Maybe it's all in how we teach the subject

In connection with the hoo-ha about Harvard Pres. Larry Summers' comments, I learned this from the NY Times:

Overall size aside, some evidence suggests that female brains are relatively more endowed with gray matter - the prized neurons thought to do the bulk of the brain's thinking - while men's brains are packed with more white matter, the tissue between neurons. To further complicate the portrait of cerebral diversity, new brain imaging studies from the University of California, Irvine, suggest that men and women with equal I.Q. scores use different proportions of their gray and white matter when solving problems like those on intelligence tests. Men, they said, appear to devote 6.5 times as much of their gray matter to intelligence-related tasks as do women, while women rely far more heavily on white matter to pull them through a ponder.

As I read this, women process information differently. And that's the springboard for the rest of this post. My children attend a Montessori school. Using Maria Montessori's unique approach to education, they've been dealing with sophisticated mathematical concepts since they were 3. For example, Maria Montessori came up with the idea of number chains. (I couldn't find good pictures of these chains, but here is a catalog with pictures of her mathematical teaching products, including the number chains I try to describe below.) For example, a three chain would consist of a rigid bar with three beads, a loose link, another rigid bar with three beads, a loose link, and a third and final rigid bar with three beads. Like this: * * *-* * *-* * *. A four chain, of course, would look like this: * * * *-* * * *-* * * *-* * * * Little children love working with the chain and counting the total number of beads. For example, they know that a three chain has a total of 9 beads; a four chain a total of 16 beads. The children also know that these chains can be snaked back and forth. Here's a three chain snaked around: * * *- * * *- * * * As you can see, the beaded three chain, when snaked, creates a square. Whooo! "Three squared" really is a square, and one that consists of 9 beads! Same for four squared (except for the 16 beads, instead of 9). Indeed, same for all of the chains, through the 10 chain. And if you take three of these three squares and stack them one on top of each other, it creates a cube, and the cube has in it 27 beads. And if you take four of the four squares, and stack them one on top of each other, that too creates a cube, this time with 64 beads in it. The kids know this because they do it and they count it and they see it. This is a simple example, and I've conveyed it poorly, but I can assure you that at every stage of Montessori math, there is this tangible approach. I've watched 9 year olds receive instruction in the binomial equation, and it makes perfect sense to them, both because of the tactical, practical way it is taught, and because they have a visual model of these concepts going back to work they did when they were 3 or 4. Unsurprisingly, Montessori kids find math fascinating and fulfilling. And, I think, unsurprisingly, they consistently test very well in math, girls as well as boys. It seems to me that boys have the mental ability to understand math whether taught in the purely abstract way of traditional education, or whether taught (much more enjoyably) in the tangible way of the Montessori approach. Girls, however, seem to do better with Montessori, where they can actually visualize the concepts they're learning. Any comments?