More Math for More People
CPM Educational Program is a non-profit publisher of math textbooks for grades 6-12. As part of its mission, CPM provides a multitude of professional learning opportunities for math educators. The More Math for More People podcast is part of that outreach and mission. Published biweekly, the hosts, Joel Miller and Misty Nikula, discuss the CPM curriculum, trends in math education and share strategies to shift instructional practices to create a more inclusive and student-centered classroom. They also highlight upcoming CPM professional learning opportunities and have conversations with math educators about how they do what they do. We hope that you find the podcast informative, engaging and fun. Intro music credit: JuliusH from pixabay.com.
More Math for More People
Episode 5.16 - Happy New Year? Yes and No... with Rafael del Castillo
A quirky holiday about Printing Ink turns into a surprising exploration of how learning really sticks. We start with soot, gelatin, CMYK, and the tactile world of flexography—plates wrapped on cylinders, color laid down in sequence, and the trained eye that spots misalignments at a glance.
That segues into our deeper conversation with CPM Executive Director, Rafael del Castillo: January acts like a second first day of school, only now we share norms, trust, and a clearer sense of what works. We talk about regrouping teams, revisiting agreements, and using the January–April window to make small changes with big payoff.
From there, we challenge the calendar. Do semesters serve learning, or do we bend learning to fit dates? We compare traditional schedules with year-round models, homeschool flexibility, and university J- or May-term intensives that compress time for focus and stronger relationships. Each structure is a choice with trade-offs—continuity versus long breaks, synchronization with family life versus localized rhythms. The thread that ties them together is intentional design: pick the cadence that supports memory, motivation, and access.
We also dig into pedagogy and mindset. Mixed-spaced practice asks us to let understanding mature over time instead of expiring at the end of a unit. That shift can feel like losing control, but it actually builds durability: spaced retrieval, interleaving, and ongoing formative checks help students replace “I can’t” with “I’m still learning.” Study teams normalize multiple approaches, move us away from speed-as-ability, and give students more chances to explain and teach. Whether you’re navigating toner versus ink or debating year-round school, the principle is the same—layer learning with intention, check alignment, and adjust.
Ready to reframe your midyear? Subscribe, share this with a colleague who needs a fresh start, and leave a review with one change you’ll try between now and spring.
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SPEAKER_07:Okay, so here we are. Yes, it is. January 13th.
SPEAKER_06:What is our traditional day today? Printing Ink Day. Yes. Printing Ink Day. Not printing ink. Printing Ink Day. Printing Ink Day. Yes. Printing Ink Day.
SPEAKER_07:So we're just celebrating our printing ink.
SPEAKER_02:It's uh the closest Tuesday to January 16th, and it started in 1977. And it's a day that we can all come together and remember one of our most essential office tools. And and so we want to celebrate Inks.
SPEAKER_06:Yeah.
SPEAKER_07:Wow. Why the closest Tuesday to January 16th?
SPEAKER_06:That's interesting.
SPEAKER_07:Oh one one six seven seven. I can't even figure out why January 16th. Okay, well, great. This is just so I feel like this is just more proof that you can have a national day about anything. I'm glad you don't even deny that at least.
SPEAKER_02:Absolutely, you can. So what's your uh huh well first of all, when do you think ink was invented?
SPEAKER_07:Do I think ink was invented? I'm pretty sure it was invented a long time ago before there were printers. I mean, I think ink was invented, and then printers were invented that used ink. Printing ink would have had to be invented at the same time as the printers. If you're talking about computer printers, that's good. You can't invent a computer printer without ink.
SPEAKER_02:Yeah. My timeline says that ink was not I was tongue-in-cheek, inventing, but developed in 2500 BC era. BCE era. And then but that was developed from what do you think that was developed from?
SPEAKER_06:Ink? Was it developed from liquid ink? What was it developed from? Could be. Anyway, now I'm stuck on that. Okay, okay. Yeah.
SPEAKER_07:I mean, what was it made from? Like uh like tree. Um my sources say soot.
SPEAKER_02:I mean animal fat and gelatin.
SPEAKER_06:Yeah.
SPEAKER_02:Separately, I think.
SPEAKER_06:They would use those items to make their when do you think the printing press was invented? Well that was like wasn't that like well okay, printing press like the movable type one that I can.
SPEAKER_07:Yes, it was Gutenberg invented. Yeah, wasn't that like the fourteen hundreds?
SPEAKER_02:So you're saying sometime between fourteen and fifteen? Okay. So that's a pretty good that's a good guess.
SPEAKER_06:Oh, there you go.
SPEAKER_07:There we go. That was a pretty pretty innovative thing. Since you didn't have to put all the type into just make, you know, carve out one thing that you print like a print block.
SPEAKER_02:I wonder if when printing ink may become obsolete. I wonder if we'll continue to have a need for printing. We do, I think we currently do.
SPEAKER_07:I think I think we yes, we currently do. Yes. I mean, we're actually using it. I mean I think I think we still I they like we still create a lot, even if I'm not printing out, like if like I don't probably need to print fewer things than I actually print. There's still a lot of things that are in print. Right? Like posters and like we still have a lot of like signage and things like that that's in our world that is still printed in some way. It's not computer printing ink, maybe. But I'm thinking about like laser printers, is that's not printing ink. Printing ink laser printers don't use ink.
SPEAKER_06:Yeah, toner.
SPEAKER_07:What the heck is toner?
SPEAKER_02:I don't know. Print yeah, printers, copiers use toner. Heat. I know that because it gets on your fingers and stuff.
SPEAKER_07:But some printers do too. Like that's yeah, it's like laser printers or whatever. Like, interesting.
SPEAKER_02:Well, I used to be a printing press operator. And I used to it was flexography, so everything they would make these plates, and I'd have to wrap them on a cylinder and different cylinders for different size labels and things like that. And and then the main four colors was it was CMYK, so cyan, yellow, magenta, black. And with those four colors, you could kind of make any color, and so the plates would determine how much of each ink would go onto the paper. And then you could have like a custom already made color if that was helpful in the process or say for efficiency, that sort of thing. But flexography is uh they're like stickers. So it comes the paper's on a roll and it goes through the machine and then it comes out on a roll. And our biggest run it through the colour. Uh you just run it through once, and then there's like each color has a tray in the process that it hits.
SPEAKER_07:So but it's putting the colors on eat at different steps.
SPEAKER_02:And then our biggest customer was scrapbooking, which was interesting. And not not pharmaceutical as much as I what would you call it like you're getting vitamins or you're getting supplements or you're getting oils or you're getting those kind of medical things.
SPEAKER_06:And then our third biggest was wine labels. Yeah.
SPEAKER_07:And that was primarily you're making labels or stickers.
SPEAKER_02:And then in the other department they did like the brochures and that sort of a thing.
SPEAKER_07:But I've seen some of those like stickers where they're at, you know, like lower quality or they didn't have the same maybe quality assurance and like the the prints off a little bit, like that you can see the blue is not lined up with the yellow.
SPEAKER_02:I know I can see that real quick. Yeah. Because that's a mistake.
SPEAKER_07:I bet. Mistake your brain is trained to notice. Awesome. So how does it suggest that we say number one?
SPEAKER_03:Learn and read more about printing ink.
SPEAKER_02:Yes. Yes.
SPEAKER_07:Wow. Oh, about printing ink, not just learn and read more. Learn and read more.
SPEAKER_02:Read something that's been printed with ink. Heck yeah, no.
SPEAKER_07:Exactly. And then about printing ink.
SPEAKER_02:Look out for coupons. So you can take advantage of some good pricing on your printing ink. And once you've found those coupons and purchased your printing ink, refill your printer ink. That's the part.
SPEAKER_07:Refill. Who refills printer ink? Oh my gosh. They never work as well. I don't know what to tell you.
SPEAKER_06:Eventually they get clumpy. I don't refill my printer ink. I just order more. Yeah. Yeah.
SPEAKER_07:Awesome. That sounds great.
SPEAKER_01:I'm gonna probably just I'll print some. And realize that you need more ink, then you'll look for the coupons. There you go.
SPEAKER_07:Well, it'll tell me if I'll do one of those color tests. Yeah.
SPEAKER_02:You know, like, yeah.
SPEAKER_07:Exactly. Yeah.
SPEAKER_02:That's true.
SPEAKER_07:It uses a lot of ink to do the color test. Well, enjoy your national or whatever it is, printing ink day. I learned we should just start the recording.
unknown:That's right.
SPEAKER_03:That's right. Yeah. We do.
SPEAKER_07:No, no. Booking is right out of the gate. It's been it's it's hard.
SPEAKER_00:So it it does remind me of my classroom days where like the first day, you're like, I forgot how to teach.
SPEAKER_07:Yeah. I know.
SPEAKER_00:Well, and the children the children are like, I forgot how to learn. Exactly.
SPEAKER_07:Exactly. It's so funny. I mean, we talk about, you know, they forget everything over summer. The two weeks of break, it's like, it's just it really is like two parts of a school year.
SPEAKER_00:Two parts of a school year. Yeah. A cool way to look at it.
SPEAKER_07:Well, and I it's always interesting too, because if you want to make the two semesters equal in days, then you have to include some of January, which always feels weird. It's just I I appreciate the schools are like, nope, we're just ending it at December and we're starting again in January. We don't care that they're not eating.
SPEAKER_02:My my schools were always like January 21st. Yeah. Yeah.
SPEAKER_07:If you yeah, if you go with the 180 days and you start at the beginning of September, then it's somewhere around, you know, the 20th of January is the middle.
SPEAKER_00:I'm not sure I ever had to navigate that. I always felt like or maybe I just split it the way I wanted to.
SPEAKER_07:Probably that's that's that sounds like how you would roll, Raphael.
SPEAKER_00:Yeah. I don't know. It just feels like to start in January with this notion that you haven't finished a thing when you in fact have like the whole year. Yeah. Happy New Year's. You know, that kind of thing. Just didn't didn't ever feel right. Yeah.
SPEAKER_02:You and I are like-minded in that way, because I I always I just said my school ended the 21st, I ended in December. Yeah. And kids, but we have till the 21st. No. It's all made up anyway. So right. Yeah.
SPEAKER_00:And but we never got in trouble, right? No, no. Yeah, right. Like people didn't really care if you had a good rationale for it. Yeah. It wasn't just willy-nilly. Oh, yeah. It was a solid ration rationale. Absolutely.
SPEAKER_06:A solid rationale.
SPEAKER_00:So, Misty, I'm intrigued by your like, okay, the two different parts, right? Let's forget about when. Let's let's just pretend it's always like coming back from break is the new second part. Like, how are they different?
SPEAKER_07:It's so as I remember it, it was like it was we started again, right? Like it's like it was a fresh start, but it was a fresh start with some experience, right? It's very different than the beginning of the school year. The beginning of the school year feels very much, oh, what's gonna happen? How's it gonna be? What what what is this year? Like, what's different? I mean, I had some of the same kids from year to year, so they were like, oh yeah, this stuff's the same and this stuff's different. And then like in January, it always felt like, well, there's two pieces for it. Like it, it always felt like it was, oh, we're getting a fresh start, but we but we know what's going on. So like it's you know, it's that it's that second half, you know, it's the second half of the football games, second half of all the things, you know, you always have like a midpoint, and then you get to the second part where you're like, okay, we know what's going on now, but now we gotta like knuckle down and do it. And it was that it was that like from a learning perspective, that profitable space between January and about the April, where it got too nice, where it was like, yeah, we might we might as well wait till next year. Like, oh, why are we even bothering? Right, yeah.
SPEAKER_02:Right.
SPEAKER_07:Yeah.
SPEAKER_02:I wonder if there's some systematic difference between high school and middle school. Because I always felt like the second part was was a fresh start because I had new rosters, I had new uh students that we were starting.
SPEAKER_07:Yeah. Like your class, even if your class continued, you still had kids come in and out, right?
SPEAKER_02:Right.
SPEAKER_03:Yeah. Yeah.
SPEAKER_07:Yeah. I think with the like the the more permanence, we'll say, of grades in high school and and actually changing classes. I mean, my my class was just continued because I was even at a smaller middle school, so I didn't even have semester classes that changed like a larger middle school would. So it was just the same kids, and we just picked up different things.
SPEAKER_00:Yeah, I keep thinking of the concept of a do-over, particularly real in terms of relationships. So for me, I would always think of the new year as, you know, may all acquaintance be forgotten. Like like let's start over, let's do over. And, you know, always coming from the perspective of the teacher. Like to your point, uh, Misty, you've gotten to know how it works, how things work, how the math works. But you've also got to know each other. And I think there's an opportunity there to restart, like even revisit like the guidelines for the classroom. I think I think sometimes there's a certain temptation to just jump back in and maybe not take full advantage of the relational restart. I I would argue that middle schoolers have, I think, have have a greater tendency to forgive and forget. I don't know. Maybe that's just me. Whereas high schoolers I think sort of continue seething if you if you've wronged them. But maybe that was just me.
SPEAKER_07:Yeah. Yeah, that's interesting. Yeah, I d I definitely that that piece of we know what's going on. It like is a bit of a relational, right? Like we know where at least we think we know where each other are in space and time, right? And of course, we're so much of that is projection and what we think we know. So much not true in that statement that I just made.
SPEAKER_02:I I think I I just treated it like the start of a year sort of thing. Like it was wow. I it's been since chapter two since I've moved you to a new group. So let's let's let's revisit let's revisit that idea, yeah.
SPEAKER_07:Oops. Yep. Not in the days of regrouping every day.
SPEAKER_02:But it it was definitely I would I would hit just as an in the beginning of the year, those team building, brain breaks, icebreakers, right? All those things, we'd hit them again in January for sure.
unknown:Yeah.
SPEAKER_07:I was I was never the person who was like, oh my gosh, here's this great idea that I think I should do or change when I how I'm doing things. But now I've already started, so I have to wait. I was I was always the one who's like, nope, okay, kids. Chapter three, chapter three, here we are. We're gonna nope, I've discovered something better. We're gonna do it, you know. We're gonna change right away. Sometimes, I mean, if I was trying to like rechange my whole grading system, that you know, like percentage of that would be harder. But like I didn't, I was pretty settled with how that was, and it was more like, oh, changing how I'm grading this thing, or I'm changing how I'm giving feedback or what we're putting on the assessment or different things like that, how we're taking care of things within the classroom. Like I I would make those changes whenever they seemed like they should be made. Right.
SPEAKER_00:Quick action.
SPEAKER_07:Quick action. Yeah, no, definitely. And then there were times when I was like, okay, here's a big program overhaul that I want to make that I would that would wait on. Yeah, I felt like I I had this sort of mixed piece though, because I had math and science. And in science, we were in the middle of our science projects. Like we always had to, like, because they needed to be done at the beginning of April, and January day April was not quite enough time. We started them before the break. And the kids did all their research and wrote their research paper part before the break, and then came back and had to get started into like doing their experiment and making the things and stuff. So that was always like this one piece that kind of connected, but you know, had a a break in it. Oh, cool. And then and then math was always like we tried to get to the end of a chapter before the break, but that didn't always happen. Sometimes we just picked up where we were. So yeah, it was it was it was more sort of like relanding back together, right? Like we have to rearrive in this space together and begin forward again. And sometimes that took a little a little.
SPEAKER_06:Yeah.
SPEAKER_00:I've always wondered what it what it's like to not have like the two part and multiple beginnings, endings. I mean, I've always been, I guess almost always, my entire career, I've been in education or education adjacent. So the academic year was thing. You know, I would buy to this day, I buy calendars that go from July. Right. Like there are those calendars. I think other people look at them and they're like, why are these calendars this way?
SPEAKER_07:Those people who buy them just late and they're like, oh no, I forgot a calendar.
SPEAKER_00:But I I wonder, I mean, as we explore different ways of doing school. You know, people are talking about year-round school again and again as the boundaries of the classroom maybe dissolve away. What will that look like for the schooling part of your life to be more like most people's life life, right? I mean, I know there's breaks, I know there's vacations, but I notice a different energy and a different approach to restarting, right? And there isn't like a new school year. It's like work, work, work, work, work, continue into the next year. And can I I just wonder about that, like what that feels like for kids as they move through K through you know, 14 plus and into the workspace. Yeah.
SPEAKER_07:Well, and and I I mean, I have interacted with a couple of schools, well, one school in particular that has a year-round schedule, right? So they but they still have chunks and a start-end, right? Like the kids still promote at some point, right, to the next grade and so on, but they and they still chunk it, right? They have long they have breaks spread out throughout the year instead of all of the conglomerated in one spot. Yeah. And it and it didn't feel very different, other than it just felt spread out. Like they and they had and it felt like they had more breaks. Like that was the part was like. Like, oh, and I was trying to work with them. Like, oh no, no, we're on, we're, you know, we have a week-long break in the middle of October. You know, like so it was it was like, oh, you know, it's like they were out of sync with everything else, which was sort of interesting. The other school stuffs, clearly for you know, parents and working and families and things like that. But again, I think a lot of families have synced up to how, you know, there is that there's the burden for parents who are working and don't have care during the you know, like the way school you know, relate is can also represent child care so parents can work. Yeah. We learned that during the pandemic, right? Pretty heavily. So yeah, it's it's I think there's there's pluses and minuses. I know that the idea of I mean, we all ought to do this when we went from school to here, right? That was one of the big things. We don't get you don't get the whole summer off anymore, quote unquote. Right. Right. In fact, summer's busiest time for us now.
SPEAKER_02:You all are making me think too of so I read the study that if and I'm just gonna make up this year, but if you're born after 1995, your brain is significantly different than people who are born before 1995. Like in the way that you learn and operate and things like that. And so like w what I'm hearing is we hold on to maybe these breaks. What do we value? Do we value the break? If I want the information, I don't have to wait till I go back to school to get it. I guess I can get the information right away. Or there's there's just different ways of thinking, and we hold on to I know I do, older ideals of a break of a space. Why is there a hundred and eighty days? Why is that even a number?
SPEAKER_00:It's it's kind of mind-bogging a little bit. There are all sorts of artifacts we can go to, right? Like credit hours and learning units and whatnot. I'm uh you you're reminding me that one of the one of the fastest growing still, really for potentially decades, uh, sectors in education is the homeschool sector. And I went to a conference a while many, many years ago, to be honest, where the premise was we should be going to homeschool conferences because they're doing some things that are really out of the box. And you know, I never I never took the dive, if you will, but maybe I should, you know. And if you think about it, they're their challenge with incorporating their year-round life, right, into an educational experience for their kids and vice versa. And that that must present huge challenges. It's curious to me that they've gravitated, the sector itself has gravitated to certain things they do together and certain things they can do more independently, right? Individually at home. And I I think that that has some potential for educators to to think about.
SPEAKER_02:One of the schools I'm supporting right now is in Houston. And I made an assumption that I could schedule a meeting this week because the break is over. It's the second half. That's part two. They said, no, we can't meet this week because as a school, we're we're going on a uh school trip. So that uh equates to me like the homeschool idea a little bit of we want to learn in a different way. And exactly what does that mean?
SPEAKER_07:Yeah, I remember I remember even like you talk about that. Like I remember when I was applying this is it ancient history now, when I was applying for university, one of the universities that I applied to had this, like I think they call it like a 414 schedule where they did like a quarter, and then the month of January basically was like a month-long internship experience kind of a thing. And then you came back for the second quarter. Like it was this sort of gap in the middle where people could take a long, you know, a time to do some intensive thing.
SPEAKER_00:And they had various things set up that you could choose from and do, and but yeah, I had I had that experience uh in my brief stint as a as a university instructor, a Pacific Lutheran. January was J term. I can't believe I just remembered this, but uh it it was a similar concept, right? There were two halves, if you will, but January was designated as J term. It was a short term where you could get regular credits, but there were also a lot of travel consultants. Right. So professors who wanted to do an overseas or, you know, across the nation kind of experience would use January. So there were all those cool experiences. But I got to teach a J Term course just right there, not anywhere exciting and mysterious. But it was grading for equity. And it was one of my favorite courses that I taught there. And it by condensing it into a January session, right? And included a couple of Saturdays even, it became this really interesting. I mean, I think the topic itself was so energizing. These were graduate students that, you know, it all it almost taught itself. But it it turned into a really cool experience, not just the content that was exciting, but also relationally, you know, we ended up spending more time together, prolonged periods of time. It impacted how I, you know, of course, arranged the classroom, did group work. And then we did like this little celebratory dinner at the very end, which was meaningful. Like it was meaningful for me and meaningful for the students. So while we didn't go to Rome or or wherever, the the nature of the compressed time did something to the teaching and the learning, which was cool.
SPEAKER_07:Well, then that time to have that intensive focus, right? That's the only class they're taking, right? It was the only class. Your attention is really focused.
SPEAKER_02:For for our my experience, what it was the May the it wasn't J term, it was May term. So that all the classes ended, and then you could stick around for and they were usually upper level courses that you needed to graduate, that sort of thing, but it was like two or three weeks. And the other thing they started here in Salt Lake City was with the Olympics being here, uh like a ski program at the university. So you they molded the classes in such a way or they planned the classes in such a way that you it was like Mondays and Fridays, so you could ski Tuesday, Wednesday, Thursday sort of thing. And just thinking outside the box a little bit.
SPEAKER_07:It's funny when you talked about it, you switched it to May term and it was like a few weeks. I was like, oh, that sounds like summer school. Which feels like the opposite of what we were just talking about. Like summer school feels like this time where you just go and you just kind of be there and then you get credit somehow. It's magical.
SPEAKER_02:Well, I am a proponent of many people don't agree with me. I think school should be all year. Like, I don't think we should take breaks.
SPEAKER_07:The the long break in the summer is definitely telling you for sure.
SPEAKER_06:Such an impact. Yeah.
SPEAKER_00:Oh so do you guys think do you all think that CPM is the way we we're thinking along the lines of the way we structure the classroom, the study teams? I'm gonna throw out a premise that we're more adaptable as a model for the mathematics classroom, right, across all these different ways we've been discussing school. Right. It feels like, you know, we'd fit in more easily because of the paradigm we bring with us. It's it's more adaptable, it's more flexible, it doesn't rely on like the one person, not necessarily the linear approach to mathematics that other spaces provide. I don't know. What do you think about that? Or are we not?
SPEAKER_07:Well, as you say that, I think it's so what's pops in my mind is at first I'm like, well, yes. And then of course, absolutely. You know, and and I'm also recognizing as I'm thinking that though, how much of that is my own mindset around teaching and because I think because I because as you're saying that, I was thinking then about teachers that were, you know, and teachers new to CPM that are sometimes really stuck feeling that CPM is very rigid. Yeah, right? Like they like we have to can like almost convince them that no, no, no, no, there's lots of ways to do it. Here's the guiding principles, here's the big ideas, here's the things, and and and or they want it to be that doesn't feel rigid enough, right? There's this because it's like teachers will still come at it from both ideas to like at times like you should just talk should talk to each other because you're not seeing it with enough guidance, and you're not seeing it what you're seeing with too much guidance. And so, as you're saying that, I was thinking about like how well, how does that message then like oh those three messages, how do they all come out of the same curriculum? And I'm really thinking that it's really maybe our own mindsets around teaching and thinking and what we value. And so then I was like, well, yes, but then I was like, how much is that is me? And how much of me is that the curriculum that matches me really well, right?
SPEAKER_02:I love that I love that you said that because so often we hear I don't teach CPM or I I only teach CPM, and CPM is not a uh way of content. Yeah. Like our resource supports multiple avenues for a lot of different things. But if you and as you read and you invest in the research, things like that with the mixed-based practice, when you do change teams frequently, when you do use your best practices, our resource supports that for sure.
SPEAKER_00:Yeah, in my in my day, what really it's interesting you mentioned mindset. So I've been thinking, okay, what what shifted my mindset? Because it needed shifting, you know, in a pretty radical way once upon a time. And it was this notion of kids mastering and understanding over time, right? Which connects now with mixed-based practice and other other other approaches that are CPM-ish, if you will. But it was this notion that there isn't like a an expiration date for this concept for that student. Yeah. Right. It's not like I'm gonna move forward. Sorry. Sorry, Johnny, you missed you missed the window of understanding for you know system of equations. Good luck. Yeah. Whereas, you know, we commit to this notion of it will come, you know, it will come over time and we will assess it over time. And that that really was the key, right? And I think that's why I'm thinking that we are actually more adaptable because we don't lock ourselves into an assessment cycle that's either weekly or monthly or quarterly or whatever. We know that assessing, you know, what kids know happens in multiple ways. And you know, I th I think our position on assessment is really nuanced and strong, you know. But to your point, some people think too much structure, too little structure. I I think it is mindset.
SPEAKER_07:Yeah, well, and and as you're saying that, I mean, we're we're agreeing and that I I think for me also mixed space practice was the place where I was like, oh, like it was the place I had to that I that I made the most changes, right? Like the most structural changes about how I was thinking about homework, how I was doing assessments, how I was even talking to my kids every day, right? Around what about they what they understood and didn't felt like didn't understand, right? And helping them see that it was like, nope, you don't need to understand it yet. We just started looking at it today, right? And or like, okay, we've been working with this, it's time to start to move away from the algebra tiles. That's how can we use that less? Like, because my kids would get stuck in an idea too, right? And so that that whole piece, I remember even when I first started working with teachers and they would say, Well, like, what if you know, how long do I wait for them to get it? Like, when, when, you know, how long? And I was like, You always wait. Like, I was just remembering I was just like, Do you just wait more? That's a really good, you know. Like just if if they're doing their homework and they're and they're and they're working, like, like there's not it's not passive waiting, right? But it is, but it is not this, oh no, they have to have it by this chapter or else, right? That and that that shift in idea. And it's and I think that that's that also then leads to where I was talking about, like people who feel like it's too willy-nilly, they're like, oh my God, but I need to know. Like, when do they have to know that I have to write these down in my grade book, or I have to do these things, I I need to have some structure that I'm not feeling enough from whatever, because I'm used to this different structure, or it's feeling too, too predicted because, you know, or too scripted because it's like, oh, well, this problem like walks them through that in this way. And I'm like, well, that's one way to do that. But again, seeing beyond what's given and what's intended, that's that's hard for teachers when they're first getting familiar with it. Yeah, space practice is always the hardest pillar, I say I tell you. I'm like, this is always the hardest one to understand.
SPEAKER_02:Well, and I can relate to this as a teacher. I'm could be called a control freak. And when things are out of my control, yeah. When it's out of my control, that feels odd to me. And so I want to take control and I want to know I hey, January 5th, I taught this. They know it now.
SPEAKER_07:Yeah, that's that's the myth we all believed.
SPEAKER_00:Yeah. Right.
SPEAKER_07:That we ever had control.
SPEAKER_00:Yeah. Control you're right. Control is part of that mindset and that mind shift that comes with realizing that you're not the only place where learning is happening in the classroom if you structure it in a certain way. This little this this little bit of a side note. I I I just started thinking about self-talk too, right? The I I had several interactions with students early on in middle school where they would approach me with, I'm never gonna get this. This problem is impossible. You know, really like pretty severe self-talk. And I would just like sometimes it was like fake it till you make it. I know you don't believe this, but you're gonna say things like, one day I will solve this problem. Or, you know, I am competent in mathematics, right? Versus like, I am so bad at math. And it was fascinating to see how the self-talk just preceded every interaction. Oh, it was really interesting.
SPEAKER_07:And the flip side of that is that the mixed space practice, right? And coming back to those problems over and over again. I did have my kids who go, Whoa, this was so hard when we started because they were still doing it. Thing go. If you do that masked practice, it's oh yeah, I'm good at this now. Uh-huh. Because I've done the same thing 20 times in a row, right? I know I'm gonna forget it in two weeks. And when I come back in two weeks, I'm like, crap, I thought I knew that. Right. So it's a it's a constant almost bashing of your understanding as opposed to the the interesting sort of like always being on the cusp of learning new things is also hard, right? Because we're like, I don't ever get to that. I feel like I have to notice that I feel comfortable with a thing from before because I'm always kind of pushing that edge as well. Mixed-based practice kind of does both for us. And I always come back to it. So how we actually actually learn. Yes. Right? We learn a thing well when we do come back to it over time. We do, you know, spread it out, sleep on, do it again.
SPEAKER_06:All the things we really have learned well.
SPEAKER_00:Right. And and you know, the ultimate I mean, that synthesis of information is when you can teach it. And that's why I think there's such power in the study teams, right? Like, let me show you, let me show you my way. It's different than your way, perhaps, but it's kind of cool. And and it just normalizes that that difference of approach uh and takes you away from I can get the answer in you know five seconds quicker than your ten seconds, therefore I'm really good at math. Right. Which which is so wrong on so many levels because that's that's you know, that's teaching the wrong thing about mathematics. And mathematicians, the real world or engineers or others, they're not sitting around big conference tables like trying to beat each other to the to the numerical answer. And if they are, the company's not gonna laugh at that.
SPEAKER_02:That's right, that's right. Yeah, I can tell you we've had a a little bit of a break here, and I was visiting with my folks, and we uh we always play a game called hand and foot. And it's a Midwestern game. I'm from the Midwest. It's you must play. Yeah, I must play. It's like five decks of cards, and our our our system last time we put it away wasn't very good. So we had to verify that we had actual decks of cards and count and things like that. And there were four of us going through the cards, and each one of us counted cards and sorted cards in different ways. Just like what we all had a strategy. We didn't care what the other strategies were. We just got there.
SPEAKER_07:We had independent verifications, yeah. Oh, goodness. Well, here we are. It's the beginning of 2026. I know it's a whole nother have you made resolutions. No, I'm not a big resolution person, not like resolutions, like yeah. I usually I feel like there's two new years for me because we generally we celebrate like the solstice and then new year, you know, so new year feels like, yeah, we already did that. So it's I usually do more of a like, well, what am I gonna let go of and what am I hoping to gain more of kind of reflection?
SPEAKER_02:Yeah, I I am more of a reflection person as well. And this this time I reflected on I've been cleaning out the house. So I have like many empty bins right now. Feels really good. But one of the things I reflected on is are you kidding me? There's another, you can see it in the background, there's another box of algebra tiles in my basement right now. What is wrong with these?
SPEAKER_07:So you are an algebra tile hoarder, that's what we are.
SPEAKER_02:Clearly.
SPEAKER_00:You're gonna corner the marks when algebra.
SPEAKER_03:Oh my gosh.
SPEAKER_00:How about you, Raphael? You know, I'm I'm not big on resolutions either. Yeah. Like it feels again kind of artificial. I also don't like framing them as things I'm gonna not do. You know, I prefer the opportunity to do. I also have like to me, the new year is very much tied with family because we we typically go home and visit my parents. And we're like, we're we'll we perish it in like the Geek Squad. We literally do a technology refresh every year. Nice.
SPEAKER_07:Yeah.
SPEAKER_00:We did that. New iPhones for everyone, along with all the various training that is required for a You know, I found a file's file that my father had lost. He intends to use words like stolen. And I was like, Dad, I assure you, no one has stolen your financial data for 2025. I guess it felt really this feels really good for us to go in and do a little bit of refreshing for someone else. And then it sort of brings you back to your place.
SPEAKER_07:Here we go. Here we go. We're starting the new year.
SPEAKER_00:Let's do 2026. By the way, Joel, we have a set a game. We prefer to our game is called Foot in Mouth game.
SPEAKER_02:That sounds much more entertaining. Badly.
SPEAKER_03:So, but yeah, to that.
SPEAKER_07:So that is all we have time for on this episode of the More Math for More People podcast. If you are interested in connecting with us on social media, find our links in the podcast description. And the music for the podcast was created by Julius H and can be found on pixabay.com. So thank you very much, Julius. Join us in two weeks for the next episode of More Math for More People. What day will that be, Joel?
SPEAKER_02:It will be January 27th, National Geographic Day. And we'll celebrate and talk about the National Graphic magazine. I remember going to the library to check out a magazine of the National Geographic and just loving to get information about the world through that periodical. And I just am excited to hear Misty's experience and talk about the goings-on for the world and the changes that are happening probably within the National Geographic World. So happy to celebrate on January 27th, and we'll see you there.