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Archive for September, 2012

Math Games: Simulators and Instruments

Posted by Patrick on September 6, 2012

I’m in the process of changing my mind about a topic I don’t know much about: the gamification of learning, in particular, the gamification of mathematics learning.

Here’s my preconceived idea about math games: it’s sugar coating.  There’s something you have to practice; it’s hard, and you’re not very interested. So to make it less painful, we’ll add points you can earn for each correct answer (or better yet, monsters you can defeat by factoring polynomials, with cool graphics and stuff).  Hopefully, you’ll want to sit in front of your computer 10 minutes longer than with your textbook to practice your math.  In my opinion:

  • The math in these games has nothing to do with the context of the game (which is often true of textbook questions too mind you [2]).
  • These games do nothing to foster internal motivation and appreciation of mathematics.
  • They focus on skills, not mathematical and conceptual thinking.
  • They are really just fancy worksheets with blinking lights and noise to keep you awake.

I’m realizing now that that idea is a bit of a Straw Man.  In a Webinar [1] he presented back in January, Keith Devlin (@profkeithdevlin) clarifies what math games have been, are, and can be.  He uses the analogy of a flight simulator, or a music instrument to convince us that well designed math games could be invaluable tools to help students investigate abstract ideas in a world that makes them more concrete.  He doesn’t want math games to replace instructions, instead he wants them to be a complimentary tool of discovery, where students can think mathematically without having to worry about the notation.

In one of his previous books, Devlin argues that what makes math hard is its level of abstraction.  The logic is often simpler than that of a soap opera. [3] Now to extrapolate a little bit from Devlin’s presentation, it seems to me that a good  way to teach mathematics would be to:

  1. Use well designed games to explore mathematical thinking and logic in a context that is intuitive and non-symbolic.
  2. Slowly introduce symbols and layers of abstraction.
  3. Practice on synthesizing these two aspects.
  4. Repeat with new concepts…

There’s a catch though, which Devlin mentions briefly: It makes no sense to test students on the second part if they are still on the first part.  Can you imagine if part of the assessment process was to have students play a game so we could see what they struggle with?


  1. Keith Devlin, Game-Based Learning Webinar Recording
  2. Dan Meyer, [PS] Critical Thinking,
  3. Keith Devlin, The Math Gene,

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