Slow motion

Some colleagues and I have been going over the standard NY State 6th grade math tests, as part of our process at the Games for Learning Institute of trying to understand how to help kids learn this stuff. I hasten to add that learning to do well on these standardized tests is definitely not the same as learning math.

In general such tests aim at only the lowest semantic level, and doing well on them requires mastery of concepts that are only barely removed from plugging in a formula. This is certainly not the sort of generative and multi-faceted view you want kids to have if you expect them even to glimpse the bracing beauty, joyful delight and sheer heart-stopping wonder of the actual mathematical universe.

Nonetheless, I was fascinated by my own process of reading these questions and answering them while simultaneously trying to catch a glimpse of what was going on in my mind. What sorts of concepts did I bring to bear upon reading a problem? When did I solve a problem by transforming it into a different one? How much energy did I spend on solving the underlying problem itself, as opposed to understanding the wording of the problem?

One of the difficulties in addressing these questions is that for most problems the answer just seemed to come to me, all at once. Because I’m not actually still a sixth grader, I ended up going through the steps and reaching a result faster than I could catch what those steps were, so the process often seemed instantaneous (as I suspect it would be to most of the people reading this).

But with a concerted effort I was sometimes able to slow the process down and watch what was going on in my head — a little like watching a film in slow motion. Some of what I observed was very interesting, and some was downright surprising. Over the next days I will try to share a bit what I saw.