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MACROSCOPE

The Music of Math Games

Video games that provide good mathematics learning should look to the piano as a model

Keith Devlin

Going Beyond

2013-03MacroDevlinFD.jpgClick to Enlarge ImageWith video games, we can circumvent the barrier. Because video games are dynamic, interactive and controlled by the user yet designed by the developer, they are the perfect medium for representing everyday mathematics, allowing direct access to the mathematics (bypassing the symbols) in the same direct way that a piano provides direct access to the music.

It’s essentially an interface issue. Music notation provides a useful interface to music, but it takes a lot of learning to be able to use it. It’s the same for mathematics notation.

The piano provides an interface to music that is native to the music, and hence far more easy and natural to use. When properly designed, video games can provide interfaces to mathematical concepts that are native to those concepts, and thus far more easy and natural to use.

Consider some of the reasons so many people are able to master the piano. You learn by doing the real thing (initially poorly, on simple tunes, but getting better over time). You use the very same instrument on Day 1 that the professionals use. You get a sense of direct involvement with the music. You get instant feedback on your performance— the piano tells you if you are wrong and how you are wrong, so you can gauge your own progress. The instructor is your guide, not an arbitrator of right or wrong. And the piano provides true adaptive learning.

We read a lot today about adaptive learning, as if it were some new invention made possible by digital technologies. In fact it is a proven method that goes back to the beginning of human learning.

What’s more, the proponents of today’s digital version have gotten it all wrong, and as a result produce grossly inferior products. They try to use artificial intelligence so an “educational delivery system” can modify the delivery based on the student’s performance.

Yet tens of thousands of years of evolution have produced the most adaptive device on the planet: the human brain. Trying to design a computer system to adapt to a human’s cognitive activity is like trying to build a cart that will draw a horse. Yes, it can be done, but it won’t work nearly as well as building a cart that a horse can pull.

The piano metaphor can be pursued further. There’s a widespread belief that you first have to master the basic skills to progress in mathematics. That’s total nonsense. It’s like saying you have to master musical notation and the performance of musical scales before you can start to try to play an instrument—a surefire way to put someone off music if ever there was one. Learning to play a musical instrument is much more enjoyable, and progress is much faster, if you pick up—and practice—the basic skills as you go along, as and when they become relevant and important to you. Likewise, for learning mathematics, it’s not that basic skills do not have to be mastered, but rather it’s how the student acquires that mastery that makes the difference.

When a student learning to play the piano is faced with a piece she or he cannot handle, the student (usually of his or her own volition) goes back and practices some more easier pieces before coming back to the harder one. Or perhaps the learner breaks the harder piece into bits, and works on each part, at first more slowly, then working up to the correct tempo. What the player does not do is go back to a simpler piano (one with fewer keys, perhaps?), nor do we design pianos that somehow become easier to play. The piano remains the same; the player adjusts (or adapts) what they do at each stage. The instrument’s design allows use by anyone, from a rank beginner to a concert virtuoso.

This lesson is the one we need to learn in order to design video games to facilitate good mathematics learning. For over 2,000 years, commentators have observed connections between mathematics and music. We should extend the link to music when it comes to designing video games to help students learn math, thinking of a video game as an instrument on which a person can “play” mathematics.




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