Friday, July 10, 2009

Math Education... Is There Room for Student Curiosity?

Bruce Smith, a guest blogger at, re-visits an important debate about mathematics education. Math in schools has been traditionally the most linear, sequential curriculum out of all the subject areas, as one skill builds on another skill. Because of this, it also tends to be the most repetitive and routine-based instruction that you see. The question is, does it have to be this way?

With the Iowa Core's emphasis on moving to real-world problems and higher-order thinking, math sticks out like a sore thumb. It requires narrowing down the curriculum, more depth and less breadth, and allowing for student creativity and curiosity. Want to do that in language arts or social studies? No problem. Math? There is resistance.

At Grinnell, I visited often with what I consider a very progressive math faculty. As a group, they used some very original "quadrant-D" lessons involving performance assessments to deepen learning. And they would have liked to do more. But as I found out, there were limits. One teacher mentioned that when regional math instructors looked through their curriculum at an AEA math conference, they found a paltry three concepts that they could remove. Which, won't get you the time you need for that type of instruction.

So in essence, math is a final frontier. If math can change to a curiosity-based, less-rigid curriculum, everything else can as well.

That's what is interesting about Smith's article. He refers to a somewhat famous critique of math education by Paul Lockhart called the Mathematician's Lament. Math instrution is described as "dull" and "mundane". Actually, that's the tame stuff. A more vivid passage from Lockhart:

If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done—I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

It is then the description of math as the "music of reason", the "purest of arts". And, this resonates with my memories of middle school math so long ago. When math is presented as "Here's the concept, here's the rules to remember, here's an example problem, and here are the 30 problems in the book to try it out yourself" (but just the odd numbered ones, of course), it does destroy any desire I had to determine natural patterns myself.

On the other hand, in my TAG pull-out sessions, we were allowed to explore topics and learn unhindered. A friend of mine and I determined a mathematical method for determining the worth of baseball players, when simply comparing home run totals or batting average isn't sufficient. I remember it being very elaborate, finding a way to factor in not only power, average, and defense, but also intangibles, like advancing the runners, hitting the cutoff person, and whether the team was better or worse when they were in the lineup.

It was very crude, but with the advent of Sabermetrics as a widely-credited method for analyzing baseball, you could almost argue the work we did was ahead of its time. It certainly wasn't irrelevant, and it definitely met the marks of "quadrant-D" and "performance assessment". Most importantly, we learned that we had to find mathematical explanations for patterns and thoughts in order to bring everything together. In other words, I learned, because I was allowed to see the art of numbers and patterns.

The problem is, I'm not sure of the scalability. Is there a way to allow math classrooms everywhere to be a place of discovery? Does the Iowa Core hurt that possibility or help it? And, are my perceptions due to being a TAG-student, perhaps more adept at one form of instruction than others?

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