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 4.13: Where Joel and Misty talk about cats and finish their conversation with Christopher Danielson
Ever had your toe stabbed by a mischievous cat? Join Joel and Misty as they share entertaining tales of their feline friends in celebration of National Cat Day. From childhood memories with beloved furballs like Perkins and Figaro to the hilariously challenging role of being a cat "manager," Joel and Misty navigate the whimsical world of cats. Whether you're a cat lover or merely cat-curious, this episode honors the quirky charm and unique quandaries of having a furry companion.
Switching gears, they dive back into their conversation with Christopher Danielson and the curious world of mathematics and the less-than-exciting methods of traditional schooling. Reflecting on their own journeys—both as students and educators—they explore how to make math a joyful adventure rather than a barrier.
You can connect with Christopher at:
https://talkingmathwithkids.com/
https://www.public-math.org/
https://christopherdanielson.wordpress.com/
Send Joel and Misty a message!
The More Math for More People Podcast is produced by CPM Educational Program.
Learn more at CPM.org
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Speaker 2:Boom. All right, we're 29th, we're being. What day is it today?
Speaker 1:It is National.
Speaker 2:Cat Day National Cat Day.
Speaker 1:Yeah, wow.
Speaker 2:Like domestic cats or any kind of cats. It is national cat day.
Speaker 1:National cat day, yeah, wow, like domestic cats or any kind of cats well, I'm just gonna go ahead and say any type of cat, but it says that there's 40 to 70 recognized cat breeds for just for your information 40 to 70.
Speaker 2:That's quite a range. Like recognizing official groups. Aren't sure we recognize this one?
Speaker 1:There might be some controversy. There's some debate In the cat groups.
Speaker 2:There's a controversy around what kinds of cats are breeds or not Interesting. I'm really curious about what those 30 breeds are.
Speaker 1:Me too. Sigmund Freud said one time that time spent with cats is never wasted.
Speaker 2:Freud said that time, that time spent with cats is never wasted. Freud said that Interesting. If he had told me that quote and said who do I think? Said that I would not have guessed Sigmund Freud, I didn't know that he was associated with the cat.
Speaker 1:Well, he's not really. I guess he said something about a cat one time.
Speaker 2:He said something about a cat that has been quoted, yeah. So he clearly said it's not significant or interesting. Are you? Are you a cat fan, Joel?
Speaker 1:You know okay, so this is a little complex for me. I've been a cat I don't want to say owner, because cats can't be owned I think a cat provider maybe or a cat manager. I do whatever the cat says, whatever that would be Cat slave. Yeah, cat slaves. I don't mind cats, but cats sometimes scare me. I've been. I've watched my friend's cats when they are on vacation and have been stabbed by a claw.
Speaker 2:You've been stabbed by a cat.
Speaker 1:Mm-hmm, mm-hmm, but I was laying on the couch and this cat.
Speaker 2:Wait, wait, okay, this needs more details.
Speaker 1:Yeah, so this my toe is hanging off the couch. This cat stuck its claw right in the end of my toe and that upset me. Yeah, of course, in all fairness, I also was messing with the cat ahead of that, and so maybe the cat got when Tilly was.
Speaker 2:A lack of boundaries of consent on both sides.
Speaker 1:Yes, they're trying to. It was hard to negotiate for the cat. I would say so. I would say so. It says that here that 44% of people say that they have owned at least one cat in their life 44% of people.
Speaker 2:So four out of nine people that have owned at least one cat.
Speaker 1:Have you owned a cat?
Speaker 2:Yes, I have several cats. I didn't really grow up with cats. We didn't have cats when I was in sixth or seventh grade, when we weren't moving so much, but all our cats were outside cats. It was very, very clear Cats have a purpose. Their purpose is to be outside eating things, right, mm-hmm? And when I was on my own.
Speaker 2:I've had cats most of my adult life, until recently, and I at some point the last two cats that I had shifted to my cats being predominantly and actually only inside cats, because I learned about how negatively impactful they are to the environment because they just they just hunt, it's not about they're hungry, it's not about, and they just they are pretty impactful to particularly the bird population in areas where they live.
Speaker 2:So I was I. I felt it was a for me, it felt more responsible to keep my cat inside and so so, yeah, so I had to inside cats for a while and then I haven't had any cats now for probably like six or eight years. Okay, yeah, I mean, cats are fine. I like cats that have particular personalities, like they have to.
Speaker 2:I really like a cat that like doesn't mind being picked up, wants to cuddle with you. I like those qualities wants to cuddle with you. Like you know, I like those qualities, yeah, like a loose cat that just exists in the same space as me.
Speaker 1:I I'm not as not as far yeah, my first cat was named perkins and perkins um. As a young child, I was given the choice to name the cat and, and I was debating between two of my favorite restaurants. So is Perkins or Mr Steak.
Speaker 1:And I ended up going with Perkins, which was good, and that cat was the inside cat, but it got out and it ended up like rabies. I don't know something, but I wanted to attack it all the time. So my parents took it to the farm or wherever they take those kind of cats.
Speaker 2:It's a feral cat then? Mm-hmm, yeah, cats are interesting. Cats are interesting, for sure. I don't mind cats, I just don't particularly want to have a cat.
Speaker 1:Did you ever see the film the Aristocats? I do, I remember seeing that as a young child, that's a good one, yeah.
Speaker 2:What are you going to do for National Cat Day, joel, I think, because I know you're big on celebrating all over?
Speaker 1:I might not do anything for this. You know I might. I'll think about the cats of my past.
Speaker 2:Ah, maybe get out their pictures, look at them.
Speaker 1:I'm still mad at my cat, figaro, who moved to Utah. I was living in this apartment, so not very good ventilation, so I kept the window open and Figaro loved to go outside. And Figaro would then roll up all the outside cats and they would come running through the house so then I'd have to close the thing and then they're like spraying on my roof and stuff, trying to get it figure out. So I'm I have a lot of negative thoughts about work, but I'm gonna try and that's how I'm gonna celebrate. I'm gonna only think about the good stuff about my kid. That's like an ending all right.
Speaker 2:Well, on that note how.
Speaker 1:How are you going to celebrate?
Speaker 2:If I see a cat today that seems like it wants to be petted, I will pet it. That's what I'll do.
Speaker 1:That's a nice one.
Speaker 2:Yeah, all right. Well, enjoy National Cat Day everyone. Woo-hoo. So this will be part two of our conversation with Christopher Danielson. If you haven't listened to part one, we encourage you to go back to the October 14th podcast, episode 411, and take a listen to part one of our conversation there and then come back here and listen to part two.
Speaker 4:Enjoy. So I want to, I want to slight shift a little pivot to. I know one of your your projects is public, together with the Minnesota Council of Teachers of Math and with funding from the Minnesota State Fair Foundation cooperation with the fair. That gives us the space. I sort of thought, well, okay, this is great, like we built this amazing thing. But it was like an end of the road and we'll go work on some other projects at some point, but tied up neat with a boat, but tied up neatly with a boat.
Speaker 4:And I think it was in about the third year that I started to think, well, what if? Instead of it being like the end of the road, what if? Or of a particular road, what if it's an example of some larger thing? And then starting to ask questions of myself and some others about what's that, what's that larger thing that this might be an example of? And so about that same time I met a fabulous former colleague of mine, desmos Chris Ngo and Molly Daly, who does beautiful work in Vancouver, washington, right across from you in Portland. Some really exciting stuff going on in their heads, and so we started to collaborate and we kind of came to a conclusion that one way to view math on a stick is that it is a playful and creative math experience designed for a particular space and a particular time, and that time and place is Minnesota State Fair that takes place outside 12 days. Every year at this, the second largest state fair in the country, 1.9 million people go to this fair over the course of 12 days. It's enormous, and that it would be fun to and exciting to think about designs for other spaces. So, like, what are some other places where we might do some of that designing? And so we started.
Speaker 4:We brought some really interesting and creative folks together to do some brainstorming and ideation and playing around with it, and cpm gave us some money and so we have some reserve funds that are enough for us to be able to sort of execute small projects as they come up, which, as a former classroom teachers like all three of us have been, have been classroom teachers and having two or three hundred dollars, like at the ready to do a project without it being a big deal, is a big deal like, yeah, you need, you need two hundred dollars in your classroom. Good luck finding it. So we're we're super, super grateful eternally to cpm for giving us the kind of funding that that makes that just not a problem, got a little idea. We want to execute something that needs printing up. We need some materials for something. We can go ahead and give it a try and in return, we try to share as much as we can the things that we're doing. So there's a public math website, public-mathorg, where we posted some of the projects that we have been working on.
Speaker 4:We've thought about and dreamed of some things that would require a lot more funding. One of the things we would be excited for is the math bus in which the right now outside my window there's there's a Metro transit bus, right, your basic city bus, and one of the things that they do with city buses or with light rail trains or subway trains is they'll wrap them right with an advertisement for the Minnesota Timberwolves or whatever. Like what is what if, instead of it being an advertisement for the sports team or for the bank or the pizza place, what if it was math engagement? That'd be super fun. And then what are the things you could do? You could have little holes that are cut out in various shapes and your job is to try to catch a rectangle as it goes by inside of that hole and we could use the space that's inside, that's up above the seats, for little prompts, because they do that with poetry all the time.
Speaker 4:Right, ride the subway in New York City and there'll be beautiful poems, right, that don't take very long to engage with. They're short, you know. This isn't time for the Iliad or the Odyssey. It's short poems that are relevant to the space. Often, right, they'll be about being in public or about going from place to place. And so what if there were a little prompt up there that just asked you to count how many shoes there were?
Speaker 4:Right, and parents and a child are riding the bus and there's a little thing up there, a little cartoony thing. If the kid can read, they do, and if they can't, they point at it. Parent reads it to them, and now we're looking around and seeing how many shoes are on the bus, or there's just a thousand things we could do with that kind of space. We're excited about that kind of thing, but that costs more money than we have, right, to be able to buy a bus and then have the bus go out into the world. So we're having conversations with folks trying to figure out how we might do that. So yeah, we try as much as we can to bring in interesting voices, people who have different perspectives. A couple times we've used some of that CPM money to have a public mass gathering where we physically bring together five or six interesting, diverse minds and spend a weekend brainstorming and prototyping, and then anything we generate we'll share on the site and hope people reach out.
Speaker 2:And is it the kind of thing that people can present or apply for ideas that they have with you?
Speaker 4:We are excited for conversations and, if there's any way, we can support you in brainstorming something. I mean, chris now is an incredible graphic designer so he can bang out a design for a thing really quickly. I got in my work here. We both with my job and math happens but also my side projects. I'm in a workshop right that has a laser cutter in the back, so we need something laser cut. We can catch something in order to try out an idea that you have. Yeah, so we're excited for conversations. We don't have money to give grants, but we certainly have money to provide some materials. We've got materials that are lying around from previous projects. We're excited to share when we can and support you in finding what you need. So you've got ideas cool.
Speaker 1:So I guess in in looking at some of your stuff online, I I watched a a little clip of you talking with some kids in what looked like a library or something and there was a photo of a pie and some of the pieces had been taken out and they're forks. And then next to that was the same photo, the same photo, the same photo, to make an infinite sort of a thing. What struck me is the conversation kind of went around well, how many? And then you had some ideas. This, the kids had some ideas, and one of my favorites was well, there's infinite amount of forks. Well, no, there's only two forks. Actually, this is a picture of two forks, so that's zero forks, like so how many do we have? But it just. Why do you think it's so important for kids to talk about lots of ideas around math in that way?
Speaker 4:Yeah, well, I mean, that's the play, right? I think a lot of this I don't know. So I as a math student was like you know, stuff always made sense to me in school so teachers could show me a thing and I would be able to do it and along I went without any like real passion. But then, like in high school, I was just cruising along on that and algebra and whatever.
Speaker 4:And two contrasting experiences Like one is I love Isaac Asimov's book on numbers devoured that as a high school student didn't see have any expectation that what I was reading about there would have any connection to my high school math work. Like it didn't see have any expectation that what I was reading about there would have any connection to my high school math work. Like it didn't seem paradoxical to me that I was getting like a c in algebra one because I was barely doing my homework but devouring this right, this amazing writer's work about mathematics at the same time. And then the contrasting experience I remember.
Speaker 4:Interesting experience is I remember one of the classic algebra struggles is I've got three minus four X times two minus X, and so I ended up at some point I got the negative, the minus four X and the minus X are going to have to get multiplied and I was like, but they're both subtracting, like what, it should just be a subtraction, right. And she's like. My algebra teacher was like no, no, no, no. And the base, like all I could get out of her was like you're gonna need it for algebra too. I was like this is a stupid game.
Speaker 4:I don't want to play this game and now, as an experienced teacher and I've had those conversations like the the direction. For me, the direction is all right. Let's plug in some numbers, let's make x5, let's compute it both ways and see how it comes out. And doing it your way, it's going to come out two different answers and then we can move on right. But no, it was. This is, this is the way you do it and you need you'll need a proud for it too. So, like it reinforced that I should have no expectation that the, the passionate side of the ideas, would be connected to the school.
Speaker 4:So I, when I was doing the curriculum work, was excited about people who were doing work that tapped into that passion and those ideas and the what happens if? What happens if we do break the rules kinds of work that can happen in schools. I think CTM does a lot of that work. Matt did a lot of that work. We did a lot of that work in our work at Desmos. But I'm also interested in even if we could never, let's still open up that world right. Let's keep doing the work for children that Isaac Asimov did for me when I was a kid. So, yeah, that's why I'm excited about the ideas, because children have ideas, no matter what age they are. They have ideas about shapes and about numbers, patterns. Why not make those joyful to play with? Absolutely.
Speaker 4:So, really the only answer I have. Your question is well, that's why would, why wouldn't you?
Speaker 1:I wouldn't you get excited? No, absolutely playing with them. But thinking about that teacher, then thinking about this play, what, what kind of math do kids really need?
Speaker 4:like yeah, so I had a really fun conversation. So we haven't mentioned the blog. So I have a blog that I haven't written on as much these days because my children are older, called Talking Math with your Kids, where they start out in me documenting my own kids' math ideas and the ways they turn in conversations in our household. The unique perspective on this that not every parent is going to know to ask these questions. But the more parents I can get, more adults I can get to read like these possibilities, maybe the more of these conversations will happen out in the world.
Speaker 1:Yeah, now I forgot what the question was well, just what kind of math do kids need?
Speaker 4:oh, yeah, so. So this project and of course my kids knew about it. Like I'm sure they could see it in my eyes just like I could. I could seal it in my brain when one of my kids would throw something out there and I'd be like, ooh, I'm going after this idea. So, like my kids were not unaware of of this project and they had this really fun conversation with my son one day because I was going to like a parent math night or I was going to talk with teachers, we're going to do a parentath night.
Speaker 4:I can't remember exactly like what all the details were. He knew that I was going to go off and talk to him about some, some adults, about this kind of work and he was asking what, what is it? What are you going to do? Like I see you're going off, going off to do this. He would always refer to it as my math, that nerdy math and stuff. I was like, yeah, okay. So let me tell you Griff his name, let me tell you Griff about this project.
Speaker 4:Like my goal for this project has never been that you love math the way I love math. Like I can't make anybody nobody can make anybody love the things that they love right. Instead, my goal has been that math would never be an obstacle for you in whatever it is that you want to do. If you want to go into math, by all means, I'm here for it, but you probably odds are you're going to want to go into something else, but for lots of people that becomes a barrier and I want to make sure that doesn't happen. And I can see again addressing the child Griff you love more than anything else to argue. He's like yeah, if you love more than anything else to argue, he's like yeah. And I have seen over the years like I've seen a lot of times where math is the basis of that argument, whether it's about how things are fairly allocated, whether it's about the relationship between the price per unit. And I've seen you build arguments about the world. I've seen you build arguments against me and your mom that have a logical or numerical or pattern-based or shape-based component to them. So from my perspective, you don't love math, fine, but you're using it to do the things you want to do. Mission accomplished, baby.
Speaker 4:And he was like oh yeah, you should probably say that at the meeting. Then I was like I will. And I was telling him about this conversation for years to come. Yeah, so that's the project for me. I would love for math. When children have a passion for it, let's support it. When children just want to dabble in it, let's support that and let's do everything we can to make sure it's not a barrier. It was a barrier for my wife. She would very much have described herself, or probably still does, when I'm not around is like not a math person, right, always headed math, barely successful in school math. She is an artist, does a lot of beautiful artwork in which she has to think about shapes in ways that school didn't value, but that I can see the way she's composing things, the way she's working with symmetry, the way she asks questions of herself about how things ought to be arranged, like there's math there, but I don't need to convince her of that because I want to keep moral harmony.
Speaker 1:Good play.
Speaker 2:And I think there's some part of like you were saying before labeling it as math.
Speaker 4:Yeah, you can see that brain shut up. Right.
Speaker 2:There's a preconceived notion for many people based on their experiences in school math, primarily that that I don't and we can label it and call it a different thing and but we've done that like as an institution, as we're involved in right, we've done that absolutely to people.
Speaker 4:So I always apologize for that as well. Do a lot of that math on a stick. Yes, people are telling me how, how bad they are at math or something. I get it. I get it. We did that to you, yeah. But there's also I don't know what you two think about this there is a little bit of movements in the spaces we operate in for us to tell other people you are a math person and I think about that. I don't really I don't enjoy running. I enjoy running if it's like I'm a dog, like, and I think about that. I don't really I don't enjoy running. I enjoy running if it's like like I'm a dog, like after a Frisbee to go catch a Frisbee, or like after a soccer ball, like to go out for a five mile run. I can't, I'm not interested in it, it's not fun for me. And if someone like I had that conversation, if I were to have the conversation with someone and they were to tell me what my identity is, I'll tell you whether I'm a math person or not.
Speaker 4:So I try not to do much of that work. Instead I try to foster sometimes people. Their barriers are too high. Even if you think you're not a math person, there's still something fun that we can engage with here.
Speaker 2:You can still make something that is mathematically beautiful to me, even if you don't believe that it's mathematical, and maybe there's some common ground yeah, totally so, as we start to wrap up our conversation, is there anything in any of your projects or things you're doing that you're really excited about? That we haven't talked about yet, but you want to be sure to include here?
Speaker 4:well, I should mention the books. So you mentioned how, and that's the back cover of the book, is the pies with the picture of the book that is on the page? Of course it has to have the picture of the book that's on the page. It was how Many? That was the second one which One Doesn't Belong was the first one with Stenhouse. The real first book here's your trivia was Common Core Math for Parents, for Dummies. I wrote the Dummies book for Common Core Math back in the day and then there's a third Stenhouse book. So the Stenhouse books which one doesn't belong, how many? And then the third one is coming out in March and it's called how Did you Count.
Speaker 4:And so, if you've seen how many, you described the photograph on the back, but all the way through it's these gorgeous photographs. We hired an amazing photographer and a food stylist for how many? So, like the pie, the crumbs are just perfectly arranged, and all that we hired a different photographer. And instead of it being taking place in a kitchen for how did you count it takes place in a rec center here in city of St Paul, my old neighborhood rec center, and so I'm really excited about the photographs. I think of it as number talks meets how many and, as with the other books, there's a teacher guide that goes along with it that builds, helps, support teachers in thinking about where if I think of myself in this K-12 trajectory of children learning about arithmetic and algebra, in this K-12 trajectory of children learning about arithmetic and algebra, where what comes before what I do, where do I find what my kids are likely to do, which is a wider span than many of us imagine when we first start teaching and where our kids going? Yeah, trying to help teachers of a wide range of age ranges to think about how these images can support kids' development, no matter what grade level they're teaching.
Speaker 4:The sweet spot for that book is probably like third through fifth grade. But I tell you, these are photographs I wanted when I was an eighth grade teacher, when I was a college algebra teacher. A lot of triangular numbers, a lot of figurate numbers. There's a tetrahedron of basketballs which I have not yet left a fifth grade classroom, with everybody agreeing on how many basketballs are there. I have not yet left a fifth grade classroom with everybody agreeing on how many basketballs are there. It's, it's hilarious. Like you'll see it like kid, everybody thinks there's one in the middle. So it'd be like they'll have this elaborate, I count them this way, and then this is this, and at the very end it'd be like and then one in the middle is one basketball. It somehow is the core. The core of this tetrahedron I'll house is the the core, the core of this tetrahedron.
Speaker 2:Right now there isn't, there's not one in the spoiler. That's pretty impressive. You can put all the dashboards with that one in the. Yeah, is there one? At least space for one, I imagine, but still, it's a filling problem now, that's right interesting well thank you so much for coming on the podcast and having this really wonderful conversation. We appreciate your passion, your knowledge and skills, and that you are still a learner. I love that. I love that you're still running and doing things. So thank you so much.
Speaker 4:Appreciate it. If you're in Atlanta for NCTM next year, come say hi and the invitation is always open. Math on a Stick 12 Days of Fun ending Labor Day. It's always a Thursday, running through two weekends and we run and ends on Monday.
Speaker 3:Labor Day.
Speaker 4:And we run entirely on volunteers to come on out, help us out. They'll have a good time. You won't be the only out-of-town visitor. We get a lot of extra time.
Speaker 2:Yeah awesome.
Speaker 3:Thank you so much. Thank you. 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 pixabaycom. 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 1:It'll be November 12th, national Pizza with the Works, except Anchovies Day, and this is an odd little holiday, but we're celebrating pizza and things like that and for some reason they left anchovies off this day Now.
Speaker 3:I love a good anchovy on my pizza.
Speaker 1:So it's interesting that there would be a day that wouldn't celebrate just pizza with the works, or perhaps there is, but it's definitely not on November 12th. So join us then, and well, Misty and I will talk about our love of pizza and maybe our love or not so much love of anchovies. See you then. Thank you.