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The Music of Math Games

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

Keith Devlin

What’s in a Game?

2013-03MacroDevlinFB.jpgClick to Enlarge ImageSo how to go about designing a good video game to help students learn mathematics? The first step should be to read—several times, from cover to cover—the current “bible” on K–12 mathematics education. It is called Adding it Up: Helping Children Learn Mathematics, and it was published by the National Academies Press in 2001. The result of several years’ work by the National Research Council’s Mathematics Learning Study Committee, a blue-ribbon panel of experts assembled to carry out that crucial millennial task, this invaluable volume sets out to codify the mathematical knowledge and skills that are thought to be important in today’s society. As such, it provides the best single source currently available for guidelines on good mathematics instruction.

The report’s authors use the phrase mathematical proficiency to refer to the aggregate of mathematical knowledge, skills, developed abilities, habits of mind and attitudes that are essential ingredients for life in the 21st century. They break this aggregate down to what they describe as “five tightly interwoven” threads. The first is conceptual understanding, the comprehension of mathematical concepts, operations and relations. The second is procedural fluency, defined as skill in carrying out arithmetical procedures accurately, efficiently, flexibly and appropriately. Third is strategic competence, or the ability to formulate, represent and solve mathematical problems arising in real-world situations. Fourth is adaptive reasoning—the capacity for logical thought, reflection, explanation and justification. Finally there’s productive disposition, a habitual inclination to see mathematics as sensible, useful and worthwhile, combined with a confidence in one’s own ability to master the material.

The authors stress that it is important not to view these five goals as a checklist to be dealt with one by one. Rather, they are different aspects of what should be an integrated whole, with all stages of teaching focused on all five goals.

So it’s not that the crucial information about mathematics learning required to design good learning video games is not available—in a single, eminently readable source—it’s that few people outside the math education community have read it.

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