I had nice teachers and I had mean teahcers. In my experience, most of the female teachers who were mean were older, probably over 50, and unmarried. Younger teachers, most married but some unmarried, were more patient and nice in general.
This, of course, is personal experience and not math, so there are a lot of exceptions. (Taught correctly, math has the advantage of very few exceptions to well defined rules.) Miss Shelley was older and unmarried and nice, for example.
Mrs. Kruger is one of the exceptions going the other direction. I was a little kid at the time, so not that good at judging ages, but I would guess Mrs. Kruger was about 30, married and mean. If she had known about the amount of money a professional dominatrix could make, she would have been out of the teaching racket faster than you can say Heinrich Himmler!
But I add her to my math story not because she was mean, but because she had a pedagogical tool I actually still use. She had a metaphor for remembering how to do something that I remember 40 years later, so I think there is a chance that some of my students will be able to remember it at least until the next test. It has to do with simplifying square roots.
Mrs. Kruger said a square root sign was like a prison, holding things captive that were multiplied together. If you had the square root of 50, it could be re-written as the square root of (5x5x2). The thing was, if you had a twin in prison, you could plan a prison break. The catch was that one twin would escape while the other would be shot and killed, never to be seen again. So in 5x5x2, one of the 5 twins gets out, one is cut down in a hail of bullets, and the 2, who doesn't have a twin, is still stuck inside the square root jail. This says that sqrt(50) = 5 x sqrt(2).
See? Even her good memorization tricks were kind of mean.
My point here is that even not particularly good teachers can hit a home run every once in a while. Good pedagogy can be practiced by teachers who really don't have the whole package of good teaching methods down. And so I still teach one topic the way that Mrs. Kruger, She Wolf of the SS, taught it to me some 40 years ago.
And, oh yeah, sqrt(40) = sqrt(2x2x2x5) = 2 x sqrt(2x5) = 2 x sqrt(10).
Tommorow, Chapter 3: Matty Boy gets the Red Card!
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