Friday, January 4, 2008


So I'm driving in the car with my 16-year old son (actually, he just got his license and he's driving), and we're listening to music, Grounds for Divorce by Wolf Parade. My son says, "Nice hemiola." I say something intelligent like, "Huh?" My son, who is a musician (saxophone) taking Advanced Harmony this year, explains that a hemiola takes two standard 3-beats (1 2 3, 1 2 3) and plays it like three 2-beats (1 2, 1 2, 1 2). It's about the way the beats are accentuated. I concentrate on the music, and I can begin to pick out the hemiola as well.

I tell him that I think what he's just done is an example of what the cognitive neuroscience literature I'm reading calls a "schema." He's curious. "What's a schema?" Explaining it to him is a good exercise for me.

Putting my thoughts into words helps me clarify my own thinking. Indeed, it often reveals how far I am from really getting it. A schema, I summarize, is like a generalizable pattern or model that helps you make sense of new information or situations. The hemiola pattern is something that my son can recognize in music he's never heard before. In fact, music and the arts are full of schemas. Those of you (not me) who dance, for instance, can readily pick up a waltz or salsa or disco beat in a novel tune. Genres of literature and art follow patterns that allow readers and viewers familiar with the genre to anticipate the flow of the story or to look for particular aspects of color or shape.

In fact, schemas are everywhere, and they don't have to be narrow and technical like a hemiola. Neuroscientist Daniel Levitin, in his wonderful book, This is Your Brain on Music, offers the example of a kid's birthday party schema. We know the pattern -- games, cake, presents -- and we recognize it from one party to the next. The children, the setting, the games, the cake, and the presents may all be different at each party, but our brains don't get overloaded with the uniqueness of each situation. Instead, we take comfort in the common underlying structure.

We relied on schema research for a program we created called GO Solve Word Problems. Our goal was to help students see the underlying patterns in arithmetic problem solving situations. Rather than treating each problem as unique or applying a weak schema (like focusing on key words or automatically dividing when one number is a factor of the other), students should focus on the mathematical patterns. For instance, is the problem about something changing or a comparison?

I think we've just scratched the surface with how schema theory can guide improved instructional strategies. Schemas help make new information and situations familiar and manageable. We all use them all the time.

Understanding the ones that struggling students use on academic tasks may provide some very useful insight. I'm curious about the overlap between schema research and the work on student misconceptions. More to come on this topic...

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