Dan Finkel, math educator and founder of mathforlove.com will share tips you can use to introduce your child to math and instill an early love for it.
Full Interview Transcript
Kelly: Dan, thank you so much for being here. I’ve been dying to have someone talk about math because it’s such a mysterious topic. I’d love to talk to you further, especially about having a young child and how you can introduce them in a positive way. So, thank you.
Daniel: Yeah, it’s great to be here. Yeah, math carries a lot of weight. It’s very fraught in our culture. There’s a lot on it. And I think it’s both, everyone has experience with it from our own time in school. And at the same time, I think it’s maybe one of the most misunderstood subjects. No one knows exactly what it really is, or very few have had real mathematical first-hand experience of the kind of matches like web mathematicians.
Kelly: why do you think people hate math so much?
Daniel: Yeah, I think that it’s really split. I think when you ask people, you’re most likely to hear that people love it, or they hate it.
Daniel: There’s not that many neutrals.
Daniel: And I actually think that they’re related. I think that people are born to love math, which maybe sounds controversial.
Daniel: Everybody, I think it’s nearly universal, I would say as universal or more universal than loving music for example.
Daniel: And I think that the reason is partly to understand what our sense of what math is, because in school, we’re used to saying, Oh, it’s just arithmetic or it’s just, you know, algebra, which is just arithmetic and some letters in it and it gets more complicated, but what it really is, is the study of numbers, shape, pattern and structure. And if you talk about human beings as being people who, especially babies, right, we’re faced with this chaotic world, and are slowly putting order on things and trying to understand how the world works. That is a very mathematical process. That is one of the fundamental gifts that mathematics gives you is, is imposing order on chaos. So I think that we’re born to love it. I think that what happens is, is when we are taught in a way where we’re either taught lessons too soon, and they don’t make sense. what I found is that kids as young as two and three start to have real ideas and insights about mathematics and about the structure of the world and ideas and when they go into school and are told, ignore your common sense, ignore your ideas, just do what I say I’m the teacher and I am going to tell you the right way to do it. We end up in this place where we understand the lesson and we got nothing at all because we actually reject our own common sense. And we end up hating it because we’re born to love it. And then it’s taken away from us.
Kelly: Interesting. So do you think some people were just born better at math?
Daniel: I mean, there’s always a range of dispositions right there. So in a way, if you think about it as putting some kind of word on the road, some people just naturally are drawn to think a little bit more abstractly, or join the shapes, are drawn to numbers. But you know, someone who’s drawn to shapes might get really into mathematics, or really, and someone who’s drawn to these kinds of patterns might be drawn to math or drawn to music or architecture or all sorts of other things. So, I think that there are different dispositions and different natural talents people bring. But I think that everybody has the potential to have mathematics be a part of their life in the same way that reading is a part of everyone’s life.
Daniel: One of the things we say is if there is a comparison between reading and mathematics, then there’s a question which is what we know to support reading, right? And we all know how to read for 20 minutes a day and our kids are like read a bedtime story. What do we do for math?
Daniel: One of the central ideas, I think, in doing math with young kids is to let play lead, to let that sense of fun lead and not get ahead of ourselves with wanting them to reduplicate what we know, but rather letting their own interest, take the first steps. I tend to advise people against even doing things like flashcards and things like that, because it’s fairly easy to just reduplicate the same mathematical experiences that we may have had that weren’t so good when math is something that very outside of us, as opposed to when we are approaching it in a spirit of play. And that can be playing with blocks and actually just naturally starting to see which are bigger and which are smaller. And if we can use these ones to build a shape that we want to build, and even just looking around the world, and noticing, that there are a certain number of things or that there is more of this one than this one, or that this piece of pizza is half this big as that piece of pizza.
Kelly: And not try to teach them something.
Daniel: Yeah, and just because that’s so many of our experience. It’s not a measurement of are you smart or not. But let’s just have a good time and see what we can see and have conversations and play around and see what happens. And that’s, I think, much truer to the sense of what math is. Mathematics starts with questions often. And for young kids, those questions are how many? and how big? And what is going on there? Is there a pattern or some kind of structure there? Even putting it into words for very young kids, it overlaps with a lot of the verbal development where it’s just about using words like on and below and inside and outside. We’re actually building the mathematical framework we’re going to be building on an elementary school with those kinds of ideas, as well as counting shapes.
Kelly: I think you have a really small child
Daniel: A 7-month-old, yes.
Kelly: Okay, so he’s very young, but I don’t know if you have any plan that what you plan to do with him?
Daniel: There’s actually a story about Piaget, which apparently he talked about the story of heard of the American problem, which was, as soon as American parents heard about the stages of development that he was describing, they asked, ‘Well, how do I get my kid into a faster? So that they can get ahead? And, so in general, what we’re trying to do with our son, is we’re trying to talk to him a lot and part of that talking involves counting sometimes and for snapping up snaps will count them when we do it. We will play games where you know, he’s a rocket ship and you have a countdown before you launch up into the air. So I’m just looking for natural playful ways to include numbers, or just being descriptive with looking for those times where instead of saying, Let me get you something to eat actually saying, oh, you’re going to have two pieces of broccoli right now and using the number of words where the shape words, but in a way that feels natural and connected. We’re trying not to say, Oh, you got this. You’re so smart. Because I think all that does set you up with this fixed mindset perspective of, oh, if you’re good at math, that means you’re smart. And that’s just something you’re born with or not born with. And we’re very much hoping for it to be the perspective of more growth mindset where you can get better at if you put the work in.
Kelly: Yeah, shove a bunch of flashcards like people do.
Daniel: There’s the whole world and then math is the thing we do, which happens in this little box. And that’s what flashcards seem to communicate. And I think that what we want to communicate more of math is integrated into the rest of the world. And it can happen anywhere. And it’s, it’s something that you do, it’s like a vision you can bring to bear when you want to look for patterns and structures in the world around you. And it can happen anytime, not just in our prescribed little math time.
Kelly: What are some of the mistakes that people do early on? That maybe can turn them off of loving math?
Daniel: I think the main thing is when it feels like something that somebody is making us do, that you’re not fundamentally interested in.
Kelly: I think that’s what it is.
Daniel: There always has been this thing of in colleges, they said tell the high schools, why aren’t the kids better and so then the high schools say to the middle school’s well they need to be good board. It goes all the way and then it’s kindergarten, and we end up often pushing ideas that the kids aren’t conceptually ready for. And I do think that if we could allow play to be central, we would.
Daniel: I feel like, from the ages of like two to eight, kids are very naturally starting to just count things in the world around them. The real gift is when you can encourage the curiosity and not get too worried about where you doing it all right all the time. The messaging we give kids is sometimes what matters is if you get a right answer and that’s the end of the story. I don’t care if people understand why it’s right. I don’t care if you were curious about that question to begin with. Just say the right answer so we can see that you are good at this thing.
Kelly: Right, I agree. So what are some like top tips you could give for teaching math
Daniel: One of the best things you can do is change your fundamental question when you’re thinking about math, or doing anything mathematics, mathematical with your kids from, do they have the right answer? to how is my child thinking? Let that be your guiding question. There’s a great line that somebody had about every wrong answer is the right answer to a different question. And there’s some way your child is thinking, that this is the way they saw it and wouldn’t it be interesting to know what’s happening in their head that led to that. I think that that is one of the main things you could do some shifting of your perception that I think is really exciting. And the thing is, that works at all ages– that works with that one and a half-year-old, who’s like scooping water between cups and might have some idea about how something happens. And it also works with a high schooler who is working on their algebra homework and just what is going on in your head. So that’s one thing and the second thing is just trust play as being what needs to happen for kids to get engaged with math. And I think there’s a lot of great toys and blocks and cards and activities that make play potentially more mathematically rich and gives you more possibilities for it.
Kelly: what are some of those toys that you think help to understand?
Daniel: I love like wooden blocks, anything that is sort of toys that just play in a very open way. Wooden blocks, Legos, Duplo blocks. Also, pattern blocks are super mathematically interesting they’re used in a lot of schools. They’re like yellow hexagons, red trapezoids and green triangles. You make these beautiful patterns with them. But there’s a lot of mathematics to see there and a lot of intuition to build. I have a game for three kids called Tiny Polkadot, which is essentially a mathematically enriched card deck. And this was something that we actually invented. My wife and I wrote the intervention curriculum for elementary schools for the summer program in Seattle. And we kept saying, oh, it would be great to play this card game that you need to take out the face cards, and it would be great if there’s a zero. Finally, we just decided to make the deck that could allow the mathematics to really be good for that. But I grew up playing card games constantly with my brothers. And I credit that with some of my early interests and ability with mathematics. And if you play cribbage, or that’s a game, you know, anyone who played cribbage as a kid knows how to make 15’s just instantly and there’s something about games which gives you the kind of practice and kind of playing around and seeing things that it’s just very hard to get any other way.
Kelly: That’s great.
Kelly: We have the game and my three or my four-year-old daughter loves the game like she loves the memory matching, loves it.
Daniel: A lot a games are very simple but there’s an idea that different number. Different collections of dots are united by the same number. It’s a very deep idea and very very exciting, I think for young kids to have a way to practice that.
Take the time to play games with your kids, play card games play, like when you have a three or four or five year old. There are a lot of great games out there. I mentioned ours, but they’re all sorts of collaborative games. They’re classic games. There’s even like pencil and paper games like tic tac toe and dots and boxes.
Daniel: mathanywhere.org is another really nice one where they’re actually trying to say, like at a bus stop, there maybe will be a mathematically suggestive picture. It’s just a question how many you see in this picture? And, it’s willfully ambiguous, it could be how many of this candy or how many of this candy and they’re actually different that you can actually have a conversation instead of just, oh, it’s this is the right answer. And involving your kid and cooking and letting them measure out the cups when they’re able to, is a great way to get thinking about accuracy and precision measurement and actually getting the intuition for those things. Some people love to craft. There’s a ton of mathematics in quilting and knitting, sewing and all of these projects, especially for young kids so rich and interesting.
Kelly: So many games. Yeah, time playing games. Now this is so informative.
Daniel: It deemed the culture as a race to Calculus, you know.
Daniel: If you look at like calculus is a 400-year-old subject. It’s weird to remember that, a lot has happened since then, a lot has happened before also. And just to get to the idea that like, like modern mathematics studies, thinks like the shape of the universe, but it also studies things like knots, and how can you mathematically tell them what knot is different from another knot.
Daniel: And also, the study of knots informs the study of the shape of the universe. So it seems like there’s so much more happening in mathematics. There’s mathematics that involves coloring things. There’s mathematics that involves infinity. I mean, there’s just so much strange stuff going on. And we’ve invented all that, not because someone was in a rush to get from Point A to Point B. But because someone took their time and said, I don’t know if I actually understand everything about it. That there was a lot more happening there than we realize.
Kelly: I didn’t know about history. That’s very interesting.
Daniel: It’s wild stuff.
Kelly: I really appreciate you coming in. I think it’s so hard to even find someone to talk about math, especially at a young age. And it’s been great to have your insight.
Daniel: It was really my pleasure and as much as possible, just, if we can approach it with play through fun, and changing our question to what’s actually happening in our kids’ head. Math can stop being something that is scary, and it can be something that’s fun for all of us. We all end up having more success.
Kelly: Where can we go for more information about your games?
Daniel: So my website is the math for love.com. That’s all spelled out.
Daniel: And that’s, you can see all my stuff for kids and teachers. I write puzzles. And then also we have two games Primetime and Tiny polka dot that you’ll see there.
About Dan Finkel
After completing his PhD in mathematics at the University of Washington, Dan decided that teaching math is the most important contribution he can make to the world. He's devoted much of his life to understanding and teaching the motivation, history, aesthetics, and deep structure of mathematics. Math is a maligned and mistreated subject, often mis-taught, often misunderstood. His goal is to give everyone the chance to fall in love with mathematics. Whether you excel or struggle, whether you’re a teacher or student, parent or child, if you want to learn what math is really about, I can help.