Thursday, August 21, 2008

Keith Devlin Continues on Multiplication

The multiplication issue continues to live on in various quarters, and now Keith Devlin, who started the current round of debates, discussions, and arguments, has posted a third column on the subject, "Multiplication and Those Pesky English Spellings." I'm still chewing over what he says there, but I can report with pleasure that this blog, along with three others, is mentioned favorably in his new column:

Of the blogs I looked at, which had threads devoted to my "repeated addition" columns, the following all had some good, thoughtful comments by their owners and by some of their contributors - by no means all agreeing with me - though the discussion in "Let's Play Math" soon descended to uninformed and repetitive name calling, and the owner eventually closed the thread, which unfortunately soon reappeared elsewhere.


Those blogs each have interesting and useful things to say on other math ed topics as well. Most of the others I saw seem to be little more than sounding boards for people who are so convinced that the overwhelming mass of evidence must all be wrong - since it runs counter to their beliefs - they don't even bother to read it. Those (other) blogs are not information exchanges from which you can learn anything, but platforms for people to espouse their own particular, unsubstantiated and often wildly wrong beliefs. Mathematicians who care about our subject and who like to think that the students who pass through our classrooms emerge with a good understanding of the mathematics we taught them, should be advised that they venture into any other mathematics education blog at their own risk.

Hard not to feel pleasure at getting that kind of comment from someone of Prof. Devlin's stature, and I like the other blogs he mentions as well, so to be put in their company is doubly flattering.

Meanwhile, as I try to digest Devlin's latest column, I thought I'd let readers of this blog know that I recently made a very fortuitous discovery at a used book sale while visiting Fenton, MI last Saturday: about 50 issues of THE MATHEMATICS TEACHER from 1965 to 1973. There are so many remarkable things in these magazines that are worth considering in light of the last 20 years or so that I may well have material for several months' worth of blog posts just from what is in them.

As a teaser, the following is from an Educational Testing Service (Cooperative Test Division) advertisement in the February 1967 issue:

Cooperative Mathematics Tests

This series reflects the ferment and change in the mathematics curricula. At the same time, content has been carefully selected to ensure appropriateness of the tests for most students.

Ability to apply understanding of mathematical ideas to new situations and to reason with insight is emphasized. Factual recall and computation are minimized.
No, I didn't make that up. No, I'm not mistyping the date. That is 1967, not 1997 or 2007. It would be fascinating to see these testing instruments, and if anyone knows of them, please let me hear from you in the comments section or directly by e-mail

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