The New York Times has relatively regular articles about mathematics education. Often they're anecdotal rants by parents against "new math," but this week's article is an interesting overview of some recent research into innate number sense. It's this number sense that they describe as allowing you to determine which grocery store line is shorter at a glance, or whether there are more blue dots or yellow dots on the screen (see the online version of the test the researchers used). Researchers determined that innate aptitude for this type of approximation correlated to stronger formal math abilities.

The article suggests that teachers should take this as a cue to incorporate more estimation and general understanding into the curriculum (though the research does not show if our inborn number sense can be improved). I strongly agree with this and tried to do a lot of estimation when I was teaching middle school math. It's very hard to teach, and very hard for some students to understand. Perhaps this begins to give some clue as to why.

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Do you think there's a difference between a gut instinct for math and a gut instinct for numbers?

Also, what's interesting about mathematics (and I guess physics) is that there's a point at which mental/visual models stop being useful or accurate. Does this mean people who have up until that point had an innate or intuitive understanding for the mathematical models "hit a wall" once certain subjects are broached?

I wish I could remember specific examples of this, would probably make it a much more interesting comment.

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