Mathematical Games Inside The Classroom

Teaching Mathematics | 0 comments

The teaching and learning of mathematics is often not very fun, but my guest today is all about helping educators see that play is really the engine of learning. I hope that you will stick around because I have a guest speaker today, Dan Finkel, who is going to talk about mathematical games in the classroom as we work to build our math minds so that we can build the math minds of our students.

Watch the video or read the transcript below:

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Before Dan gets started, I want to share this awesome short video that he created about his three top tips to make games be easier to implement in your classroom, so watch this and then when we come back it’ll be me and Dan here for you today.

Hi, I’m Dan Finkel. I’m the founder of Math for Love.

So I am a mathematical game designer, that’s one of the things I do, and the way I got into that was I built a lot of games to be used in the classroom. And I would like to share my top three, main fundamental points about using mathematical games in the classroom. So here they are.

Number one, choice needs to be a part of the game.

And this is really a failure of so many standard textbooks for kids of any age. They say okay, here’s the game, you roll this die, and then you write down what you get, and then you add these things up and then whoever gets the highest amount wins, and there are no choices to make. And that might be more fun than a lot of normal lessons, but it’s missing a huge opportunity.

Because first of all kids will get tired of games where there are no choices way faster than games where there are choices. Second of all, there’s no strategy, and as soon as you have a choice, there’s a question which is did you make the right choice? Would this have been a better choice? You can start having questions about the strategy of the game and these become a great opportunity for mathematical richness to enter the classroom.

So, look for games with choice, and really emphasize that choice, and ask kids about why they made the choices they made. This is just using what games have to offer in a way that supports mathematical thinking in the classroom. So that’s one, choice.

Number two, math should be the engine of the game.

And here the biggest culprit is online games, flash games, computer games. When they are trying to use math it is the classic way they do is you’re flying a little airplane, you’re having a great time and then something happens it stops, you’re running out of fuel and you need to solve this math problem in order to get past it. And literally what that is teaching is the game stops, the fun stops, mathematics is you know the money you need to put into the video game machine to make it keep going again. It is the suffering. It is the work you have to do so you can have fun and that’s just not the lesson we wanna teach about mathematics.

Playing games where math is actually an element of the game or ideally the engine of the game, that teaches the different lesson where the better you get at the math, the better you get at the game. The more you see the more options you have. The more powerful you get at the game, and what we ideally want people to see, and this is true about the world, is if you really know math it’s almost like you’re cheating. You just know too much. You can win the game. So that’s two, math should be the engine of the game.

Number three, it should be simple to use and quick to play.

And that’s just because as a teacher you have to get in there and it can’t be too long. I love the game cribbage, great game, I’ve never used it in the classroom because there are just too many little strange rules. Great math game though.

So, those are my three rules. Number one the game should have a choice. Number two math should be the engine of the game. Number three it should be simple to learn and quick to play. Look for that when you play games in the classroom and you will see what they can do to transform the way your students respond to mathematics.

Why Should We Use Games In The Classroom

[CHRISTINA] All right weren’t those three just such great tips for helping us implement games into the classroom. And you guys I can not believe it but I have Dan Finkel, the guy in that video, right here with me.

[CHRISTINA] If you don’t know Dan, he is the co-creator of two fabulous games, Tiny Polka Dot and Prime Climb with Katherine Cook and I am so honored to have him here today to talk about math games. Because he is all about having the play be the engine of learning and you can find out more about him after this video at his site mathforlove.com because math should be something we love right Dan,

[DAN] Yeah, absolutely.

[CHRISTINA] It’s one of the powerful things. I want to start off with why we should be playing games and I know for me personally, I think the love of math came from playing games. I grew up playing games.

[DAN] Me too, yeah.

[CHRISTINA] But as a teacher how can we help build that, why should we build it??

[DAN] Yeah so, it’s totally the same for me. I grew up in a game playing family. We were always playing games and I realized when I got to school that I had an advantage in math over the kids who didn’t play games. I just knew so much arithmetic so quickly because I’ve been playing cribbage like a maniac with my brothers and I just had those sums to 15 in my blood.

But I think that the use of games in the classroom is really enormous. They’re great for skills practice but they’re also great for deeper thinking. They’re great for motivating students and engaging them, and they’re even useful as formative assessment.

For me there was an amazing moment that happened when I was teaching a workshop for teachers and there’s a third-grade teacher in the class who came to the workshop, she was a little skeptical, she went back to her classroom. She tried out one of the games that we had taught in the workshop and she came back the next month to the next session and she said well I found out that my students don’t know how to add. Not all of them, but there were some students in her classroom that had been hiding and no matter whether tests or formative assessment or questions she has done, lessons she’d done they had been able to slip through the cracks.

But when she had played this game, the students wanted to play and so for the first time they’re desired to be involved was so great that when they couldn’t do the addition, they actually showed it. They would ask her or ask the other students how to do it and then she said the more amazing thing was other students would actually help those students to learn it themselves. So she had students not only showing that they didn’t know it and want to figure out why, but also other students then explaining the work to those students.

So, with one minor change, a seed change in the culture of the classroom, and that’s a game I’ve actually come back to again and again. That’s one I’ll talk about in the course when we get there for sure, yeah.

[CHRISTINA] Awesome. So you kind of mentioned it there, but one of the things that you’re doing with build math minds, is we’re gonna be offering a mini-course all about using games in the classroom.

[CHRISTINA] Now for those who don’t take it, we wanted to give some information though, just to get you started because we both really feel like gameplay is so powerful. So whether you take the course or not, but there’s often a lot of resistance to implementing games in the classroom. I’ve heard from teachers all the time, they play games in their home life.

Why Don’t Educators Implement The Use Of Games

[CHRISTINA] But then doing it in the classroom, it’s often like a really big step to get teachers to take. So why do you feel like there’s so much resistance and how do we help teachers combat that?

[DAN] Yeah, I think that part of it is, you know when we’re teaching we’re in a system and things don’t always go the way we want them to go. We feel like well we have this curriculum we have to abide by, or our administrators are going to be looking in and there are these impediments that feel like they are real and we’re worried well if we take the time to use this game in the classroom then what are we gonna be leaving.

Are our students going to be behind? I would say though that it’s actually really the other way around. You said one of my favorite lines that play is the engine of learning and kids in active playing are really engaging themselves as full learners, and we want to use that in the classroom, so even though it can feel like there is a risk of not covering everything we need to cover or getting into an amount of trouble, what I’ve seen is administrators actually want teachers to be using games and engaging kids in a playful way in the classroom. That’s usually a positive.

Second, using games tends to pay off in a huge, huge way. And if you’re worried about actually the cost in time and the other things you have to do, what you can find is there are games you can play in just five or 10 minutes. You don’t have to change your whole lesson, it can just be a little change you make with the time you already have and it’s time really well spent because you’ll find the students just so engaged and interested in playing.

And finally and I think this is really maybe even more central, I think that there’s something culturally in all of us that we, it’s hard to believe that you are really learning math if you’re not just feeling miserable. Because we all kind of were taught this lesson that you’re supposed to suffer. You’re not supposed to enjoy this, and the idea that you can actually be having a great time in math and because you’re having a great time maybe you’re learning even more.

That is actually a really challenging thing and it’s something we have to contend with. I’ve been introduced in classrooms by people saying it’s time to stop having fun and learn math. That’s been my introduction by a teacher.

It communicates to me how deep it is that we say well this isn’t supposed to be fun. This is supposed to be miserable, but in a way, games can be one of the first steps to actually reversing that and say you know what, we can actually enjoy this and we can learn it better as a result.

[CHRISTINA] I totally agree. It often times, it just feels like sometimes the math just seems like it becomes a chore.

[Dan] Mmhmm.

[CHRISTINA] Not something that we do for fun.

[Dan] Yeah.

[CHRISTINA] I mean, and we want it to be fun. We want to build that love. That’s why I love your site mathforlove.

Where Should You Start

[CHRISTINA] All right so we are gonna actually end here with a place for everybody to start. So we’re ending this video, but we’re gonna give people a place to start. If you haven’t done games, you’ve been wanting to do games, and you’re just not quite sure where to start, Dan’s video that I played before gave some tips, and Dan and I are actually gonna play a game right now.

[DAN] Yeah.

[CHRISTINA] And tell you how this really can be something simple to implement in your classroom. So, tell us about this game.

[DAN] Yeah so this is a game called 31, and it does exactly what we want to do. This is one you can take right now. You can find five minutes and play it. It is simple to learn, quick to play. Math is the engine of the game, and it also has a choice involved and even though it’s a very simple choice, it can actually lead us to go beyond the arithmetic that is in the game and into some really interesting and really deep thinking, which that’ll be kind of the puzzle for you the listeners and viewers right now to figure out. Because there is a way to win this game, but I’m gonna leave it there.

The way the game starts is, you can play this with two or more players. The real mystery kind of really comes out especially with two. So it’ll be good if the two of us play it. So, Christina, we’ll go back and forth. I’m gonna start by saying 31, and the next number you say can be any number, either one less, two less, three less, four less, or five less than whatever number I said last.

You subtract any number from one to five from the last number I said, then I’ll subtract any number from one to five from the last number you said, and we’ll go back and forth making the number smaller and smaller until one of us says zero. And whoever says zero wins. That’s the whole game, and if it’s a little confusing to hear it, I think just seeing it will make it really clear.

So I’ll start it off. 31.

[CHRISTINA] Okay, I’m gonna say that I’m gonna go down two, and that would get us to 29.

[DAN] Great. So we’re at 29, I’m gonna say 29 minus five and that is 24.

[CHRISTINA] Okay I am going to do 24 minus five as well, and that gets us to 19.

[DAN] Okay, 19 minus two is 17.

[CHRISTINA] I’m going to minus five again, so that gets us to 12.

[DAN] And I will do 12 minus two, that’s 10.

[CHRISTINA] I think you got me.

[DAN] I don’t know, I don’t know. I don’t know. We’re at 10.

[CHRISTINA] Oh, okay.

[DAN] Yeah I think you might have a way to beat me here. This is something if you’re a teacher, you might want to encourage students to look and be like oh do you have a way to beat me? Maybe not. Sometimes you just have to take a shot and see what happens.

[CHRISTINA] Okay, I’m just gonna subtract one. 10 minus one is nine and I think.

[DAN] And I’ll do nine minus three is six.

[CHRISTINA] Oh, dang it. No, I didn’t have you. Okay, so I have to do something that is five or less so right here I know that Dan’s got me.

[DAN] You’re already seeing ahead in the game. Kids won’t see this, but they will on their second game usually.

[CHRISTINA] Ha, ha, ha.

[DAN] So let’s finish it up. So it’s at six, so what are you gonna do.

[CHRISTINA] Six minus five gets us to one.

[DAN] And then I’ll say one minus one is zero so I win that game and that’s how the game works. This is a great one. I recommend when you try it in the class. Demo it with a student to just make it clear. Because the rules, it’s always hard to learn games from just hearing the instructions. You really wanna see a demonstration game, that’s one of the ways to make sure that students actually understand it. It’s terrible to learn games by reading instructions or just hearing them.

But then once people see it, then they’ll be ready to go and this one is, you can see how we were laughing even playing it. This is one that it’s so simple but students will really enjoy playing this. I think it’s a great first step for a game to play and if those numbers are too hard, make them smaller. You can start with 10 and take away one or two. So that’s a great game for younger kids.

[CHRISTINA] Yeah and the upper-grade kids, I can see already even though the mathematics that they have to do here is simple and should be stuff that they are fluent with, the piece that I love is that choice and strategy. Because now we are thinking and we have to think a couple moves ahead and try to strategize. And the mathematics incorporates all of that. It’s not just about the content that we have in the game, it’s the other things that kids are learning that.

[DAN] Do you know what’s amazing about this game actually? This is a nim style game. It’s in the family of nim games. There’s actually modern mathematical research happening with games in this family of games, nim. There’s actually a whole mathematics forum called nimbers which are based on these game positions and a lot of these games are still on. This one is though, you can figure out how to play this one perfectly, but there are others that nobody knows how to do it.

[Christina] Wow.

[DAN] Something really exciting about that.

[CHRISTINA] Yes, yeah, yeah that challenge. It can really spark some of your kids.

[Dan] Yeah.

[CHRISTINA] Who may not feel that spark in mathematics.

[Dan] Yeah, absolutely.

[CHRISTINA] Yeah. This was really awesome, thank you, Dan.

[Dan] Yeah.

[CHRISTINA] Again it hits those pieces of, it gives kids a choice.

[CHRISTINA] Mathematics is the engine.

[Dan] Yeah.

[CHRISTINA] Yeah. That makes this a powerful game.

– [Dan] Yup.

[CHRISTINA] It is so simple to do. I mean we didn’t even need anything.

[Dan] That’s right.

[CHRISTINA] No dice, nothing to get this going in the classrooms.

– [Dan] Right.

[CHRISTINA] So our challenge to you is to go try that game with your kids, modify it if you need too.

If you enjoyed it, you saw some powerful stuff, Dan and I would love for you to come and join Dan’s mini course where you can learn so much more about implementing games and learn even more games like this to use in your classroom.

There is one for PreK-2, and one that’s geared for 3rd-5th because the challenges of implementing this in those grade bands are slightly different and things you want to watch out for.

So click the link below and get more info on that.

And Dan, thank you so much for helping to build our math minds so that we can go out there and build math minds of the students we work with.

[DAN] Absolutely, super fun. I’m really looking forward to this.

[CHRISTINA] Awesome, have a great day everybody.

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As you start off the school year, I want you to keep in mind what is really important as we're trying to teach mathematics to our students.