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 4.12: Where Joel and Misty talk about cheese curds and begin a conversation with Christopher Danielson
Have you ever wondered about the origin of cheese curds or how they became such a beloved snack? Join Joel and Misty as they kick off National Cheese Curd Day with some mouth-watering stories and a sprinkle of history. Get ready to celebrate in style with tips on how to enjoy this day, whether by crafting your own batch at home or setting out on a delicious road trip to Wisconsin.
Our episode takes an exciting turn as we spotlight Christopher Danielson, a trailblazer in transforming math education into a joyful adventure. Christopher shares his inspiring journey from teaching in St. Paul to spearheading innovative math play initiatives at the Math Happens Foundation. Discover how he encourages a playful exploration of math by challenging traditional educational boundaries, captivating communities with his imaginative approach.
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
X: @cpmmath
Facebook: CPMEducationalProgram
Email: cpmpodcast@cpm.org
You are listening to the More Math for More People podcast. An outreach CPM educational program Boom. An outreach CPM educational program Boom.
Speaker 2:Here we are, october 15th 2024. What is the national day today? Joel?
Speaker 1:Well, it's a good one? For me, I think yeah, it's National Cheese Curd Day.
Speaker 2:Oh, I do like me some cheese curds.
Speaker 1:Me too Nice.
Speaker 2:Yeah, when was the first time you ever had cheese curds?
Speaker 1:So I would say, the first time I remember experiencing cheese curds was the Minnesota State Fair.
Speaker 3:Oh.
Speaker 1:And since then anytime I get to the fair I eat the cheese curds, morning, noon and night. That was my first memory. And then I got to Utah and they were selling cheese curds but they didn't have like corn, like fried, around them. I was like, oh, they weren't like fried cheese curds, cheese curds.
Speaker 2:What is this stuff? Oh, so the first time you had them they were like cooked cheese curds.
Speaker 1:Yeah, they were delicious. How about you?
Speaker 2:I remember it was sometime, probably like at university or something, when I was in the Midwest. We were traveling somewhere it might have been like to the Upper Peninsula or somewhere but they had them and I had never heard of such a thing and they were quite delicious because they were like fresh and delicious. And since then I got excited because I saw them at grocery stores. Cheese curds they have my cheese curds here. You can buy them here in the grocery stores in Portland now. But they're like vacuum pack.
Speaker 2:And I mean they're not fresh, but they're like they've been packaged and they're not the same. I don't know.
Speaker 1:They're not as delicious. Exactly that's what I'm talking about the other worms. Well, so a couple things about cheese curds, because I started searching the history of the cheese curds and and the 1100s. There is a celtic song that makes reference to the cheese curd and it's like first reference to a cheese curd and the lyric is then I went in the door of it was hung beef, the threshold was dry bread, cheese curds on the wall. That's. That's the lyric.
Speaker 2:Did they tell you the rest of this song or just that obscure bit of out of context lyrics they have all the lyrics.
Speaker 1:Okay, there's not like a recording it's clearly metaphor the music. Yeah, I'm actually on a site called the quest for perfect curds and on that site you can see the true cheese curd history. There's links to the cheesy times or the cheesy underground, cheese Curds 101.
Speaker 2:So if you're interested, quest for Perfect Curds is what you're looking for the whole cheese culture Interesting, Interesting, yeah Well, I mean cheese curds clearly have been around since people started making cheese. Oh my gosh.
Speaker 1:And I remember one time working in the dairy I think this was cheese, but tell me what you think. I was the Sunday night pasteurizer. So I'd come in on Sunday nights and I'd start everything up, but on Saturday mornings, when the last pasteurizer left, we always started the buttermilk. So you start the buttermilk, you cook it and then, before you leave you cool it, or that pasteurizer had forgot to cool it, so it just kept cooking for a day.
Speaker 2:So when I got there it had curded over like the lid and there was a mountain of curd the size of me that I had to then shovel away. That to me is like a cheese curdds. I mean, I suppose the first cheese curds I ever actually had were cottage cheese.
Speaker 1:Yeah, there you go. Those are curds If you're from the Midwest or you know of the Midwest, high V cottage cheese with some ruffles delicious, Wow, okay.
Speaker 2:Any kind of ruffles, or just regular ruffles, just the regular ruffles, no flavor. You don't want flavors in there.
Speaker 1:You just want that salty, rigid edge to dip into your cottage cheese.
Speaker 2:I like large curd cottage cheese I'm going to have cottage cheese.
Speaker 1:Do you have a way you might celebrate today?
Speaker 2:I might have some cottage cheese actually.
Speaker 1:I was going to think about it, it sounds delicious, it does sound delicious. I do like a cottage cheese. Actually, I was not thinking about it. It sounds delicious. It does sound delicious. I do like a cottage cheese, I like mine with a little pepper.
Speaker 2:Oh, how are you going to celebrate?
Speaker 1:Well, the choices that are in my information say that you could take pictures, and every time you take a picture, say cheese, you could try and make some cheese curd on your own. I don't think I'll do that cheese. You could try and make some cheese curd on your own. I don't think I'll do that. Or you could go crazy and take a trip to wisconsin. Wow, to me that's actually suggested it's suggested. I don't think wisconsin is like the place to get curd but well, we're gonna have some pushback on that yeah, I think so.
Speaker 1:I I might I like your cottage cheese idea. I haven't had cottage cheese in a long time, all right.
Speaker 2:Sounds great, all right. Well, enjoy your cheese curd day, however you celebrate, and if you're in Wisconsin, then you clearly could take a trip to Wisconsin.
Speaker 1:Exactly Go crazy.
Speaker 2:So this week on the podcast, we are very excited to bring to you part one of our conversation with Christopher Danielson. Christopher Danielson talking with Christopher was a delight. Christopher Danielson, if you don't know, is the instigator, is the founder, is the primary person in charge and making happen the Math on a Stick at the Minnesota State Fair. If you've never heard of it, I highly recommend you go look it up. The Math on a Stick is a large-scale family math play space at the Minnesota State Fair every year. He also works on Public Math, a nonprofit that supports informal math experiences for families in public spaces, and so we'll talk about that. And he's also an author of three books, which One Doesn't Belong. How Many and how Did you Count? And you can find those anywhere that you can find books.
Speaker 2:He started teaching in 1994 in the St Paul Public Schools, earned his PhD in Mathematical Education from Michigan State University in 2005, and he taught at the college level for 10 years. After that, he's worked at Desmos, he's worked at Amplify. He now is doing his own thing and he is delightful in talking about all things math, and I also happen to know from looking at his bio that apples are his favorite fruit. Enjoy part one of our conversation with Christopher Danielson. All right, we're today with Christopher Danielson. All right, we're here today with Christopher Danielson. Thank you for coming on the podcast.
Speaker 4:Yeah, thanks for the invitation.
Speaker 2:Absolutely. I tried to do a little bit of background research on you and there's a lot I mean, there's just different things there, a lot of different projects and really exciting stuff. And we actually asked some of our coworkers if you had Christopher Danielson on podcast conversation, what would you want to know? And one of the questions was I loved this question was what is it like to play with math as a job?
Speaker 4:Yeah, well, it turns out that any job has administrative stuff that's got to happen right In order to make make room for the play.
Speaker 4:So, yeah, my my current title is director of Math Play at an organization called Math Happens Foundation. We are a private operating foundation, which means that we're not a grant-making organization, but instead we have funding stream and our job is to use that in order to spread math love everywhere we can. So what's it like to have math, I mean? But there is a certain amount of of playing that is that is kind of necessary. One of the things that's really interesting is that when you put for me. Interesting for me is when you put materials out, whether it's in like a situation where children are going to play with them, or, if we're talking about children, maybe you're going to play with them.
Speaker 4:We have it's almost like a personality test, like people have very different capacities for imagining what children will do, and it's not a thing. I would have really thought that there was expertise that I would develop over time, but it absolutely is a thing. And just like as a teacher right, when you're a first year teacher and you start making teaching prompts or writing quiz questions, you learn a lot in those first few years about what kinds of answers you're going to get. And it's exactly the same with math play. You develop instincts, you're wrong about it, like as a 10th year teacher, you're still going to be wrong about it. You're still going to write a test question and everybody's going to vomit, or it's going to be way easier than you thought because there was, like this backdoor technique for solving it and you wanted kids to do a thing that nobody did. And it's exactly the same with math play Like we'll be wrong sometimes you, you get better at it absolutely so what?
Speaker 4:so what's it like to have? So there is a certain amount of having to get some materials out and imagine myself as somebody who is known to these materials, to think about how we might play with them and how somebody who isn't me might view these. What, what might they find intimidating? What might, what opportunities might they find intimidating? What opportunities might they find? And that's super fun. It's actually the thing that I also love the most about the curriculum work. So my background is as a middle school teacher.
Speaker 4:I taught middle school for six years Very, very long time ago, and that was CMP, the Connected Math Project and got involved in a bunch of professional development work there, took a tour through grad school, got my PhD, taught casual for a long time and then was at Desmos and while I was at Desmos I was leading the development of the activities for the CC1, 2, and 3 series.
Speaker 4:No-transcript can be a lot like that. Yeah, right, uh, but without the standards. Like it's so nice not have to argue with my colleagues about you know, just so. It mentions, you know, polygons and fifth grade standard, but it doesn't mention polygons. And does that mean that we can't talk like we don't have to worry about any of that because we're designing for a much broader audience? If we're designing something we just uh started collaborating with, uh um, with an engineering museum here in the twin cities it's called the works we'll be there with what we call a math room, just bringing bunch of math play stuff into one of their classrooms for open play every other Saturday for the foreseeable future and we don't know who's going to show up there.
Speaker 4:We don't know what the audience is. I've spent some time in the museum, but not tons of time in the museum, but certainly one of the units that shows up there is families, and so last Saturday, a couple days ago, was the first time that we got into that space. Yeah, and there was a family that came through Three children, two adults and we had successfully found something for each one of them to do, although there was about a little bit more than one year old, who played with a little hexagon-shaped puzzle for about a minute, but his favorite game was clearly throwing one pattern block at a time onto the floor. That was extremely good times.
Speaker 4:Yes, we don't have standards because we're designing for that wide range, right? We want to keep a 40-year-old mom and dad occupied in the same way for similar amounts of time, that we want to keep the 8-year-old and the two-year-old occupied, and so that's fun I love. For me, that is most exciting, much more than getting down to the nitty gritty of one particular idea, one particular way of factoring that has to happen, like. I get that. That's all important in a particular context, but being able to let go of some of those constraints.
Speaker 1:When you're in that space, how do you promote the play? So I'm envisioning there's not maybe a task written there, there's just an activity.
Speaker 4:Yeah, that is like there's a delicate balance there between too open, so that some people get intimidated because they don't even know what the possibilities are. They can't imagine the possibilities.
Speaker 2:What am I supposed to do, yeah?
Speaker 4:Because I mean, play is also like a thing that you can practice and get better at, just like I can get better at anticipating what people are going to want to do. There's also, especially as you get to teens and adults, there can be like I don't even know how to engage with this, but math also brings that out in people no-transcript pretty useful, but it can also be a tool that you overuse. Is like with pattern blocks filling frames, right. So if we design an interesting set of frames that is compelling on its own, but then also once you start getting into it, there are lots of things that might like, ideas that might suggest themselves as you play around. We found that to be a really interesting space. My favorite example of that is from the large-scale math play space that I've been working on together with my Minnesota colleagues called Math on a Stick.
Speaker 4:That takes place in Minnesota State Fair every year. We just finished our ninth year. We just give you. It's a wooden frame that has a regular standard pattern blocks have a one inch edge on them. So we made a wooden frame that has a whole cut out of it. That's a two inch regular hexagon cut out of it, and they're using 21st century pattern blocks, which is a little set that I designed and that Dan Sinkle from Master Loves is now has turned into a whole commercial product. That is lovely, and the premise was that we knew there were lots of ways to fill this hexagon. We're curious how many there are. Must be at least a hundred right Within.
Speaker 4:So the stationery takes place for 12 days. We're there 11 hours a day, from nine in the morning to late in the evening, for all 12 days of the fair. And by the second or third day we had I don't know 150, 175 solutions, and each time you found a new solution we would take a picture of it with a little modern Polaroid camera, a little instant camera, and then we'd display them, and we had space for about 100 of them. But by the end of day two, like we were, instead of each one being like clothes pinned on, we had them taped in these long trains of snakes of photographs, and putting them away at night was a very delicate operation. All that, and by the end of that first, so by the end that first year of collecting them, we had about 250 different solutions for x-con challenge, with no evidence that we were anywhere close to done and at that point it was really fun to see volunteers. It's all volunteer runs, see volunteers every day, like having these conversations with a kid, because they would fill it and then they'd walk over. It was in the frame so they could carry, fill it and then they'd walk over. It was in the frame so they could carry the frame over and they'd look at all the pictures that we'd sort of tried to organize a little bit and there were some really productive conversations about what does it mean for something to be new? Right, and how do I like what do I look for? Yeah, so some really productive, spontaneous conversations that arose from this little challenge we had put out.
Speaker 4:The next year we made a book that had them the ones we collected the previous year, organized them, made a little book of them and then started taking additional pictures. We collected like another hundred pictures, but by the time that second year was done, by that time we had like 350 solutions. There were now so many of them that it was almost tedious, day after day, all day long, to be like our job was checking whether they had new solutions or not, and so we stopped collecting them. We made a beautiful poster of them, but we stopped collecting them and instead we have now a hexagon, hexagonal shaped frame that contains seven of the smaller hexagons, and so the new hexagon challenge is fill it seven different ways. Have mom or dad take the picture and then we have the poster. So if you think you know you want to see if you found a new one, awesome, go ahead, take a look. And if you think you found a new one, you take the picture, email, email it to us and we'll add it to our ongoing collection.
Speaker 4:Yeah, so the that idea of frames is is a way of inviting people in because there is a thing to do, but I also worry sometimes that the frame has been suggests that there isn't something else you can do. Right, I'm supposed to put them in the frame and I'm not. Also supposed, so we off at that same table where we have the hexagon challenge, in 21st century pattern box, we also put out big 12 inch vinyl mirrors taped together your basic mirror book, but nice and big, so you can really get your whole face in there. And yeah, kids will make fun designs and they'll put their hexagon challenges in there and take a look at how many of them hexagons they can spin around. Yes, we try to have a combination of it's clear how you might engage with these, but also it's clear that there might be other ways as well. Delica Valens inadvertently perhaps.
Speaker 2:I remember reading one of the things on one of your posts around. There's a fine line but as adults and how we interact with kids in that space, that can sometimes deter or limit what they're doing, also just because of our perhaps need to direct or need to point something out and you found really interesting.
Speaker 4:Yeah, that comes to from like there are hazards about labeling it math on a stick. Like, if you stand outside of math on a stick, we're outside on a I don't know 50 by 100 foot plot of land, like it's a pretty big space, but we have these two big popsicle sticks with an archway between them that says math on a stick, so it's bright and colorful and draws certain people in. But also, if you stand outside there and listen in on conversations, you'll definitely hear math Hi, what I do, math. You'll also get like some math majors from a local college who all want to take their picture in front of math on a stick but then they don't come in right and play with the math. We see all types, types and labeling. Math certainly has some consequences, and one of them is that parents have as a group obviously not all parents, but as a group on average parents have this sense that math is a right, wrong thing, that math is what happens in school, and so there's both a danger and an opportunity there. The danger is that, yes, parents are hovering over their kids, saying now, wait a minute, we're supposed to be engaging with it this way, or they're asking a lot of schooly questions. And one thing that we find we would love to have with kids in ways that suggest a goal or that suggest connections to school. The shorter the interactions are and the more parents or other adults engage in ways that take up kids' ideas, regardless of whether they're school-based or not. That tends to extend the conversation. So we do have in our second year at Math on a Stick that tends to extend the conversation. So we do have in our second year at Math on a Stick. We had a research team from Vanderbilt University that came out and spent all 12 days putting GoPro cameras on kids' heads and doing pre and post-interviews and collecting a whole bunch of data and they've written a couple of really interesting research papers.
Speaker 4:But we have this one. They have this one just beautiful video of this girl who's like 11 years old and she's sitting next to her mom Mom's kind of on her phone and the girl is playing with the eggs. So we have a bunch of plastic eggs and a five by six egg carton, which is how eggs come in balls, and almost nobody realizes that. Everybody assumes, looking at it, that it's square and so it's going to be six by six. Every day you realize, oh wow, it's square and so it's going to be six by six, which is every day you realize. Oh wow, it's five by six. So she has it turned so that it's six across and five high.
Speaker 4:She's trying to make a and, in particular, what she wants to do is she's trying to get the point of the heart where the, where the two lobes come together at the top. She's trying to get that really pointy while maintaining symmetry within the frame, and she just can't do it because, as we know as math teachers, there is no, there is no middle of six. Right, you got three on either side. You don't have, you don't have that one in the middle if you're doing discrete math. So you watch it and she rearranges it and every once in a while she pokes her mom does this, does this look right? Is this like art?
Speaker 4:I model say something or point out or something like this goes on before like 10 minutes. It's amazing and at some point she kind of pulls all the eggs out and she rotates it 90 degrees and then 15 seconds later she's got a perfect heart very satisfying shows her mom. They have a little celebration and away they go, like this beautiful little moment where mom was clearly playing a role in this extended interaction, but the goal was very much the kid's goal. Like the kid wanted to make this hard. Mom didn't tell her to make a heart. Mom wasn't telling her, no, that's a bad heart. Like the kid was internalizing but wanting to have that input from somebody else about how successful she was being. So that was that kind of thing we see, go on a lot.
Speaker 4:I wish I could say that everybody who picked up those eggs spent 10 minutes on their own goal-based idea, but it's not true. But so that danger is around labeling it math and of having parents feel like this should be school math is that kids don't get a chance to play because of parents' anxieties or because of their own anxieties, who then get projected on the parents. The opportunity, though, so you two are involved in math education, so you've met new people, and when you meet somebody new outside of the you know world of NCTM or XETM, odds are pretty good that somebody, if you meet 10 new people, odds are pretty good that at least one of them is going to tell you about how much they hated math or how bad they were at math, et cetera, et cetera, et cetera.
Speaker 4:I've heard that so at math on a stick. We hear that too, but it usually comes out not as I was always bad at math, but comes out in like a skeptical forms how is this math? But the opportunity there is. We have their kid right in front of us like we could do like a little. Let me show you what your kid's doing right now and they can see that their kid is having fun. We can connect it to school math without changing what the child is doing.
Speaker 4:If that parent came up to me as the child was trying to make the heart, I could have talked to them all about grid and pixel and problem solving within these constraints and we would have had symmetry and we would have had a great time. And about the middle right and how important that is when we're studying data, that the median sometimes is a number. That's impossible because it's between the two discrete values, and so we can have those conversations in a way that it's not about the parent's relationship with math. It's about what we can see the kid doing and how it is productive and the kid is having a good time and just bring some some good vibes to that anxious adult conversation I I can back that up.
Speaker 1:and a few years ago with cpm we were we were in minneapolis for a learning event and so a few of us volunteered at math on a street and I brought my daughter and my daughter would have been one of those voices out of 10 that would have said I'm not very good at math and and samantha was able to run a booth or one of the events and afterwards got so much out of watching kids play and their own play extended to wow this, this is math.
Speaker 4:This is crazy how old was your daughter at the time?
Speaker 1:Probably 22.
Speaker 4:Okay, nice.
Speaker 1:Yeah, so it was a lot of fun. All these things we're talking about adults and the kids and interacting here. We had a case where somebody had a mindset that was way different about math and left with a different mindset, so that was really cool.
Speaker 4:I appreciate that. We'd love to see that happen. Thanks for coming out and helping us make it happen.
Speaker 2:So I want a slight shift, a little pivot to. I know one of your projects is public math, which is related to these same ideas. So one of our questions was what is public math ideas? So one of our questions was what is public math? Unfortunately, that is all we have time for with our conversation with Christopher Danielson on this podcast. Tune in in two weeks for the next episode of More Math for More People to hear part two of our conversation with Christopher Danielson. Cheers, part two of our conversation with Christopher Danielson Cheers.
Speaker 3: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. It 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 October 29th, national Cat Day, and we'll take a look at all the different kinds of cats out there. I've had my share of cats and I'll share the story when we talk on the 29th. But from my childhood to adulthood I do have a dog. Now and I'm more of a dog person, I will say this year we've had a stray cat in the backyard this year and I have had much less squirrels and much less mice and such running around the yard. So that's been, I think, a good thing. So I can't wait to tell you all my tales. Hear Misty's tales. We'll see you on October 29th, thank you.