Tuesday, January 25, 2005

Thought Shows

We can’t see the mental machinery people carry around in their heads but since Arthur Conan Doyle added Sherlock Holmes’s quirky deductive powers to crime stories, detective shows featuring intelligence at work solving problems have been popular. The differences between the smart and dumb detectives make for great plot and dialogue. The latest in this genre is a mathematician hooked up with his detective brother in Numb3rs.

I like shows that celebrate the triumph of human intelligence over situations. I’d love to see the biography of Richard Feynman, my son’s favorite scientist, used as a rich source for a TV series. These kind of shows give weight to the idea that the logical/deductive powers that come from developing an understanding of logico-mathematical systems is a powerful reason for studying mathematics in school.

Mathematics as the valid forms of all kinds of diverse, intelligent thought is often trivialized when people try to justify the importance of mathematics in the school curriculum. The tendency is to reduce it to knowing specific content—so we can use the formula for area to compute how much carpet we need to cover our living room floor. The power of mathematics is much more general. It lies in the rich mathematical forms the mind uses to organize and make sense out of things. But it’s hard to separate the mathematical form of thought from its content so mathematics looks topical to most people, even to the extent that is appears unrelated to most thought. But research is getting us there.

Too bad we can’t yet recognize the huge differences among the different forms of thinking about the content of education reform just yet. I’m sure we’d find the differences in their forms would define a scale of intelligence from overly simplistic models to advanced, valid forms. Imagine if we had the IQ score for the Chalkboard Project’s inside the box thinking or politicians’ thinking about education and reform before an election. How would politicians campaign if voters knew their education reform IQ?