A Tale Of Two Teachers
Long, long ago but not too far away– if memory serves, it was at Harding Junior High School– I was taking an algebra course with a teacher of stern and rigid principles. I don’t remember her name, and I don’t want to guess, lest I slander the innocent. I will simply call her Miss Straitjacket.
The subject under discussion was negative numbers. Miss Straitjacket said something to the effect that minus 2 is less than plus 2. I raised my hand said, no, minus 2 is the same quantity as plus 2; they only have different signs. I could have mentioned that minus 2 multiplied by minus 2 is plus 4, but I didn’t. I rested content with asserting an obvious truth.
Did Miss Straitjacket commend me for my insight and initiative? No, she did not! Instead she viciously berated me and ridiculed me for daring to put forth such a nonsensical proposition. I said nothing. I just sat there and took it. Needless to say, I didn’t believe a word she said.
Down through the decades, hardly a week has gone by when I haven’t thought of that incident. Until recently, the meaning was beyond dispute: Miss Straitjacket hadn’t really mastered her subject, and the insecurity resulting from this or other faults led her to commit an inexcusable attack against any student – such as me – who would even slightly challenge her authority.
Then, a few years ago, I was looking over my Income Tax form. I happened to glance at the instructions for a certain calculation, and I saw the following: “If the result is less than 0, write 0.” So from the IRS point of view, minus 2 is less than 0, and therefore less than plus 2!
That put a new light on the incident. Miss Straitjacket’s sin, in addition to the unconscionable personal attack, was failing to recognize a teachable moment. She could have pointed out that for some purposes minus 2 is less than plus 2, while for other purposes they are the same quantity with different signs. It all depends on the situation, and we need to reason out what the situation requires. (Thus she would be anticipating the philosophy of the estimable Wittgenstein, but that’s another story.) She didn’t say that: however, because she was Miss Straitjacket and she had a ready-made set of beliefs for us to accept.
In sharp contrast to my memory of Miss Straitjacket is my memory of another teacher, Margaret Warner (AKA Maggie), from whom I took a high school course in Modern European History.
Of the many virtues of Miss Warner’s course, perhaps the one I remember most is the text she assigned, Carl Becker’s history of modern Europe. How I relished that book! I still remember my pleasure in reading how Bismarck pre-empted the Socialists; how the crowned heads of Europe and their ministers danced the nights away at the Congress of Vienna after they had spent the days plotting the suppression of Europe’s masses; how Gladstone and Disraeli dueled with one another through the decades; how the Man on the White Horse scared French republicans (no, it wasn’t Napoleon). But alas- those are surely lost glories, for Carl Becker must have died long ago, and his textbook must be out of print. I feel so sorry for the students of today, deprived of Becker’s text because the assignment of old textbooks is considered cause for shame.
A more important addition to my education was Miss Warner’s teaching me how to outline the course material. This was more important than I realized at the time, for it was one of only two glimpses into the ways in which our thoughts are structured so as to promote clear and effective thinking– the premise-conclusion form of geometric proofs being the other.
Learning how to structure our thoughts– how to recognize the relation between one idea and another, how to recognize premises and conclusions and so on– is not to be confused with “learning to think for yourself.” Of course we would like to think for ourselves instead of having our beliefs and decisions handed out for our submissive acceptance. But if we are to think for ourselves, our thinking must provide a better product than the stuff that’s handed us. After all, what good does it do to think for yourself if your thinking is misguided, confused, and ineffective? And if we are to avoid misguided, confused and ineffective thinking, we need to analyze the unformed mass of information swirling around us and follow our ideas down the path of logical reasoning.
So we need more Margaret Warners in our classrooms. Or even better, we might make the art of good thinking part of the overall curriculum, incorporated into existing subjects. Introduction to the notion of reasoning and its components, on the most elementary level, might begin around the fifth grade. Further instruction in recognizing arguments would continue through the eighth grade and introduction to definitions, unstated premises, analysis of issues (questions), fallacies, and such concepts as hypotheticals and counterexamples would continue through high school. But I digress into the realm of fantasy.
Still, it is not beyond the realm of possibility that some day, somewhere, good reasoning will be recognized as a pearl of great price, worth recognizing as part of our proper educational objective. Maggie Warner would approve. Miss Straitjacket wouldn’t even have to know.