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Math Education, Non-Euclidean Geometry, and Politics

Yesterday’s NYTimes featured an op ed piece by Christopher J. Philips titled “The Politics of Math Education”. The premise of the article was that even a subject like how to teach mathematics, a subject that appears to be based on unequivocal facts, can be politicized. He explains how in this section:

This is because debates about learning mathematics are debates about how educated citizens should think generally. Whether it is taught as a collection of facts, as a set of problem-solving heuristics or as a model of logical deduction, learning math counts as learning to reason. That is, in effect, a political matter, and therefore inherently contestable. Reasonable people can and will disagree about it.

Philips uses the balance of the article to describe the recent history of mathematics instruction, from the Sputnik era where it was handed off to mathematicians through NCLB where it was highly charged politically.

In the comment I left, I noted that the “new mathematics” designed by real mathematicians emphasizes the fact that mathematics is a mental construct and, as such, one needs to look carefully at the premises to determine if there is a clear “right answer”. A quick example: in non-Euclidean geometry two points define a curve and not a line. By changing that one premise, all of the premises of the Euclidean geometry we learned in HS become worthless. One’s faith in the order of the world can be challenged when you realize that the “rules of geometry” can be rendered useless… and that lack of faith might compel one to question the fundamental premises of a political system.

My comment concluded with this unequivocally political comment:

Those who think it is plausible that a Democratic Socialist could become President, like the new math. Those who want to reinforce the dominant paradigm are more comfortable with Euclid.

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