Re: The Heinemann Science Scheme Book 2 Answers
Melanie Council
Today we are passing things over to Kent Haines. Kent is a Heinemann Fellow Alum and middle school math educator based in Alabama. He is joined by Dan Finkel, founder of Math for Love, a Seattle-based organization devoted to transforming how math is taught and learned.
Kent: I am a big fan of games, both inside and outside the classroom. When I'm at home with my kids or spending time with friends and family, there is nothing I like more than pulling out a board game. But I also love the catalytic effect that games have in the classroom. There's just something about a little strategy and competition to get my students thinking deeply about math. So I am thrilled to talk today with the inventor of some of my favorite math games, Dan Finkle. Dan is a math educator, and the creator of Prime Climb, a board game for upper elementary kids that my middle schoolers love, as well as Tiny Polka Dot a set of games that are perfect for preschoolers and early elementary students. He has thought a great deal about what makes a math game great, how we can use them in the classroom and how parents can instill a love of math in their kids by using games. Dan, thank you so much for being here.
The second layer is that games involve a kind of thinking that is deeply important in mathematics. Kind of an if/then thinking: if I do this, what will my opponent do? If I make this choice, is there a better choice or will I be able to get taken advantage of somehow if I do that? This kind of thinking, to imagine the game from your opponent's perspective, to consider whether you've done the best thing, or if there is an even better way to go, that kind of strategic thinking is really important in mathematics also, and you're practicing, I think, some of the deeper skills of a mathematician.
And then at the third level, and maybe we're getting quite deep here, there's a way that games actually put you in touch with some of the heart of what mathematics is. And by that, I mean that there's a lot of mathematics that has to do with setting some set of rules. Maybe it's the axioms in your system. Maybe it's a kind of technique that involves some particular approach. And there's this question of what is possible here? What is the realm of possibility? And then in a game, you're thinking about that in order to see what's possible.
I think... And similarly, in mathematics, some little rule changed like, oh, what if the parallel postulate were different? What's possible now? In a way you see, okay, rule change and now what can we do? This act of playing with rules and within rules and in the space generated by rules, is in a very real way, what deep mathematics looks like. So really at every level, I think it is a huge win to play games in math classrooms and when you're learning math.
Kent: And when I see students playing math games in a lot of classes or even the games that they try to play in my classroom when we have free time, I see a lot of digital games that to me feel like they're not taking full advantage of those elements of math, that show up in games. So I remember when I was a kid, I played a game called Math Blaster, which was you were shooting asteroids, but the asteroids just had an addition problem on them and you just had to type the sum and then it would shoot the asteroid or whatever.
Kent: Yeah. Okay. And then another one was, I think it was called Number Muncher or something, where you had to eat different numbers. And there was one category called the Primes, and I actually memorized all the prime numbers under 100 by pure trial and error. Like just, oh, I ate that one and I died, so I guess that number's not prime. And I had like a sheet of paper that had a list of all the primes, but I had no idea what a prime number was. But people would say, well, those are math games. So what makes a math game rich or interesting or deeply mathematical to you?
Dan: Yeah. There are two things that I think really you're looking for. And the first is that there's some element of choice in the game. And this is often where the paper and pencil curricular games fail is they say, Hey, instead of doing this edition problem, you're going to roll these dice and it'll give you two numbers and then you add those numbers together. And really you're just rolling your own worksheet, but there's no choices, or whoever rolls the biggest number wins. It's just there's a lost opportunity when there's no choices. But the other piece is that math should really be the engine of the game. And this is something that I think about a lot, because every time it's not, every time ... Like any of those games you're describing, it could have been a math game, but it could have been a spelling game. It could have been a historical facts game. It's just a thin veneer of you're playing something and then there's some question you have to answer.
And I always feel like those are a missed opportunity and even worse, they send a message that doing the math in that context is like the quarter you have to put into the game. It's the toil and the annoying work you have to do to actually do the fun thing. The fun thing is shooting the asteroids or munching the monsters or whatever you're doing. The annoying thing you have to do to get to that part is to solve the math problem. And I think that those end up being ... They're very easy to make in a way, because you can slap together some very obvious game and just put that veneer of, okay, here's some arithmetic to do. And because people's conception of what mathematics is so narrow, it's always like, oh, here's arithmetic, here's a new thing to memorize. So we'll just slap that on. And that piece of math not being at the heart of the gameplay, is what makes those games so thin and I think fundamentally does really represent a missed opportunity.
Kent: I would love to try to zero in on an example then, of a great game and hopefully a fairly straightforward game that we can talk about, where math really is the engine as you say, where the interesting decisions or choices that you have to make are mathematical choices. Do you have an example or two of a game that you could use that you feel like does meet your criteria of a good math game?
Dan: Yeah. So there's a really simple game for example, called Don't Break The Bank. I learned this game from a book of dice games, and this was something that they were playing in like 18th century Irish pubs. And that's a good sign that it's actually a good, interesting game.
Dan: Exactly! Shut the box is in this category also. People were playing this not to learn math. They were just choosing to do it because it was fun. And this is a game is a great game for the classroom. Super simple. You just roll a dye, you roll it nine times in all. And over the course of those nine roles, after every roll you fill in nine spaces that form three, three digit numbers, and your goal is to make those numbers sum to the highest amount possible that's not a four digit number. So if you go over 999, you've busted. So you roll a six, where you going to put that? Should that go in the 100s column of your first number? Or maybe you'll put that in the 10s column, or maybe you should put it in the ones column. What's the best place to put it? A very simple choice, but choice is in there and it's fundamental to play the game and math is very much at the heart of the game.
That's not a game that could be a spelling game or any other kind of game. It is very specifically a math game, and yet it is addictive. I've yet to play it with a group of students where they haven't begged to play again. And what's even more interesting is that students want to play it so much, is I had a breakthrough with a teacher once where she taught her third graders this game, and she came back to the professional development session a week later. And she said, well, I found out that a number of my students don't actually know how to add three digit numbers. They just been faking it, but that was the time when they wanted to do it. And suddenly they started asking her and asking each other how you actually add the three digit numbers, because they were genuinely motivated for the first time to actually understand how that worked.
Kent: Okay. So this is great because I'm imagining a teacher listening to this and they're working with elementary students on multi-digit addition and they're like, oh my gosh, this is perfect. I'm going to use this in my classroom. And I do think that just playing this game would actually do a fair amount of work to get her students excited and engaged about playing the game and therefore practicing their mathematics. But as a teacher, I'm still not 100% satisfied unless I feel like I'm getting every little bit of learning out of this activity. We're deviating from our normal routine to play this game, so how do you see a teacher being able to leverage the underlying interest in this game? Kids want to have fun. They want to play, they want to learn the strategy and how do we make this as strong a learning opportunity as possible, where the kids are really learning something deep about numbers and about addition?
Dan: Partly this is going to depend on what your ambitions are as a teacher. And I will say there are, for some teachers, there is the sense of, I don't have time to spare. And in those cases, I think the idea of the, I'm going to spend five minutes on this opening game or this closing game, I've got an extra couple minutes at the end of class. Let's play this game rather than just do nothing. And that actually represents a real sort of huge possibility and huge motivating kind of place to go. However, if you are now saying, "Okay, I want to go deeper into this game or deeper into any game. "One of the places and one of the questions you can always come back to. And this is when your game has choices involved, you can always do this. Is you can start a discussion around, "What is the best way to play this game?" Or, "What is the strategy you use to play this game? Is there a better strategy that you could have used?"
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