the Pharisees in a similar way, telling them that they are filling up the cup of their judgment. v. Like when you cook rice on a stove top… vi. The starches in the rice react to the boiling water and produce bubbles. And those bubbles if not kept in check with rise to the top and overflow. vii. Burnt rice water on a glass stove top is one mess you don't want to have to clean up – Not that I know from experience

Ed Sheeran BioSnap a weekly updated Biography.Ed Sheeran has been lighting up stages across the pond this week, kicking off with a festive headline at Coventry Building Society Arena on December 5, where fan videos captured him belting out Heaven and his cheeky Merry Christmas single to a roaring crowd, according to clips from Ed Sheeran on Tour YouTube channel. He kept the holiday vibes rolling two days later at Manchesters Co-op Live on December 7, performing Sapphire from his fresh eighth album Play, as shared in vlogs by Thomas Rodger and Ed Sheeran on Tour, complete with surprise Christmas encores like Afterglow and Fairy Tale of New York that left fans buzzing. These intimate UK arena dates, part of his Mini Play Tour celebrating the September-dropped Playwith hits like Azizam and Old Phone, signal a pivot from his massive Mathematics era, teasing bigger European legs and underscoring his post-megastar return to rootsy, loop-pedal magic.Stateside, Sheeran owned Madison Square Garden on December 12, closing the 2025 iHeartRadio Z100 Jingle Ball with a jaw-dropping entirely live set, layering guitar loops and harmonies for his biggest smashes, iHeartRadio reports hailed it as show-stopping holiday gold alongside stars like Conan Gray and Nelly. Backstage in the Mercedes-Benz lounge, 1035 Kiss FM caught him spilling tea on nixing a third collaborations album after No.6s ego-clashing logistical nightmare, bluntly saying never again while nodding to his minimal collab on Plays deluxe with Arijit Singh. Gossip mills swirled around a cozy Taylor Swift reunion turned joint therapy session, AOL dishing it quelled tension rumors. Midweek, he popped up for a star-packed duet with Sam Smith and Brandi Carlile at Smiths Brooklyn residency on December 10, Mix 987 photos confirming the onstage magic. Looking ahead, Audacy just announced him headlining their 12th We Can Survive benefit gig. No fresh social media drops spotted, but these gigs cement Sheerans hot streak, blending biography-shaping album promo with unmissable live charisma.Get the best deals https://amzn.to/3ODvOtaThis content was created in partnership and with the help of Artificial Intelligence AI

December 12, 2025 - Zach and Asheef discuss the current landscape of international value investing, focusing on the unique perspectives that come from investing outside the US.Asheef Lalani as an independent director to the board of Sailfish Royalty Corp. Mr. Lalani graduated from the University of Waterloo with a Bachelor of Mathematics and Masters of Accounting, earned the CA/CPA designation in 2002 and is a CFA charterholder since 2003. Asheef first started his career with PricewaterhouseCoopers in 1998 and went on to become a portfolio manager at UBS Securities. Currently, Mr. Lalani is the Chief Investment Officer at Berczy Park Capital – a private family office in Toronto, Canada.

Amy Boros and Shari Insley teach middle school science in different parts of the state, but they share a passion for bringing the real world into their classrooms for their students. Over the summer, the Perrysburg Education Association member and the North Olmsted Education Association member shared grant funding to travel far out into the real world for a once-in-a-lifetime learning experience that will enhance their students' learning for years to come. On this episode, they share how they're using what they saw and did in Iceland to help their students learn and grow in Ohio, and their advice for other educators who want to experience this kind of real-world professional development for themselves.SEE THE HIGHLIGHTS | Click here to see some of Shari's photos from the Fund for Teachers fellowship in Iceland. Click here to see Amy's highlights from the trip. EXPLORE THE OPPORTUNITIES | Amy and Shari mentioned several grants and learning opportunities available to Ohio science educators. See the following links for more information about some of them:Fund For Teachers Grant  Teacher Air Camp  Yellowstone Educator Opportunity Summer 2026 Amy and Shari also shared an OEA Technology Grant to buy cameras and go pros to use on their trip and in their classrooms back home. Please note, OEA is in the process of redeveloping and streamlining the Affiliate Grant Program, and as part of the transition, no applications are being accepted for Technology Grants for the 2025-26 cycle. Make sure you listen to Episode 16 of Public Education Matters to learn more on the OEA grants being offered right now.SHARE YOUR THOUGHTS | If you'd like to share your feedback on the Public Education Matters podcast, including your ideas for what you'd like to hear about - or talk about - on future episodes, please email educationmatters@ohea.org. SUBSCRIBE | Click here to subscribe to Public Education Matters on Apple Podcasts or click here to listen on Spotify so you don't miss a thing. You can also find Public Education Matters on many other platforms. Click here for some of those links so you can listen anywhere. And don't forget you can listen to all of the previous episodes anytime on your favorite podcast platform, or by clicking here.Featured Public Education Matters guests: Amy Boros, Perrysburg Education Association memberAmy Boros teaches 5th and 6th grade Science at Hull Prairie Intermediate School in Perrysburg. She has experience in classroom teaching at the elementary, middle school and collegiate levels; educational classroom technology; grant researching, authoringand evaluation, as well as educational consulting and conference presentations in both mathematics and science. With degrees from Bowling Green State University and the University of Toledo, Amy is currently in her 30th year in education.Amy is an accomplished grant writer who has been awarded thousands of dollars in grants for her classroom, school, district, and outside organizations. In addition, Amy has authored several articles about middle school science education in Science Scope Journal and Science and Children Journal, publications of The National Science Teachers Association.In 2019, Amy was invited to participate in an extensive research project onboard the Lake Guardian, an EPA research vessel on Lake Erie; selected as one of 15 educators to collect data alongside scientists. While on board, she evaluated the presence ofmicroplastics, toxic algae and microbial organisms in surface water and sediment throughout Lake Erie's basins.She continues to work alongside scientists by helping with research, most recently in Costa Rica and Yellowstone National Park.Amy was awarded the 2022 President's Innovation Award in Environmental Education, a joint award from the White House and the EPA for her environmental education work inside and outside of the classroom.Shari Insley, North Olmsted Education Association memberShari Insley is a middle school math and science teacher for North Olmsted City Schools with 20 years of experience in education. Of her 20 years in education, the past 18 years have been dedicated to North Olmsted, and her first 2 years were spent teaching in Gallup, New Mexico.Shari earned a B.S. in Middle Childhood Education in Mathematics and Science and a Master's degree in Curriculum and Teaching from Bowling Green State University in Bowling Green, Ohio. In addition to her teaching expertise, Shari was honored as the recipient of the 2024 Presidential Innovation Award for Environmental Educators. She has also served on the Strategic Planning Committee for the Science Education Council of Ohio the past 2 years.Since 2016, Shari has dedicated her summers to participating in educator courses to expand her knowledge of freshwater ecosystems in the Great Lakes. She has taken part in grant opportunities through Ohio Sea Grant at The Ohio State University's Stone Laboratory, sailed aboard the R/V Lake Guardian with the EPA, and worked with the Gelfand STEM Center at Case Western Reserve University. Most recently, Shari was awarded a Fund for Teachers grant to travel to Iceland in the summer of 2025, where she explored the country's unique geothermal and glacial environments to enrich her environmental science curriculum.Connect with OEA:Email educationmatters@ohea.org with your feedback or ideas for future Public Education Matters topicsLike OEA on FacebookFollow OEA on TwitterFollow OEA on InstagramGet the latest news and statements from OEA hereLearn more about where OEA stands on the issues Keep up to date on the legislation affecting Ohio public schools and educators with OEA's Legislative WatchAbout us:The Ohio Education Association represents nearly 120,000 teachers, faculty members and support professionals who work in Ohio's schools, colleges, and universities to help improve public education and the lives of Ohio's children. OEA members provide professional services to benefit students, schools, and the public in virtually every position needed to run Ohio's schools.Public Education Matters host Katie Olmsted serves as Media Relations Consultant for the Ohio Education Association. S...

Nigeria's education sector is entering a new era.With the Federal Government unveiling a redesigned national curriculum that reduces subject overload and introduces more practical, skill-based learning, the country is set for a shift that could redefine how students learn and how teachers teach.But the big question lingers is Nigeria ready?In today's episode of Nigeria Daily, we break down what has changed, how schools plan to implement it, and what the reforms mean for millions of students across the country.

It's YOUR time to #EdUpIn this episode, part of our Academic Integrity Series, sponsored by ⁠Integrity4EducationYOUR guest is W. Ila Peterson, Professor of Mathematics & Director of Faculty Development, Arizona Western CollegeYOUR cohost is Thomas Fetsch, CEO, Integrity4EducationYOUR host is ⁠Elvin Freytes⁠How is Arizona Western College serving approximately 8,000 students across Yuma & La Paz County with online education while maintaining academic integrity, & why does Ila believe AI breaks down language barriers for their Hispanic serving institution?What creative faculty responses is Ila seeing like podcast style presentations instead of essays, 30 to 45 minute "technology snack" PD sessions on tools like Notebook LM, & why does she believe faculty ingenuity is key to adapting to AI?How does Arizona Western's current policy leave AI decisions to individual faculty with required syllabus statements, what institutional AI governance principles are being drafted for the next year, & why does Ila believe this is the 1st moment we're truly training students for jobs that don't yet exist?Listen in to #EdUpThank YOU so much for tuning in. Join us on the next episode for YOUR time to EdUp!Connect with YOUR EdUp Team - ⁠⁠⁠⁠⁠ ⁠⁠⁠⁠⁠Elvin Freytes⁠⁠⁠⁠⁠⁠⁠⁠⁠ ⁠& ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ Dr. Joe Sallustio⁠⁠⁠⁠⁠● Join YOUR EdUp community at ⁠The EdUp Experience⁠We make education YOUR business!P.S. Want to get early, ad-free access & exclusive leadership content to help support the show? Then ⁠⁠​subscribe today​⁠⁠ to lock in YOUR $5.99/m lifetime supporters rate! This offer ends December 31, 2025!

Learning to teach mathematics better with Ariel Beggs, program coordinator, professional development facilitator, and Presidential Award winning educator. Ariel shares her journey from two decades of middle school mathematics teaching to supporting mathematics educators through the University of Arizona Center for Recruitment and Retention of Mathematics Teachers. Throughout the conversation, she highlights the power of supportive relationships, noting the difference between toxic and tolerable stress is the presence of community and connection, and how this belief shapes her coaching, collaboration, and leadership. Links from the episode Center of Recruitment and Retention of Mathematics Teachers (CRR) (https://crr.math.arizona.edu/) ReEngaging Aspirational Learners (Getting REAL) (https://crr.math.arizona.edu/getting-real) Mathematics Educator Appreciation Day Conference (MEAD) (https://crr.math.arizona.edu/mead-conference) TODOS: Mathematics for ALL (https://www.todos-math.org/) Teaching Math Teaching Episode 99 - Rodrigo Gutiérrez and Melissa Hosten: Being Responsive and Engaged to Elevate the Work of Math Teachers (https://www.teachingmathteachingpodcast.com/99) Teaching Math Teaching Episode 116 - Marian Dingle: You Teach Who You Are (https://www.teachingmathteachingpodcast.com/116) Coaching the 5 Practices (https://www.corwin.com/books/coaching-the-5-practices-287127?srsltid=AfmBOooUWNugdxYQl2YERZudkbpjkxohjun78q96FBdqRAeYL6q9S073) Powerful Mathematicians Who Changed the World from A to Z (https://www.nctm.org/Store/Products/Powerful-Mathematicians-Who-Changed-the-World-from-A-to-Z/) Reimagining the Mathematics Classroom (https://www.nctm.org/Store/Products/Reimagining-the-Mathematics-Classroom/) The Anxious Generation (https://bookshop.org/a/1964/9780593655030) What Video Games Have to Teach Us About Learning and Literacy. (https://bookshop.org/a/1964/9781403984531) Special Guest: Ariel Beggs.

Ready to learn the history, philosophy, and practice of an experienced professional in the test prep industry? MEET OUR GUEST Meet Angie Kelley. Angie is the founder of Land Run Learning, a test prep and tutoring company dedicated to helping high-performing students train smart, test strong, and claim their futures. A licensed Oklahoma educator and graduate of Oklahoma Christian University with a B.S.E. in Mathematics, Angie draws on twenty years of classroom experience and a passion for strategic learning to help students reach their potential on high-stakes exams. Her work bridges the gap between academic mastery and confident performance, empowering students to thrive under pressure. Find Angie at angie@landrunlearning.com. ABOUT THIS PODCAST Tests and the Rest is THE college admissions industry podcast. Explore all of our episodes on the show page. ABOUT YOUR HOSTS Mike Bergin is the president of Chariot Learning and founder of TestBright, Roots2Words, and College Eagle. Amy Seeley is the president of Seeley Test Pros and LEAP. If you're interested in working with Mike and/or Amy for test preparation, training, or consulting, get in touch through our contact page.  

Chris Holman welcomes back Sean Cervantes – Business Development & Growth Officer at LAFCU, Lansing, MI. Welcome Sean, remind everyone about LAFCU? Sean, you've been in your role since the Spring, how are things going? Recent news for LAFCU: being Nationally Recognized as a 2025 Best Place to Work for Women, tell us about that? LAFCU's CFO Leslie Rorie was Honored with a 2025 Real McCoy Award in Mathematics talk about that? Big community event last month for LAFCU, Heritage Day 2025 how did that go? » Visit MBN website: www.michiganbusinessnetwork.com/ » Subscribe to MBN's YouTube: www.youtube.com/@MichiganbusinessnetworkMBN » Like MBN: www.facebook.com/mibiznetwork » Follow MBN: twitter.com/MIBizNetwork/ » MBN Instagram: www.instagram.com/mibiznetwork/

A huge cold blob of air above Antarctica and bushfires spreading along ridgelines don't appear to have anything in common, yet the strange behaviour of these natural phenomena — and many others — can be understood and explained by mathematics. You can binge more episodes of the Lab Notes podcast with science journalist and presenter Belinda Smith on the ABC Listen app (Australia). You'll find episodes on animal behaviour, human health, space exploration and so much more.Get in touch with us: labnotes@abc.net.auFeaturing:Chantelle Blachut, mathematician at UNSW Canberra

In this episode, Dean takes the host's chair to interview Maegan and Kyle, who have both recently co-authored books in the Building Thinking Classrooms series with Peter Liljedahl. They discuss the release of the new Building Thinking Classrooms Tasks in Mathematics, Grades 6-12 book and how it complements Maegan's previously released Building Thinking Classrooms Tasks in Mathematics, Grades K-5. Together, the group explores the process of selecting tasks, the importance of thin-slicing, and why the pedagogical research found in the rest of the book is just as critical as the tasks themselves. They also open up about the vulnerability required to write these resources, including the realization that even experienced teachers often need to relearn math concepts to teach them effectively. Tune in for a behind-the-scenes look at creating these resources and how they can support your journey in the classroom.Links:⁠Building Thinking Classrooms Tasks in Mathematics, Grades K-5⁠Building Thinking Classrooms Tasks in Mathematics, Grades 6-12Saskatchewan Understand Math Conference 2026

In this fascinating episode, Amb. Elisha sits down with renowned composer, pianist, educator, and music theorist Kurt Ellenberger

Episode: 1484 Georg Cantor, the man who counted beyond infinity.  Today, we wonder about counting to infinity.

Jacob Barandes is Senior Preceptor in Physics at Harvard University, where he works widely across the philosophy of physics, with focuses on the foundations of quantum mechanics, the philosophy of spacetime, and the metaphysics of laws. In this episode, Robinson and Jacob focus on the foundations of quantum mechanics. They discuss the importance of history and philosophy in the same, its connections to mathematics, many of the biggest puzzles in quantum physics, and Jacob's new approach to the foundations, which he refers to as the “Indivisibility” approach.Jacob's Website: https://www.jacobbarandes.comOUTLINE00:00 Mathematics, Nature, and Physics07:55 The Deep Link Between Math and Physics CLIP15:21 Scrutinizing the History and Philosophy of Physics28:11 A Digression on Achille Varzi36:53 The Etymology of “Matrix”41:17 Learning from the History of Physics52:38 Why Does Quantum Mechanics Need New Foundations?59:04 Does Quantum Gravity Need New Quantum Foundations?01;08:26 What Is a Constructive Physical Theory?01:32:31 Markov Laws and Determinism01:45:30 The Wave Function02:06:53 Inconsistencies in Quantum Mechanics02:12:20 What Is Quantum Decoherence?02:23:10 The Biggest Problems in Quantum Foundations?02:33:49 Interpretations of Quantum Mechanics02:38:57 Quantum Mechanics, Many Worlds, and the Problem of Induction02:50:05 The Indivisibility Interpretation of Quantum Mechanics03:04:42 What Are the Fundamentalia of the Universe?Robinson's Website: http://robinsonerhardt.comRobinson Erhardt researches symbolic logic and the foundations of mathematics at Stanford University, where he is also a JD candidate in the Law School.

On Thursday, November 20, the Oregon Department of Education released At-A-Glance School and District Profiles for the 2024-25 school year. The Profiles are designed to provide a consistent set of school and district level information to local communities. They contain previously released assessment data for last school year, previously released graduation data for the class of 2024, and some new data for the 2024-25 school year. Because the state uses consistent sources of data and calculation methods for all schools and districts, its reports are useful for comparison purposes - both between schools and districts and within individual entities on a year-over-year basis. However, data on statewide standardized assessment results in English Language Arts and Mathematics tell a bit of a misleading story of our students' knowledge and skills. A number of students opt out of these tests, and because they are not used for placement, grade promotion, or for any other success measure in school, we have seen students and families place far less importance on them in recent years. For this reason, we have identified other measures for determining students' growth and learning on a rolling basis and are using that data to track progress toward our Strategic Plan goals. For example, we are using HSD-administered assessments called Running Records to measure proficiency in English and/or Spanish reading. You can find the District's and each school's At-A-Glance Profile in the Accountability section of our website. Additional information can be found in ODE's press release and on their At-A-Glance Profiles and Accountability Details webpage. Our featured event is the fall Career and College Pathways Steering Committee meeting that was held on Thursday, November 20, at Hilhi. This amazing group of industry partners, educators, and community leaders plays a key role in helping us create clear and exciting pathway opportunities for every HSD student. Superintendent Travis Reiman kicked off the morning by sharing the latest district data and indicators tied to student success and postsecondary readiness. Melissa Pendergrass, Coordinator of Career and College Pathways, framed the day by emphasizing the value of authentic partnerships and high-quality work-based learning. She spoke about how real world experiences not only benefit students but also create a powerful return on investment for local employers who are building their future workforce. Participants then jumped into a lineup of interactive workshops that explored everything from supervising youth at worksites to designing meaningful hands-on experiences, understanding the long term benefits of investing in youth career development, and more. Conversations were lively, solutions oriented, and full of ideas that will directly support students. HSD extends a huge thank you to everyone who joined us. Your partnership helps ensure that students discover their interests, build real skills, and feel excited about their futures. We look forward to continuing this work together throughout the year.Hot News is produced and emailed to HSD families and staff each week school is in session. Please add the address to your “safe sender” list to make sure you always receive the latest issue. Please also bookmark our district website: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠hsd.k12.or.us⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ to stay informed about what's happening in our district and schools.

Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase ROUNDING UP: SEASON 4 | EPISODE 7 When students aren't sure how to approach a problem, many of them default to asking the teacher for help. This tendency is one of the central challenges of teaching: walking the fine line between offering support and inadvertently cultivating dependence.  In this episode, we're talking with a team of educators about a practice called the strategy showcase, designed to foster collaboration and help students engage with their peers' ideas.  BIOGRAPHIES Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut. Mhret Wondmagegne, Anna Strauss, and Jenna Waggoner are all recent graduates of the University of Connecticut School of Education and early career elementary educators who recently completed their first years of teaching. RESOURCE National Council of Teachers of Mathematics  TRANSCRIPT Mike Wallus: Well, we have a full show today and I want to welcome all of our guests. So Anna, Mhret, Jenna, Tutita, welcome to the podcast. I'm really excited to be talking with you all about the strategy showcase. Jenna Waggoner: Thank you.  Tutita Casa: It's our pleasure.  Anna Strauss: Thanks.  Mhret Wondmagegne: Thank you. Mike: So for listeners who've not read your article, Anna, could you briefly describe a strategy showcase? So what is it and what could it look like in an elementary classroom? Anna: So the main idea of the strategy showcase is to have students' work displayed either on a bulletin board—I know Mhret and Jenna, some of them use posters or whiteboards. It's a place where students can display work that they've either started or that they've completed, and to become a resource for other students to use. It has different strategies that either students identified or you identified that serves as a place for students to go and reference if they need help on a problem or they're stuck, and it's just a good way to have student work up in the classroom and give students confidence to have their work be used as a resource for others. Mike: That was really helpful. I have a picture in my mind of what you're talking about, and I think for a lot of educators that's a really important starting point.  Something that really stood out for me in what you said just now, but even in our preparation for the interview, is the idea that this strategy showcase grew out of a common problem of practice that you all and many teachers face. And I'm wondering if we can explore that a little bit. So Tutita, I'm wondering if you could talk about what Anna and Jenna and Mhret were seeing and maybe set the stage for the problem of practice that they were working on and the things that may have led into the design of the strategy showcase. Tutita: Yeah. I had the pleasure of teaching my coauthors when they were master's students, and a lot of what we talk about in our teacher prep program is how can we get our students to express their own reasoning? And that's been a problem of practice for decades now. The National Council of Teachers of Mathematics has led that work. And to me, [what] I see is that idea of letting go and really being curious about where students are coming from. So that reasoning is really theirs. So the question is what can teachers do? And I think at the core of that is really trying to find out what might be limiting students in that work. And so Anna, Jenna, and Mhret, one of the issues that they kept bringing back to our university classroom is just being bothered by the fact that their students across the elementary grades were just lacking the confidence, and they knew that their students were more than capable. Mike: Jenna, I wonder if you could talk a little bit about, what did that actually look like? I'm trying to imagine what that lack of confidence translated into. What you were seeing potentially or what you and Anna and Mhret were seeing in classrooms that led you to this work. Jenna: Yeah, I know definitely we were reflecting, we were all in upper elementary, but we were also across grade levels anywhere from fourth to fifth grade all the way to sixth and seventh. And across all of those places, when we would give students especially a word problem or something that didn't feel like it had one definite answer or one way to solve it or something that could be more open-ended, we a lot of times saw students either looking to teachers. "I'm not sure what to do. Can you help me?" Or just sitting there looking at the problem and not even approaching it or putting something on their paper, or trying to think, "What do I know?" A lot of times if they didn't feel like there was one concrete approach to start the problem, they would shut down and feel like they weren't doing what they were supposed to or they didn't know what the right way to solve it was. And then that felt like kind of a halting thing to them. So we would see a lot of hesitancy and not that courage to just kind of be productively struggling. They wanted to either feel like there was something to do or they would kind of wait for teacher guidance on what to do. Mike: So we're doing this interview and I can see Jenna and the audience who's listening, obviously Jenna, they can't see you, but when you said "the right way," you used a set of air quotes around that. And I'm wondering if you or Anna or Mhret would like to talk about this notion of the right way and how when students imagined there was a right way, that had an effect on what you saw in the classroom. Jenna: I think it can be definitely, even if you're working on a concept like multiplication or division, whatever they've been currently learning, depending on how they're presented instruction, if they're shown one way how to do something but they don't understand it, they feel like that's how they're supposed to understand to solve the problem. But if it doesn't make sense for them or they can't see how it connects to the problem and the overall concept, if they don't understand the concept for multiplication, but they've been taught one strategy that they don't understand, they feel like they don't know how to approach it. So I think a lot of it comes down to they're not being taught how to understand the concept, but they're more just being given one direct way to do something. And if that doesn't make sense to them or they don't understand the concepts through that, then they have a really difficult time of being able to approach something independently. Mike: Mhret, I think Jenna offered a really nice segue here because you all were dealing with this question of confidence and with kids who, when they didn't see a clear path or they didn't see something that they could replicate, just got stuck, or for lack of a better word, they kind of turned to the teacher or imagined that that was the next step. And I was really excited about the fact that you all had designed some really specific features into the strategy showcase that addressed that problem of practice. So I'm wondering if you could just talk about the particular features or the practices that you all thought were important in setting up the strategy showcase and trying to take up this practice of a strategy showcase. Mhret: Yeah, so we had three components in this strategy showcase. The first one, we saw it being really important, being open-ended tasks, and that combats what Jenna was saying of "the right way." The questions that we asked didn't ask them to use a specific strategy. It was open-ended in a way that it asked them if they agreed or disagreed with a way that someone found an answer, and it just was open to see whatever came to their mind and how they wanted to start the task. So that was very important as being the first component.  And the second one was the student work displayed, which Anna was talking about earlier. The root of this being we want students' confidence to grow and have their voices heard. And so their work being displayed was very important—not teacher work or not an example being given to them, but what they had in their mind. And so we did that intentionally with having their names covered up in the beginning because we didn't want the focus to be on who did it, but just seeing their work displayed—being worth it to be displayed and to learn from—and so their names were covered up in the beginning and it was on one side of the board.  And then the third component was the students' co-identified strategies. So that's when after they have displayed their individual work, we would come up as a group and talk about what similarities did we see, what differences in what the students have used. And they start naming strategies out of that. They start giving names to the strategies that they see their peers using, and we co-identify and create this strategy that they are owning. So those are the three important components. Mike: OK. Wow. There's a lot there. And I want to spend a little bit of time digging into each one of these and I'm going to invite all four of you to feel free to jump in and just let us know who's talking so that everybody has a sense of that.  I wonder if you could talk about this whole idea that, when you say open-ended tasks, I think that's really important because it's important that we build a common definition. So when you all describe open-ended tasks, let's make sure that we're talking the same language. What does that mean? And Tutita, I wonder if you want to just jump in on that one. Tutita: Sure. Yeah. An open-ended task, as it suggests, it's not a direct line where, for example, you can prompt students to say, "You must use 'blank' strategy to solve this particular problem." To me, it's just mathematical. That's what a really good rich problem is, is that it really allows for that problem solving, that reasoning. You want to be able to showcase and really gauge where your students are. Which, as a side benefit, is really beneficial to teachers because you can formatively assess where they're even starting with a problem and what approaches they try, which might not work out at first—which is OK, that's part of the reasoning process—and they might try something else. So what's in their toolbox and what tool do they reach for first and how do they use it? Mike: I want to name another one that really jumped out for me. I really—this was a big deal that everybody's strategy goes up. And Anna, I wonder if you can talk about the value and the importance of everybody's strategy going up. Why did that matter so much? Anna: I think it really helps, the main thing, for confidence. I had a lot of students who in the beginning of starting the strategy showcase would start kind of like at least with a couple ideas, maybe a drawing, maybe they outlined all of the numbers, and it helps to see all of the strategies because even if you are a student who started out with maybe one simple idea and didn't get too far in the problem, seeing up on the board maybe, "Oh, I have the same beginning as someone else who got farther into the problem." And really using that to be like, "I can start a problem and I can start with different ideas, and it's something that can potentially lead to a solution." So there is a lot of value in having all of the work that everyone did because even something that is just the beginning of a solution, someone can jump in and be like, "Oh, I love the way that you outlined that," or "You picked those numbers first to work on. Let's see what we can use from the way that you started the problem to begin to work on a solution." So in that way, everyone's voice and everyone's decisions have value. And even if you just start off with something small, it can lead to something that can grow into a bigger solution. Mike: Mhret, can I ask you about another feature that you mentioned? You talked about the importance, at least initially, of having names removed from the work. And I wonder if you could just expand on why that was important and maybe just the practical ways that you managed withholding the names, at least for some of the time when the strategy showcase was being set up. Can you talk about both of those please? Mhret: Yes, yeah. I think all three of us when we were implementing this, we—all kids are different. Some of them are very eager to share their work and have their name on it. But we had those kids that maybe they just started with a picture or whatever it may be. And so we saw their nerves with that, and we didn't want that to just mask that whole experience. And so it was very important for us that everybody felt safe. And later we'll talk about group norms and how we made it a safe space for everyone to try different strategies. But I think not having their names attached to it helped them focus not on who did it, but just the process of reasoning and doing the work. And so we did that practically I think in different ways, but I just use tape, masking tape to cover up their names. I know some of—I think maybe Jenna, you wrote their names on the back of the paper instead of the front. But I think a way to not make the name the focus is very important. And then hopefully by the end of it, our hope is that they would gain more confidence and want to name their strategy and say that that is who did it. Mike: I want to ask a follow up about this because it feels like one of the things that this very simple, but I think really important, idea of withholding who created the strategy or who did the work. I mean, I think I can say during my time in classrooms when I was teaching, there are kids that classmates kind of saw as really competent or strong in math. And I also know that there were kids who didn't think they were good at math or perhaps their classmates didn't think were good at math. And it feels like by withholding the names that would have a real impact on the extent to which work would be considered as valuable. Because you don't know who created it, you're really looking at the work as opposed to looking at who did the work and then deciding whether it's worth taking up. Did you see any effects like that as you were doing this? Jenna: This is Jenna. I was going to say, I know for me, even once the names were removed, you would still see kids sometimes want to be like, "Oh, who did this?" You could tell they still are almost very fixated on that idea of who is doing the work. So I think by removing it, it still was definitely good too. With time, they started to less focus on "Who did this?" And like you said, it's more taking ownership if they feel comfortable later down the road. But sometimes you would have, several students would choose one approach, kind of what they've seen in classrooms, and then you might have a few other slightly different, of maybe drawing a picture or using division and connecting it to multiplication. And then you never wanted those kids to feel like what they were doing was wrong. Even if they chose the wrong operation, there was still value in seeing how that was connected to the problem or why they got confused. So we never wanted one or two students also to feel individually focused on if maybe what they did initially—not [that it] wasn't correct, but maybe was leading them in the wrong direction, but still had value to understand why they chose to do that. So I think just helping, again, all the strategies work that they did feel valuable and not having any one particular person feel like they were being focused on when we were reflecting on what we put up on display. Mike: I want to go back to one other thing that, Mhret, you mentioned, and I'm going to invite any of you, again, to jump in and talk about this, but this whole idea that part of the prompting that you did when you invited kids to examine the strategies was this question of do you agree or do you disagree? And I think that's a really interesting way to kind of initiate students' reflections. I wonder if you can talk about why this idea of, "Do you agree or do you disagree" was something that you chose to engage with when you were prompting kids? And again, any of you all are welcome to jump in and address this, Anna: It's Anna. I think one of the reasons that we chose to [have them] agree or disagree is because students are starting to look for different ways to address the problem at hand. Instead of being like, "I need to find this final number" or "I need to find this final solution," it's kind of looking [at], "How did this person go about solving the problem? What did they use?" And it gives them more of an opportunity to really think about what they would do and how what they're looking at helps in any way. Jenna: And then this is Jenna. I was also going to add on that I think by being "agree or disagree" versus being like, "yes, I got the same answer," and I feel like the conversation just kind of ends at that point. But they could even be like, "I agree with the solution that was reached, but I would've solved it this way, or my approach was different." So I think by having "agree or disagree," it wasn't just focusing on, "yes, this is the correct number, this is the correct solution," and more focused on, again, that approach and the different strategies that could be used to reach one specific solution that was the answer or the correct thing that you're looking for. Tutita: And this is Tutita, and I agree with all of that. And I can't help but going back just to the word "strategy," which really reflects students' reasoning, their problem solving, argumentation. It's really not a noun; it's a verb. It's a very active process. And sometimes we, as teachers, we're so excited to have our students get the right answer that we forget the fun in mathematics is trying to figure it out.  And I can't help but think of an analogy. So many people love to watch sports. I know Jenna's a huge UConn women's basketball… Jenna: Woohoo! Tutita: …fan, big time. Or if you're into football, whatever it might be, that there's always that goal. You're trying to get as many more points, and as many as you can, more points than the other team. And there are a lot of different strategies to get there, but we appreciate the fact that the team is trying to move forward and individuals are trying to move forward. So it's that idea with the strategy, we need to as teachers really open up that space to allow that to come out and progressively—in the end, we're moving forward even though within a particular time frame, it might not look like we are quite yet. I like the word "yet." But it's really giving students the time that they need to figure it out themselves to deepen their understanding. Mike: Well, I will say as a former Twin Cities resident, I've watched Paige Bueckers for a long time, and… Tutita: There we go. Mike: …in addition to being a great shooter, she's a pretty darn good passer and moves the ball.  And in some ways that kind of connects with what you all are doing with kids, which is that—moving ideas around a space is really not that different from moving the ball in basketball. And that you have the same goal in scoring a basket or reaching understanding, but it's the exchange that are actually the things that sometimes makes that happen. Jenna: I love it. Thank you.  Tutita: Nice job. Mike: Mhret, I wanted to go back to this notion that you were talking about, which is co-naming the strategies as you were going through and reflecting on them. I wonder if you could talk a little bit about, what does co-naming mean and why was it important as a part of the process? Mhret: Mm-hmm. Yeah. So, I think the idea of co-naming and co-identifying the strategies was important. Just to add on to the idea, we wanted it all to be about the students and their voice, and it's their strategy and they're discussing and coming up with everything. And we know of the standard names of strategies like standard algorithm or whatever, but I think it gave them an extra confidence when it was like, "Oh, we want to call it—" I forgot the different names that they would come up with for strategies. Jenna: I think they had said maybe "stacking numbers," something like that. They would put their own words. It wasn't standard algorithm, but like, "We're going to stack the numbers on top of each other," I think was maybe one they had said. Mhret: Mm-hmm. So I think it added to that collaboration within the group that they were in and also just them owning their strategy. And so, yeah. Mike: That leads really nicely into my next question. And Anna, this is one I was going to pose to you, but everyone else is certainly welcome to contribute.  I'm wondering if you could talk a little bit about what happened when you all started to implement this strategy showcase in your classroom. So what impacts did you see on students' efficacy, their confidence, the ways that they collaborated? Could you talk a little bit about that? Anna: So I think one of the biggest things that I saw that I was very proud of was there was less of a need for me to become part of the conversation as the teacher because students were more confident to build off of each other's ideas instead of me having to jump in and be like, "Alright, what do we think about what this person did?" Students, because their work became more anonymous and because everyone was kind of working together and had different strategies, they were more open to discussing with each other or working off of each other's ideas because it wasn't just, "I don't know how to do this strategy." It was working together to really put the pieces together and come to a final agree or disagree.  So it really helped me almost figure out where students are, and it brought the confidence into the students without me having to step in and really officiate the conversation. So that was the really big thing that I saw at least in some of my groups, was that huge confidence and more communication happening. Mhret: Yeah. This is Mhret. I think it was very exciting too, like Anna was saying, that—them getting excited about their work, and everything up on the board is their work. And so seeing them with a sticky note, trying to find the similarities and differences between strategies, and getting excited about what someone is doing, I think that was a very good experience and feeling for me because of the confidence that I saw grow through the process of the kids, but also the collaboration of, "It's OK to use what other people know to build upon the things that I need to build upon." And so I think it just increased collaboration, which I think is really important when we talk about reasoning and strategies. Mike: Which actually brings me to my next question, and Jenna, I was wondering if you could talk a little bit about: What did you see in the ways that students were reasoning around the mathematics or engaging in problem solving? Jenna: Yeah, I know one specific example that stood out was—again, that initial thing of when we gave a student a problem, they would look to the teacher and a little bit later on in the process when giving a problem, we had done putting the strategies up, we'd cocreated the names, and then they were trying a similar problem independently. And one of my students right off the bat had that initial reaction that we would've seen a few weeks ago of being like, "I don't know what to do." And she put a question mark on the paper. So I gave her a minute and then she looked at me and I said, "Look at this strategy. Look at what you and your classmates have done to come together." And then she got a little redirection, but it wasn't me telling her what to do. And from there I stepped away and let her just reference that tool that was being displayed. And from there, she was able to show her work, she was able to choose a strategy she wanted to do, and she was able to give her answer of whether she agreed or disagreed on what she had seen. So I think it was just again, that moment of realizing that what I needed to step in and do was a lot smaller than it had previously been, and she could use this tool that we had created together and that she had created with her peers to help her answer that question. Anna: I think to add onto that, it's Anna, there was a huge spike in efficiency as well because all these different strategies were being discovered and brought to light and put onto the strategy showcase. Maybe if we're talking about multiplication, if some student had repeated addition in the beginning and they're repeatedly adding numbers together to find a multiplication product, they're realizing, "Oh my goodness, I can do this so much more efficiently if I use this person's strategy or if I try this one instead." And it gives them the confidence to try different things. Instead of getting stuck in the rut of saying, "This is my strategy and this is the way that I'm going to do it," they became a little more explorative, and they wanted to try different things out or maybe draw a picture and use that resource to differentiate their math experience. Mike: I want to mark something here that seems meaningful, which is this whole notion that you saw this spike. But the part that I'm really contemplating is when you said kids were less attached to, "This is my strategy" and more willing to adopt some of the ideas that they saw coming out of the group. That feels really, really significant, both in terms of how we want kids to engage in problem solving and also in terms of efficacy. That really I think is one to ponder for folks who are listening to the podcast, is the effect on students' ability to be more flexible in adopting ideas that may not have been theirs to begin with. Thank you for sharing that. Anna.  I wonder if you could also spend a bit of time talking about some of the ways that you held onto or preserve the insights and the strategies that emerged during a showcase. Are there artifacts or ways that a teacher might save what came from a strategy showcase for future reference? Anna: So, I think the biggest thing as a takeaway and something to hold onto as a teacher who uses the strategy showcase is the ability to take a step back and allow students to utilize the resources that they created. And I think something that I used is I had a lot of intervention time and time where students were able to work in small groups and work together in teams and that sort of thing, keeping their strategies and utilizing them in groups. Remember when this person brought up this strategy, maybe we can build off of that and really utilizing their work and carrying it through instead of just putting it up and taking it down and putting up another one. Really bringing it through. And any student work is valuable. Anything that a student can bring to the table that can be used in the future, like holding onto that and re-giving them that confidence. "Remember when this person brought up that we can use a picture to help solve this problem?" Bringing that back in and recycling those ideas and bringing back in not just something that the teacher came up with, but what another student came up with, really helps any student's confidence in the classroom. Mike: So I want to ask a question, and Tutita and Mhret, I'm hoping you all can weigh in on this. If an educator wanted to implement the strategy showcase in their classroom, I want to explore a bit about how we could help them get started. And Tutita, I think I want to start with you and just say from a foundational perspective of building the understanding that helps support something like a strategy showcase, what do you think is important? Tutita: I actually think there are two critical things. The first is considering the social aspect and just building off of what Anna was saying is, if you've listened carefully, she's really honoring the individual. So instead of saying, "Look," that there was this paper up there—as teachers, we have a lot on our walls—it's actually naming the student and honoring that student, even though it's something that as a teacher, you're like, "Yes, someone said it! I want them to actually think more about that." But it's so much more powerful by giving students the credit for the thinking that they're doing to continue to advance that. And all that starts with assuming that students can. And oftentimes at the elementary level, we tend to overlook that. They're so cute—especially those kindergartens, pre-K, kindergarten—but it's amazing what they can do. So if you start with assuming that they can and waiting for their response, then following up and nurturing that, I think you as teachers will get so much more from our students and starting with that confidence. And that brings me to the next point that I think listeners who teach in the upper elementary grades or maybe middle school or high school might be like, "Oh, this sounds great. I'll start with them." But I want to caution that those students might be even more reticent because they might think that to be a good math student, you're supposed to know the answer, you're supposed to know it quickly, and there's one strategy you're supposed to use. And so, in fact, I would argue that probably those really cute pre-K and kindergartners will probably be more open because if anyone has asked a primary student to explain what they have down on paper, 83 minutes later, the story will be done.  And so it might take time. You have to start with that belief and just really going with where your class and individuals are socially. Some of them might not care that you use their name. Others might, and that might take time. So taking the time and finding different ways to stay with that belief and make sure that you're transferring it to students once they have it. As you can hear, a lot of what my coauthors mentioned, then they take it from there. But you have to start with that belief at the beginning that elementary students can. Mike: Mhret, I wonder if you'd be willing to pick up on that, because I find myself thinking that the belief aspect of this is absolutely critical, and then there's the work that a teacher does to build a set of norms or routines that actually bring that belief to life, not only for yourself but for students. I wonder if you could talk about some of the ways that a teacher might set up norms, set up routines, maybe even just set up their classroom in ways that support the showcase. Mhret: Yeah. So practically, I think for the strategy showcase, an important aspect is finding a space that's accessible to students because we wanted them to be going back to it to use it as a resource. So some of us used a poster board, a whiteboard, but a vertical space in the room where students can go and see their work up I think is really important so that the classroom can feel like theirs. And then we also did a group norm during our first meeting with the kids where we co-constructed group norms with the kids of like, "What does it look like to disagree with one another?" "If you see a strategy that you haven't used, how can you be kind with our words and how we talk about different strategies that we see up there?" I think that's really important for all grades in elementary because some kids can be quick to their opinions or comments, and then providing resources that students can use to share their idea or have their idea on paper I think is important. If that's sticky notes, a blank piece of paper, pencils, just practical things like that where students have access to resources where they can be thinking through their ideas.  And then, yeah, I think just constantly affirming their ideas that, as a teacher, I think—I teach second grade this year and [they are] very different from the fourth graders that I student taught—but I think just knowing that every kid can do it. They are able, they have a lot in their mind. And I think affirming what you see and building their confidence does a lot for them. And so I think always being positive in what you see and starting with what you see them doing and not the mistakes or problems that are not important. Mike: Jenna, before we go, I wanted to ask you one final question. I wonder if you could talk about the resources that you drew on when you were developing the strategy showcase. Are there any particular recommendations you would have for someone who's listening to the podcast and wants to learn a little bit more about the practices or the foundations that would be important? Or anything else that you think it would be worth someone reading if they wanted to try to take up your ideas? Jenna: I know, in general, when we were developing this project—a lot of it again came from our seminar class that we did at UConn with Tutita—and we had a lot of great resources that she provided us. But I know one thing that we would see a lot that we referenced throughout our article is the National Council of Teachers of Mathematics. I think it's just really important that when you're building ideas to, one, look at research and projects that other people are doing to see connections that you can build on from your own classroom, and then also talking with your colleagues. A lot of this came from us talking and seeing what we saw in our classrooms and commonalities that we realized that we're in very different districts, we're in very different grades and what classrooms look like. Some of us were helping, pushing into a general ed classroom. Some of us were taking kids for small groups. But even across all those differences, there were so many similarities that we saw rooted in how kids approach problems or how kids thought about math. So I think also it's just really important to talk with the people that you work with and see how can you best support the students. And I think that was one really important thing for us, that collaboration along with the research that's already out there that people have done. Mike: Well, I think this is a good place to stop, but I just want to say thank you again. I really appreciate the way that you unpack the features of the strategy showcase, the way that you brought it to life in this interview. And I'm really hopeful that for folks who are listening, we've offered a spark and other people will start to take up some of the ideas and the features that you described. Thanks so much to all of you for joining us. It really has been a pleasure talking with all of you. Jenna: Thank you.  Anna: Thank you Mhret: Thank you.  Tutita: Thank you so much. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org

I don't often have repeat guests on How To Fail but Mo Gawdat is the exception. When he first came on this podcast in 2019, he fundamentally changed my mindset and my approach to life. Back then, he was on a mission to make 1 billion people happier. Now, he returns to focus his brilliant philosophical and analytical brain to the perpetual human question: how to find true love, then nurture and sustain it. He joins me to discuss the three most frequent mistakes we make in love - and to explain how AI could be the saving of us. Mo is about to launch a game-changing AI-powered app called Emma that promises to help us all navigate the dating game with compassion and insight. This is the first time Mo has spoken in depth about this revolutionary new app so, yes, that IS a How To Fail exclusive, no biggie. ✨ IN THIS EPISODE: 00:00 Introduction 04:29 Personal Growth and Relationships 05:40 Heartbreak and Grief 10:03 Reflections on Love and Breakups 18:12 The Complexity of Modern Dating 21:45 Introducing Emma: The AI for True Love 29:53 The Mathematics of Dating 30:33 The Law of Large Numbers in Love 32:54 Dating Fatigue and Its Consequences 33:39 Game Theory in Relationships 36:52 AI's Role in Modern Relationships 39:15 The Economics of Love and Relationships 47:52 Finding Contentment Amidst Global Chaos

Renaissance Man Thomas Harriot was noted for many things - devising the theory of refraction, creating mathematical symbols including ‘greater than' and ‘lesser than', and being the first person to draw the Moon through a telescope. But the contribution for which he's most remembered is bringing back the potato to Britain - an event commonly credited to 3rd December, 1586. On first spotting the vegetable on Roanoke Island, he wrote: ‘They are a kind of roots of round form, some of the bigness of walnuts, some far greater, which are found in moist & marish grounds growing many together one by another in ropes, or as though they were fastened with a string. Being boiled or sodden they are very good meate.' In this episode, Arion, Olly and Rebecca ask what a ‘versifier' is; come up with a new name for Accountancy; and discover the bizarre means by which Antoine-Augustin Parmentier popularised spuds in France… Further Reading: • ‘The history of the potato: The humble vegetable that changed the world' (Sky HISTORY): https://www.history.co.uk/articles/the-history-of-the-potato-the-humble-vegetable-that-changed-the-world • ‘Thomas Harriot (1560 - 1621) - Biography' (MacTutor History of Mathematics, St Andrews University): https://mathshistory.st-andrews.ac.uk/Biographies/Harriot/ • ‘History through the eyes of the potato' (Leo Bear-McGuinness, TEDx 2015): https://www.youtube.com/watch?v=xROmDsULcLE This episode first aired in 2021 Love the show? Support us!  Join 

Rob riffs on the fifth studio album by No Doubt, “Rock Steady,” from December 2001 (Intro / Hella Good / Hey Baby / Platinum Blonde Life / Making Out). STAFF PICKS: “Blurry” by Puddle of Mudd — Lynch. “In Too Deep” by Sum 41 — Bruce.   ENTERTAINMENT TRACK: “A Kaleidoscope of Mathematics” (from the motion picture "A Beautiful Mind"). 

On today's episode, Kyle Grieve discusses powerful mental models from systems thinking and mathematics and applies them directly to investing and life. He breaks down concepts like feedback loops, kill criteria, scale, compounding, randomness, and regression to the mean to show how they shape real-world outcomes. He'll also share practical frameworks for improving decision-making, managing uncertainty, and positioning your portfolio to benefit from long-term compounding. IN THIS EPISODE YOU'LL LEARN: 00:00:00 - Intro 00:03:23 - How feedback loops stabilize or reinforce outcomes in investing 00:10:11 - How kill criteria help you make predetermined decisions in a noisy world 00:14:09 - Why the cone of uncertainty is useful for evaluating conviction and position sizing 00:17:33 - How scale changes the behavior, costs, and risks of a growing business 00:25:06 - How algorithms clarify which inputs drive the conclusions you rely on 00:30:20 - How to evaluate a company's ability to reach critical mass and become self-sustaining 00:35:35 - The hidden forms of compounding that are just as powerful as the visible ones 00:40:02 - Why power laws should influence your portfolio concentration 00:43:12 - How randomness shapes investing outcomes, and how to take advantage of it 00:51:24 - Why regression to the mean matters during periods of strong or weak performance Disclaimer: Slight discrepancies in the timestamps may occur due to podcast platform differences. BOOKS AND RESOURCES Join the exclusive ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TIP Mastermind Community⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ to engage in meaningful stock investing discussions with Stig, Clay, Kyle, and the other community members. Buy Thinking in Systems ⁠here⁠. Buy The Great Mental Models Vol 3: Systems and Mathematics ⁠here⁠. Buy Quit ⁠here⁠. Listen to my interview with Annie Duke ⁠here⁠. Follow Kyle on ⁠⁠⁠X⁠⁠⁠ and ⁠⁠⁠LinkedIn⁠⁠⁠. Related ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠books⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ mentioned in the podcast. Ad-free episodes on our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ ⁠⁠⁠⁠⁠⁠⁠⁠Premium Feed⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. NEW TO THE SHOW? Get smarter about valuing businesses in just a few minutes each week through our newsletter, ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠The Intrinsic Value Newsletter⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Check out our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠We Study Billionaires Starter Packs⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Follow our official social media accounts: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠X (Twitter)⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠LinkedIn⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Instagram⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Facebook⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ | ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TikTok⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Browse through all our episodes (complete with transcripts) ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠here⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Try our tool for picking stock winners and managing our portfolios: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠TIP Finance Tool⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Enjoy exclusive perks from our ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠favorite Apps and Services⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. Learn how to better start, manage, and grow your business with the ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠best business podcasts⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠. SPONSORS Support our free podcast by supporting our sponsors: Simple Mining Human Rights Foundation Unchained Onramp HardBlock Amazon Ads reMarkable Alexa+ Linkedin Talent Solutions Public.com Vanta Netsuite Shopify Abundant Mines Horizon Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://theinvestorspodcastnetwork.supportingcast.fm

In today's episode of Next Level University, hosts Kevin Palmieri and Alan Lazaros break down why so many people stay stuck by relying on emotion instead of objective data. You'll learn how understanding your numbers builds real confidence, how measurable feedback improves decision-making, and why tracking your behavior is a cornerstone of long-term personal development. This conversation highlights the role of data, clarity, and self-awareness in creating consistent results, especially for anyone serious about growth, success, and high performance. If you've been feeling uncertain, frustrated, or unclear about your next step, this episode reveals the skill that elevates focus, accuracy, and long-term progress. Press play and become the person who builds their future with intention and evidence, not emotion or chance.Learn more about:Next Level Hope Foundation – GoFundMe donation link https://gofund.me/5c6abcf7f Episode Reference:The Map of Mathematics - https://www.youtube.com/watch?v=OmJ-4B-mS-YVisual Asset:Foundational Mathematical Thinking - https://drive.google.com/file/d/1MVXeaS3F_7pK_aR3xHnQ7UGg-NPwbE31/view?usp=drive_link_______________________NLU is not just a podcast; it's a gateway to a wealth of resources designed to help you achieve your goals and dreams. From our Next Level Dreamliner to our Group Coaching, we offer a variety of tools and communities to support your personal development journey.For more information, check out our website and socials using the links below.

About David Cohen:David Cohen, FACHE, serves as the Chief Product and Technology Officer at Greenway Health, leading the company's technology and product strategy to drive digital healthcare innovation. Since joining in 2019, he has played a key role in modernizing Greenway's solutions and driving better outcomes for providers and patients. He also serves on the Board of the CommonWell Health Alliance, promoting interoperability across the healthcare ecosystem.Previously, David spent over 13 years at Cerner Corporation in leadership roles spanning Cerner Intelligence, Clinical Solutions, and Innovation. He began his career in technology and consulting with Pfizer and ThoughtWorks. David holds an MBA from The University of Chicago Booth School of Business and a BA in Integrated Science and Mathematics from Northwestern University.Things You'll Learn:Intelligent automation is central to transforming ambulatory healthcare, enabling providers to reduce administrative tasks and allocate more time to patient care.Greenway's “agentic-first architecture” treats AI not as a tool but as the core product, enabling end-to-end workflow automation across the encounter-to-cash spectrum.By working closely with customers and using a “working backwards” approach, Greenway designs solutions that directly address real-world practice challenges.Automation in documentation, chart review, and revenue cycle management enhances efficiency and improves care coordination through platforms like AWS HealthLake.David emphasizes “time compression,” focusing on delivering innovation within months rather than years to meet the urgent needs of healthcare providers.Resources:Connect with and follow David Cohen on LinkedIn.Follow Greenway Health on LinkedIn and visit their website. 

On October 16, 1843, William Rowan Hamilton was taking a walk with his wife Helen. He was on his way to preside over a meeting of the Royal Irish Academy. As Hamilton came to Broome Bridge, over the Royal Canal, the solution to a vexing problem finally emerged in front of him. He was so excited, and perhaps so afraid that he might forget, that he pulled out his penknife and carved the equation he had so suddenly conceived on the stonework of the bridge. That might not seem like such a revolutionary moment. But as my guest Robyn Arianrohd explains, Hamilton's equation was the result of long centuries of mathematical effort. And its consequences would be immense. Because Hamilton's thought made possible the concepts known as vectors and tensors. And vectors and tensors underlie much of modern science and technology, because they are used whenever a scientist or an engineer wants to use locations in space–everything from designing a bridge, to predicting the path of a gravitational wave; and there's quite a lot of territory in between those two applications. That moment by the Broome Bridge ushered in a new era. Robyn Arianrohd is a mathematician, and a historian of science. Her previous books include Thomas Harriot: A Life in Science, which she and I discussed in a conversation that was published on April 30, 2019. Her latest book is Vector: A Surprising Story of Space, Time, and Mathematical Transformation. For show notes, resources, and our archive, go the Historically Thinking Substack ChaptersThomas Harriet and the Birth of Modern AlgebraNavigation, Collisions, and Early Vector ConceptsNewton's Definition of Force and DirectionAugustus De Morgan and the Formalization of AlgebraHamilton's Breakthrough: Quaternions and Four DimensionsThe Non-Commutative RevolutionJames Clerk Maxwell and Electromagnetic TheoryMaxwell's Equations and the Nature of LightThe Vector Wars: Quaternions vs. VectorsTensors: Beyond Vectors to General RelativityThe Playful Seriousness of Mathematical DiscoveryConclusion: The Journey into History of Mathematics

What is the true structure of reality? In his fourth appearance on Mind-Body Solution, cognitive scientist Donald Hoffman returns with the most significant update yet to Conscious Realism: trace logic, decorated permutations, the emergence of spacetime from networks of conscious agents, and the strongest mathematical progress so far toward deriving Minkowski space from consciousness itself. Across nearly three hours, we explore what has changed in Hoffman's thinking since our last dialogue two years ago: breakthroughs in the trace-order formalism, new clarifications on evolution and perception, deeper implications for identity and suffering, and the surprising philosophical consequences of consciousness being fundamental. This is Hoffman at his most refined - technically rigorous, personally honest, and metaphysically bold.TIMESTAMPS:(00:00) — Intro(03:12) — What has changed in Hoffman's thinking in the last two years? (07:45) — Why Spacetime Is Doomed: The 2026 Case(12:58) — Conscious Agents: What's Changed in the New Theory(18:30) — Traces of Consciousness (2026): Don's Biggest Breakthrough Yet(25:44) — Restricted Channels of Consciousness (RCCs)(32:02) — The Mathematics of Trace Order & Trace Logic(38:55) — Is Reality Built from Relations, Not Things?(45:40) — What the Spacetime Headset Really Is(52:18) — Scattering Amplitudes & the Illusion of Objects(59:50) — Why Evolution Hides the Truth (Updated Evidence)(1:07:14) — Perception as a User Interface, Not a Window on Reality(1:14:32) — Are Particles Just Icons? The Physics Implications(1:22:10) — Causality, Emergence, Time & the √n Structure of Trace Chains(1:29:48) — Can We Test Conscious Realism in the Lab?(1:37:05) — AI, Conscious Agents & Synthetic Phenomena(1:45:22) — Conscious Realism vs Idealism, Physicalism & Competing Frameworks(1:53:44) — The Meaning Question: Why Is There Something It's Like?(2:02:58) — What This Theory Says About Death & Identity(2:10:00) – Identity, the Avatar, Death, Suffering & the “Infinite Self” (2:30:00) – Meditation & Waking Up from the Headset (2:40:00) – The New Paper Timeline & Call for Collaborators (2:48:00) – Closing reflectionsEPISODE LINKS:- Donald's Website: https://www.cogsci.uci.edu/~ddhoff/- Donald's Books: https://tinyurl.com/5x7bmzbd- Donald's Publications: https://tinyurl.com/bp7btw9a- Donald's Round 1: https://youtu.be/M5Hz1giUUT8- Donald's Round 2: https://youtu.be/Toq9YLl49KM- Donald's Round 3: https://youtu.be/QRa8r5xOaAA- Donald's Lecture 1: https://youtu.be/r_UFm8GbSvU- Donald's Lecture 2: https://youtu.be/YBmzqNIlbcICONNECT:- Website: https://mindbodysolution.org - YouTube: https://youtube.com/@MindBodySolution- Podcast: https://creators.spotify.com/pod/show/mindbodysolution- Twitter: https://twitter.com/drtevinnaidu- Facebook: https://facebook.com/drtevinnaidu - Instagram: https://instagram.com/drtevinnaidu- LinkedIn: https://linkedin.com/in/drtevinnaidu- Website: https://tevinnaidu.com=============================Disclaimer: The information provided on this channel is for educational purposes only. The content is shared in the spirit of open discourse and does not constitute, nor does it substitute, professional or medical advice. We do not accept any liability for any loss or damage incurred from you acting or not acting as a result of listening/watching any of our contents. You acknowledge that you use the information provided at your own risk. Listeners/viewers are advised to conduct their own research and consult with their own experts in the respective fields.

In this episode of Room to Grow, Curtis and Joanie reconsider the balance of conceptual understanding and procedural fluency in math instruction. Although this topic has been discussed before, our hosts acknowledge that there is great nuance and many considerations in considering these two ideas in the teaching and learning of mathematics.Curtis and Joanie discuss how inquiry-based, discovery-style learning opportunities are more open ended, are student centered, and are less teacher directed. They support these types of lessons in math instruction while recognizing that there are times when an explicit approach where teachers are sharing important information also has a place. Additionally, our hosts consider that teaching procedures and algorithms also provides and opportunity to cultivate conceptual understanding. When teachers help student find the  conceptual understanding within the procedures, they engage in mathematical reasoning. This type of reasoning through concepts and procedures contributes to a broader and more robust understanding of meaningful mathematics. Additional referenced content includes:·       NCTM article From Rules That Expire to Deeper Mathematical Thinking. Mathematics Teacher: Learning & Teaching PK-12 Volume 118 Issue 4. April 2025. (Membership required).·       NCTM article Teaching Is a Journey: From Rules That Expire to a Journey Aspired. Mathematics Teacher: Learning & Teaching PK-12 Volume 118 Issue 4. April 2025. (Membership required).·       Robert Kaplinski's website and Open Middle websiteDid you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy. 

One on One Video Call W/George https://tidycal.com/georgepmonty/60-minute-meetingSupport the show:https://www.paypal.me/Truelifepodcast?locale.x=en_USThe Lila Code: https://orcid.org/0009-0008-4612-3942

Machine learning using neural networks has led to a remarkable leap forward in artificial intelligence, and the technological and social ramifications have been discussed at great length. To understand the origin and nature of this progress, it is useful to dig at least a little bit into the mathematical and algorithmic structures underlying these techniques. Anil Ananthaswamy takes up this challenge in his book Why Machines Learn: The Elegant Math Behind Modern AI. In this conversation we give a brief overview of some of the basic ideas, including the curse of dimensionality, backpropagation, transformer architectures, and more.Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/11/24/336-anil-ananthaswamy-on-the-mathematics-of-neural-nets-and-ai/Support Mindscape on Patreon.Anil Ananthaswamy received a Masters degree in electrical engineering from the University of Washington, Seattle. He is currently a freelance science writer and feature editor for PNAS Front Matter. He was formerly the deputy news editor for New Scientist, a Knight Science Journalism Fellow at MIT, and journalist-in-residence at the Simon Institute for the Theory of Computing, University of California, Berkeley. He organizes an annual science journalism workshop at the National Centre for Biological Sciences at Bengaluru, India.Web siteAmazon author pageWikipediaSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Bob revisits capital and interest theory to show why the textbook result “interest = MPK” only holds in a one-good world, and why in actual markets the interest rate emerges from time, prices, and capital valuation—not raw productivity.Bob and Alberto Bisin Discuss the Use of Mathematics in Economics: Mises.org/HAP527aBob's Dissertation, "Unanticipated Intertemporal Change in Theories of Interest": Mises.org/HAP527bThe Mises Institute is giving away 100,000 copies of Hayek for the 21st Century. Get your free copy at Mises.org/HAPodFree

Bob revisits capital and interest theory to show why the textbook result “interest = MPK” only holds in a one-good world, and why in actual markets the interest rate emerges from time, prices, and capital valuation—not raw productivity.Bob and Alberto Bisin Discuss the Use of Mathematics in Economics: Mises.org/HAP527aBob's Dissertation, "Unanticipated Intertemporal Change in Theories of Interest": Mises.org/HAP527bThe Mises Institute is giving away 100,000 copies of Hayek for the 21st Century. Get your free copy at Mises.org/HAPodFree

Episode: 1475 The tragic tale of Evariste Galois.  Today, let's tell the remarkable tale of Evariste Galois.

The Space Show Presents KATHRYN BOLISH, WEX Foundation, Friday, 11-21-25Brief Summary:The program focused on discussing the WEX Foundation's educational programs, particularly their space STEM initiatives for K-12 students through their LCATS program, which provides free education and mentorship in space-related topics. The discussion covered the foundation's approach to teaching mathematics and programming, as well as their collaboration with NASA and other aerospace companies to develop student projects and curriculum. The conversation concluded with an exploration of the program's impact on student engagement and academic performance, while addressing challenges related to the COVID pandemic, funding, and policy issues in public education.Detailed Summary:David, John Jossy, and Kathryn Bolish, our guest from the WEX Foundation, discussed the WEX Foundation, its projects, and its namesake, Judge Waldo Jimenez. Kathryn explained the power outages at her office causing WIFI issues for this broadcast. We lost audio and video with our guest a few times during the program but were fortunate that we were able to reconnect with a minor delay. We do apologize for the audio/video issues during this discussion.Kathryn discussed her passion for mathematics and her plans to pursue a PhD at UTSA. John Jossy and I welcomed Dr. Ajay Kothari to the meeting and others as they joined us. I provided a formal introduction for Kathryn Bolish, a mathematician pursuing a PhD, who discussed her passion for mathematics and its applications in space travel. They explored the disconnect between theoretical and numerical mathematics in education, with Kathryn highlighting the importance of teaching math theory and logic from an early age to improve understanding and reduce remedial needs. Before commencing with the full program, I announced upcoming guests and program changes, including a fundraising campaign after Thanksgiving which is essential for supporting The Space Show for 2026.Kathryn discussed the importance of teaching propositional logic and set theory to students early on to help them understand math as a tool rather than a monster. She explained how WEX Foundation provides free space STEM education to K-12 students, focusing on lunar exploration. The program, called LCATS, accepts 30-40 students annually for a three-year commitment, meeting bi-weekly Saturdays at San Antonio area universities. Kathryn emphasized the need for teachers to understand basic programming and math theory to effectively teach these subjects. The discussion also touched on the challenges of AI in education, with Kathryn advocating for using AI as a tool for learning rather than for cheating. David inquired about the program's impact on students' general academic performance, including students not in a WEX program but in the class with a WEX student. Kathryn replied that it has led to increased interest and engagement in STEM subjects among participating students.Kathryn explained that the WEX Foundation's LCATS program, which was piloted by NASA in 2017, faced challenges due to the COVID-19 pandemic and staff changes in 2020. She emphasized the importance of ensuring that the program's content remains relevant to the space industry and highlighted the need to find suitable locations and teachers willing to conduct classes on Saturdays. Kathryn also discussed the foundation's approach to connecting young students with space industry experts, noting that while the experts may initially seem intimidating, the students often view their feedback as valuable learning opportunities. She mentioned that the foundation plans to finalize a comprehensive LCATS curriculum by May 2026, which will then be used to expand the program to other regions.Kathryn discussed the benefits of exposing students to industry challenges, noting that while some SMEs may be harsh, the experience helps build student confidence. She shared an example of a student project that led to a 3D printer prototype for lunar construction, now displayed at a museum. David raised concerns about magical thinking among graduate students and asked how Kathryn addresses it with young minds, to which she responded that embracing the “magic” of unknown possibilities is crucial for innovation, drawing parallels to historical achievements like the moon landing.The meeting discussed the NASA-funded New Worlds program, which trains pre-service educators in lunar habitat design. Kathryn explained that the program teaches students about lunar lava tubes and challenges them to design habitat systems. Ajay raised concerns about landing on the lunar surface, suggesting that the program could help address this issue by developing solutions for landing on uneven terrain. Marshall inquired about the transition from Earth-based biospheres to lunar habitats, and Kathryn mentioned that the program partners with experts in this field to provide students with relevant constraints and knowledge. The conversation ended with a reminder that the show had a strict 60-minute time limit.Kathryn explained that her parent company, Astroport, evaluates student proposals for space-related projects by assessing their feasibility for terrestrial demonstrations before advancing to lunar applications. She noted that while Astroport works with major aerospace companies like Boeing and SpaceX, WEX focuses on space STEM education and collaborates with these organizations through mentorship and partnerships. Kathryn also mentioned that WEX operates from the same building as Astroport and occasionally hosts engineers to help students brainstorm solutions for their projects, while acknowledging the challenges of addressing policy and regulation issues in their curriculum.Kathryn explained that WEX Foundation's space education programs are structured to be self-sustaining and low-cost, allowing them to continue operations despite NASA's education budget cuts. She clarified that while students can propose their own ideas for lunar projects, the program focuses on teaching established concepts like lava tube habitation and letting students develop their own solutions. The discussion concluded with Ajay offering to share a paper about space exploration with Kathryn, who expressed gratitude for the collaborative spirit among the participants.This program featured a discussion with Kathryn from the WEX Foundation, who shared insights about her math-focused educational programs in San Antonio. She explained how her mathematical background supports her work in program management and curriculum development, despite not directly using advanced math in her current role. The conversation highlighted the diversity of her student cohorts and the collaborative nature of her programs, which bring together students of different ages and backgrounds. The discussion concluded with questions about the demographics of her students and plans for program expansion, as well as a brief conversation about the challenges of public education and the role of money in society.Special thanks to our sponsors:Northrup Grumman, American Institute of Aeronautics and Astronautics, Helix Space in Luxembourg, Celestis Memorial Spaceflights, Astrox Corporation, Dr. Haym Benaroya of Rutgers University, The Space Settlement Progress Blog by John Jossy, The Atlantis Project, and Artless EntertainmentOur Toll Free Line for Live Broadcasts: 1-866-687-7223 (Not in service at this time)For real time program participation, email Dr. Space at: drspace@thespaceshow.com for instructions and access.The Space Show is a non-profit 501C3 through its parent, One Giant Leap Foundation, Inc. To donate via Pay Pal, use:To donate with Zelle, use the email address: david@onegiantleapfoundation.org.If you prefer donating with a check, please make the check payable to One Giant Leap Foundation and mail to:One Giant Leap Foundation, 11035 Lavender Hill Drive Ste. 160-306 Las Vegas, NV 89135Upcoming Programs:Broadcast 4466: ZOOM: Dr. Avi Loeb | Sunday 23 Nov 2025 1200PM PTGuests: Dr. Abraham (Avi) LoebZOOM: Dr. Avi Loeb returns to discuss our latest interstellar visitor and more. Get full access to The Space Show-One Giant Leap Foundation at doctorspace.substack.com/subscribe

Thomas Morel joins Jana Byars to tell the story of subterranean geometry, a forgotten discipline that developed in the silver mines of early modern Europe, talking about his book Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe (Cambridge UP, 2022). Mining and metallurgy were of great significance to the rulers of early modern Europe, required for the silver bullion that fuelled warfare and numerous other uses. Through seven lively case studies, he illustrates how geometry was used in metallic mines by practitioners using esoteric manuscripts. He describes how an original culture of accuracy and measurement paved the way for technical and scientific innovations, and fruitfully brought together the world of artisans, scholars and courts. Based on a variety of original manuscripts, maps and archive material, Morel recounts how knowledge was crafted and circulated among practitioners in the Holy Roman Empire and beyond. Specific chapters deal with the material culture of surveying, map-making, expertise and the political uses of quantification. By carefully reconstructing the religious, economic and cultural context of mining cities, Underground Mathematics contextualizes the rise of numbered information, practical mathematics and quantification in the early modern period. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/new-books-network

Get the book, Leading Educator Wellness: Six Critical Actions to Support All Staff About The Authors Bill Barnes is the superintendent of the Howard County Public School System in Maryland. He has served in leadership roles with the Maryland and National Council of Teachers of Mathematics, and has won a number of state and national teaching awards. Barnes holds a master of science in mathematics and science education from Johns Hopkins University, and has served as an adjunct professor for Johns Hopkins University, the University of Maryland–Baltimore County, McDaniel College, and Towson University.   Dr. Erin Lehmann is an associate professor for the University of South Dakota. She has experience as an elementary principal at a Title I school, as well as being a math teacher, math coach, and curriculum specialist. Dr. Lehmann is the author or co-author of several books, including Teaching Mathematics Today. She is a frequent speaker at national conferences, advocating for mathematics and grading practices. She holds EdD in educational leadership from the University of South Dakota.

After 27 years, Melvyn Bragg has decided to step down from the In Our Time presenter's chair. With over a thousand episodes to choose from, he has selected just six that capture the huge range and depth of the subjects he and his experts have tackled. In this third of his choices, we hear Melvyn Bragg and his guests discuss Greek philosophy. Their topic is Zeno of Elea, a pre-Socratic philosopher from c490-430 BC whose paradoxes were described by Bertrand Russell as "immeasurably subtle and profound." The best known argue against motion, such as that of an arrow in flight which is at a series of different points but moving at none of them, or that of Achilles who, despite being the faster runner, will never catch up with a tortoise with a head start. Aristotle and Aquinas engaged with these, as did Russell, yet it is still debatable whether Zeno's Paradoxes have been resolved. With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Barbara Sattler Lecturer in Philosophy at the University of St Andrews and James Warren Reader in Ancient Philosophy at the University of Cambridge Producer: Simon Tillotson In Our Time is a BBC Studios Production Spanning history, religion, culture, science and philosophy, In Our Time from BBC Radio 4 is essential listening for the intellectually curious. In each episode, host Melvyn Bragg and expert guests explore the characters, events and discoveries that have shaped our world

From Rakim to Kendrick Lamar, this is the story of hip-hop's obsession with numbers. Dissect's Cole Cuchna breaks down the evolution of “number bars” - a lyrical tradition where rappers use math, numeric sequences, and wordplay to showcase technical skill and encode hidden meaning. Beginning with Rakim's groundbreaking verse on “My Melody” (1986) - a quatrain built around groups of seven that secretly mirrors his own 21-letter name - we trace how MCs have used numbers as both a mathematical signature and a symbolic device for decades. From Melle Mel's divine 7-count in “Superrappin” to Jay-Z's “22 Twos”, Biggie's “Ten Crack Commandments,” and Mos Def's “Mathematics,” numbers became an essential part of hip hop tradition and lyricism. By the 2000s, artists like Lupe Fiasco, J. Cole, JID, Vince Staples, and Kendrick Lamar transformed number schemes into complex storytelling tools. We unpack everything from Lupe's hidden 3–2–1 countdown on Kanye West's “Touch the Sky” to Kendrick's quantum-level equations on “Nosetalgia.” Learn more about your ad choices. Visit podcastchoices.com/adchoices

What happens when a government abruptly cuts off the lifeline of pure science? Imagine canceling Albert Einstein just before he published [E = mc². Terence Tao, the “Mozart of Mathematics,” was one of the unlucky researchers hit when the Trump administration suddenly terminated his federal research funding. Today, I walk and talk with Tao at UCLA to understand how America's greatest living mathematician found himself blindsided by a bureaucratic earthquake — and what it means for the future of discovery. This is Part 1 of our deep dive into Tao's work, his warnings about the collapse of U.S. research infrastructure, and why mathematics is the unseen root system supporting all of modern technology.

Episode: 1472 New uses for huge numbers.  Today, big numbers find new meaning.

This week on Schauer Thoughts we have a special guest - please give a warm welcome to Mina Neuberg, CEO of WonderMath! Also, this episode is NOT an ad, I am not being paid, I just really love math and wanted to discuss learning and executive functioning with the executive putting the “fun” in functional learning. No but seriously, math is incredibly important and I appreciate y'all listening and *hopefully* expanding the communal comfort zone! Learn More About WonderMath: https://www.wondermath.com/  Where to Reach Mina: mina@wondermath.com  New Book Club Information: https://www.patreon.com/posts/new-book-for-143088045  Resources: What We Value: The Neuroscience of Choice & Change - Emily Falk The Power of Fun - Catherine Price Mathematics for Human Flourishing - Francis Su Is Math Real? - Eugenia Cheng  The Knowledge Illusion: Why We Never Think Alone - Philip Fernbach  Neural correlates of hate https://pubmed.ncbi.nlm.nih.gov/18958169/ What Is Hate and Where Does It Live in the Brain? https://www.psychologytoday.com/us/blog/your-brain-on-food/202208/what-is-hate-and-where-does-it-live-in-the-brain The premotor cortex https://www.physio-pedia.com/Premotor_Cortex#:~:text=The%20premotor%20cortex%20is%20a,of%20the%20contralateral%20hemisphere%20alone. Behavioral energetics in human locomotion: how energy use influences how we move https://pmc.ncbi.nlm.nih.gov/articles/PMC11993254/  Demonstration and Pantomime in the Evolution of Teaching https://pmc.ncbi.nlm.nih.gov/articles/PMC5361109/ Total Physical Response (TPR) - Teaching Method https://www.researchgate.net/publication/392376539_Total_Physical_Response_TPR Screen Apnea  https://www.npr.org/2024/06/10/1247296780/screen-apnea-why-screens-cause-shallow-breathing  Olfactory Enrichment to Improve Memory https://pmc.ncbi.nlm.nih.gov/articles/PMC10405466/ What the Thalamus Does https://teachersinstitute.yale.edu/curriculum/units/2012/3/12.03.02/4#:~:text=In%20this%20way%2C%20the%20thalamus%20is%20screening,matters%20of%20value%20and%20filtering%20out%20distractions.  This is How the Brain Filters Out Unimportant Details https://www.psychologytoday.com/us/blog/brain-babble/201502/is-how-the-brain-filters-out-unimportant-details#:~:text=This%20%E2%80%9Creciprocal%E2%80%9D%20connectivity%20can%20be,popcorn%2C%20and%20air%20conditioning). Movement-Based Learning: Students Need to Use Their Bodies to Learn  https://www.teachhub.com/teaching-strategies/2025/03/movement-based-learning-students-need-to-use-their-bodies-to-learn/  Math Has Its Own Language. How Can Students Learn to Speak It? https://www.edweek.org/teaching-learning/math-has-its-own-language-how-can-students-learn-to-speak-it/2024/09 Conceived linearities in mathematics education and how to disrupt them https://www.tandfonline.com/doi/full/10.1080/14794802.2025.2579307?src=#d1e125 How Did You Solve It? Metacognition in Mathematics  https://www.ascd.org/el/articles/how-did-you-solve-it-metacognition-in-mathematics Writing Problems in Possessive Form https://www.ef.edu/english-resources/english-grammar/forming-possessive/ Learn more about your ad choices. Visit podcastchoices.com/adchoices