Monday, July 24th, 2017

Games Aren’t Fun

Sad game pieces on a gameboardHow would you finish this sentence?

Students love classroom games because _______.

I’ll make a bold claim: It isn’t because they’re fun.

“Fun” is about lighthearted amusement. Frivolity. Laughter and playfulness.

Some classroom games might have these aspects. In fact, I hope you are enjoying some laughter and playfulness during your classroom games. But I don’t believe this is why students love classroom games.

It’s not because they’re fun. I believe it has to do with:

  • Achievement. There are goals and those goals are attainable and satisfying to achieve.
  • Wonder. The game has multiple pathways to achieving the goals.
  • Growth. By playing the game you grow — in understanding of the content, how to work with other people, in some metric, or in a way that’s a side effect of the original goal.

Tag, You’re It

Consider the game of Tag. A global phenomenon, the game of Tag can be found in almost every culture and time period. Avoiding being “It” might be the goal, but to do so you can employ speed, cunning, or some strategy borne of experience. It involves social organization, conflict resolution, cardiorespiratory fitness, hand-eye coordination, spatial recognition, and a host of other areas of positive growth.

But though kids will say they play Tag because it’s “fun”, I believe it’s because they are engaging with their peers, being competitive, and — in a nutshell — doing what their bodies and minds were designed to do. There isn’t any frivolity here; Tag is serious business! There might be laughter, but there is just as much drama and pathos and fear and triumph.

Is Your Classroom Game Fun?

If the primary goal of your classroom game is to have fun, then I think you’re off track. Instead, ask yourself if the game you’re playing gives everyone a chance to achieve something and to figure out their own ways to get there. Does your game show them how they’ve grown in their ability to play better over time? Try recording times elapsed, or points scored, or any other metric. A good game automatically gives them feedback, like a basketball hoop gives you feedback on whether you scored or not. Find ways to build community through competition. And when you hear the words, “This is fun!” make sure you immediately respond with, “Why?” Then you’ll get to hear the real reasons why your students love playing classroom games.

Saturday, June 18th, 2016


Solutions to making 24 using 1, 9, 5, 2I love the game of 24. Two marks of a good game or math problem are that it doesn’t take long to explain the rules and you can jump in right away. 24 has both of those. If you haven’t played here are the rules:

    1. Take 4 digits
    2. Make 24 using arithmetic operations
    3. Use all the numbers, but only once

With the card game you get to claim the card if you’re the first to solve it, and then you grab another card. But we play it in our classroom more like this: students walk in, start finding solutions on their whiteboards, then we progressively share them out on the classroom whiteboard. We play every Tuesday morning for grades 6–8.

As with all teaching the beauty is in the execution. So what’s the best way to play 24?

At a recent math conference I heard Judith Montgomery from MBAMP explain how she flattens the slope for entering into 24. First things first: a number talk! Put the number 24 on the board and let students respond. Why 24? 24 hours in a day? 24 pickles? And eventually someone will say something like 20+4 and then you’re off.

Interestingly enough she does not do what I want to do and jump right into the rules of the game. No, the number talk winds down and the game is never brought up. And then you return to 24 later — maybe the next day, maybe the next week — and start another number talk. I love this. Because not everyone sees factor pairs when they see 24. Let the students lead you there (as you refine where they’re going).

Tips & Tricks

As students play 24 the tricks for finding them will come out and you should highlight them as often as possible. I urge you to not just give these away. Let them arise naturally. Introduce them over time, not in the same day or week. A few to look out for:

  • Make factor pairs: 8×3 and 6×4 will appear quite often
  • Find points that are n units away from 24: If you have a 6, try to make 18 or 30 with the other numbers (And be sure to bring this up when you are working on absolute values, like |x-6|=24)
  • Use perfect squares to yield other numbers: If you have a 4, you have a 2, since √4=2 — likewise with 9 and 3

The rules of the game will establish themselves. In our classroom students want to go beyond the basic four arithmetic operations. “Can we use exponents?” “Can we use square roots?” (hence that last trick above). When you allow them, they will take off. If some students don’t understand right away how to use these other operators, that’s okay! I promise they will want to once they see how advantageous it is to have those extra tools. As the months go on in the year I might drop a hint on a new method, especially factorials.

Using! factorials! in! 24!

Here’s where it gets really interesting. Eventually when playing 24 a student will get really excited about their solution and write something like this:


And I can say, “I appreciate your enthusiasm, but did you know that ! is a math symbol? In fact, 24! is a really, REALLY big number.” [fun fact for chem nerds: 24! is really close to Avogadro’s constant]

Once the students know that 24! = 24 x 23 x 22 x … x 1, then you are about 30 seconds away from someone saying, “Hey, 4! is 24. Cool!” And now they have a new trick:

  • If I can make 4, I can make 24

And pair that up with square roots and you have:

  • If I can make 16, I can make 24 since (√16)! = 24

My favorite 24s

Check out some of the results from our class. I’ll add more as time goes on. Please note that there might be mistakes in here (or worse, missing numbers from my thumbs wiping the boards accidentally!). There are also some tricks in here I haven’t mentioned yet.  Bonus points when you find them!

IMG_20141104_120959285 IMG_20141216_113725476 IMG_20150203_154808195

Sunday, June 12th, 2016

Why Swahili?

Combined flags of Kenya, Uganda, and Tanzania

The combined flags of Kenya, Uganda, and Tanzania

I’m not a native speaker of Swahili but I love the language. Grammatically, historically, and phonically it is really one of the most beautiful languages spoken on Earth.

The rules for pronouncing Swahili — which is called Kiswahili — are very clear. There are only 5 vowel sounds (English has 5 vowels but over 25 different ways to say them). Consonants have a singular pronunciation (as opposed to, for example, the confusing letter g in English having a different sound in get, gel, ring, rough, or assuage). The grammar removes ambiguity. Most of all, I love the history.

Originally just a language spoken by the coastal Swahili people on the East African coast, Swahili quickly became a lingua franca used by merchants from all over. Kiswahili is filled with Arabic and Persian loanwords, and being part of the Bantu language family means it has similarities to languages from southern Africa too. Over the centuries, it evolved into the beautiful language it is today, synthesizing elements from a wide geographic region but remaining orderly and accessible (as opposed, once again, to English which has more exceptions than rules!).

In this regard, Swahili is much like the language of mathematics. Orderly, yet flexible in how it can expand. Encompassing and uniting many different disciplines — hence why we call it “mathematics” in the plural. And so using the language of mathematics, we delve into finding the beauty and orderliness of the world around us.

Maji usiyoyafika hujui wingi wake. You can’t know how much water is in the pond that you’ve never been in.

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