Algebra, Again

It seems to me that Americans, at least those in the Atlantic drainage, have an odd relationship with algebra.   About seven years ago, Andrew Hacker argued in the The New York Times that algebra should not be required in high school.This exercised quite a few people for some days, after which it was probably forgotten as thoroughly as the formulas of Algebra I.

Last month, Jay Matthews suggested in The Washington Post that Algebra II should no longer be required. His suggestion received many responses for and against. I did take Algebra II in high school, though it I don't know that it was a required class there. It was third in the sequence of math classes, but only for students who had done well enough in Algebra I and Plane Geometry; other students took Trigonometry.

Nor do I remember what the class covered. I remember the instructor, and I remember my resentment at a poor grade for a proof that he considered too compressed.  (I'm sure that he was right.) But what we did that was in advance of Algebra I, I can't tell you. Maybe we did more work with equations of two or more variables. I recall that a couple of the young, now in their upper 20s or approaching middle age, mentioned logarithms when I asked them about Algebra II ten or twenty years ago.

Maybe it isn't just Americans, or hasn't always been. In his autobiography, Stendhal wrote (Chapter XXVI)

From [M. Chabert] I learnt about Euler and his problems on the number of eggs a peasant woman brings to market when a rascal robs her of one-fifth, and then she drops half the rest, etc, etc.

This opened my mind; I caught a glimpse of what it meant to use the instrument called algebra. I'm hanged if anyone had ever told me about this; M. Dupuy was always making pompous phrases on the subject, but never told us, quite simply: it's a division of labour which works miracles like all divisions of labour, and allows the mind to concentrate all its strength on a single aspect of things, on one of their qualities.

 But Stendhal was still bothered in middle age by the consideration that the multiplication of two negative numbers produces a positive one. He accepted it, on the practical ground that such calculations form part of others yielding true results; but clearly it still bothered him. The illustration that accompanies his statement of perplexity in Chapter XXXIV is much too complicated: he hasn't divided the labor far enough  Clearly his teachers weren't up to explaining.