Jason Dyer writes a very important post highlighting Tiny Games, a listing of games you can play quickly, almost anywhere, with only limited materials. He then pivots to ask about tiny math games.
Could one make an all-mathematics variant — mathematical scrimmages, so to speak?
His post, and Tiny Games, are important because they reject an article of faith of the blended learning and flipped classroom movements, that students must learn and practice the basic skills of mathematics before they can do anything interesting with them.
For example, here's John Sipe, senior vice president of sales at Houghton Mifflin Harcourt, talking about Fuse, their iPad textbook:
So teachers don’t have to “waste their time” on some of these things that they’ve always had to do. They can spend much more time on individualized learning, identifying specific student needs. Let students cover the basics, if you will, on their own, and let teachers delve into enrichment and individualized learning. That’s what the good teachers are telling me.
This is a bad idea. People don't mind practicing a sport because playing the sport is fun. It's easy to tell a tennis player to practice 100 serves from the ad side of the court, for instance, because the tennis player has mentally connected the acts of practicing tennis and playing tennis. The blended learning movement, at its worst, disconnects practice and play.
Take multiplication of one- and two-digit numbers for instance.
If you need to learn multiplication facts, one option is to watch a video and then drill away. Or we can queue up all that practice in a tiny math game that'll have students playing as they practice:
Pick a number. Say 25. Now break it up into as many pieces as you want. 10, 10, and 5, maybe. Or 2 and 23. Twenty-five ones would work. Now multiply all those pieces together. What's the biggest product you can make? Pick another. What's your strategy? Will it always work? [Malcolm Swan]
Easy money says the student who's practicing math while playing it will practice more multiplication and enjoy that practice more than the student who is assigned to drill practice alone.
Jason Dyer helpfully highlights two examples of tiny math games, Nim and Fizz-Buzz, but he and I are both struggling to define a "tiny math game." The success of the Tiny Game Kickstarter project indicates serious interest in these tiny games. I'd like to see a similar collection of tiny math games. Here's how you can help with that.
1. Offer Examples of Tiny Math Games
This may be tricky. We all have games we play in math class. What distinguishes those games from "tiny math games?"
2. Help Us Define "Tiny Math Games"
This may be a better starting point. I'll add your suggestions to this list. Here are some seeds:
- The point of the game should be concise and intuitive. You can summarize the point of these games in a few seconds or a couple of sentences. It may be complicated to continue playing the game or to win it, but it isn't hard to start.
- They require few materials. That's part and parcel of being "tiny." These games don't require a laptop or iPhone.
- They're social, or at least they're better when people play together.
- They offer quick, useful feedback. With the multiplication game, you know you don't have the highest product because someone else hollers out one that's higher than yours. With Fizz-Buzz, your fellow players give you feedback when you blow it.
- They benefit from repetition. You may access some kind of mathematical insight on individual turns but you access even greater insight over the course of the game. With Fizz-Buzz, for instance, players might count five turns and then say "Buzz," but over time they may realize that you'll always say "Buzz" on numbers that end in 5 or 0. That extra understanding (what we could call the "strategy" of these tiny math games) is important.
- The math should only be incidental to the larger, more fun purpose of the game. I think this may be setting the bar higher than we need to, but Jason Dyer points out that people play Fizz-Buzz as a drinking game. [Jason Dyer]
What can you add to our understanding of tiny math games?
2013 Apr 17. Nobody wanted to tackle the qualities of tiny math games, which is fine since you all threw down a number of interesting games. I'll be compiling those on a separate domain at some point soon.
Jason Dyer elaborates on his contribution above.
Other teachers go in on the lie that students need basic skills before they can do anything interesting in their disciplines:
2013 Apr 24. Jason Dyer elaborates in another post.