Sunday, May 18, 2014

Quoting Pólya quoting Shaw

Along with Richard Feynman's "total temperature of the stars," this is my favorite comment on 'new math.'

From The Random Walks of George Pólya:
In the immediate post-Sputnik era Pólya had been an outspoken critic of the formalism of the School Mathematics Study Group (SMSG) and the “new math." He often cited an example taken from the SMSG geometry text that gave a theorem with proof—taking up half a page—stating that with three points on a line, one point must lie between the other two. He argued that though this is a necessary theorem for a foundations course in geometry, it has no place in an elementary text. He said that had he been asked to study the proof of such a theorem in high school, he would almost certainly have given up on mathematics, having concludcd that the subject is dumb! In support of this viewpoint— that there was excessive rigor in the “new math"—he was one of the signers of a manifesto on curriculum reform that appeared in The Mathematics Teacher and The American Mathematical Monthly decrying the direction of the reform movement of the 50's and 60's.

In talking about what he regarded as the excess of rigor in SMSG. he cited the oft‘repeated story about Isadora Duncan's proposal of something like marriage to George Bernard Shaw. She argued that their children would have his intelligence and her beauty. Of course, Shaw pointed out that the children might well have... Pólya suggested that SMSG had been put together by research mathematicians and high school teachers. on the assumption that the material would reflect the mathematical sophistication of the researchers. and the pedagogical skills of the high school teachers. But then, like Shaw, he pointed out that the material in fact reflected... The observation was unkind but there was, perhaps. some truth in it.

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