Calculus IV
Published by admin January 28th, 2008 in Uncategorized, CalculusWould teachers teach calculus if they had a choice? This is also an ethical question: Why do teachers teach calculus? There are two reasons. 1) To earn their living. 2) They have no choice.
I have never met a teacher of calculus who taught calculus because that was her purpose in life. Teachers have no choice. For them teaching calculus is a chore. They cannot teach what they think is good for students, they must teach what they are told to teach. This means that most teachers teach what they thing should not be taught. And this seems to be an ethical question.
If you are a teacher of calculus would you teach calculus if you had a choice?
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I’ve used calculus quite frequently ever since I learned it back in the 1975-1976. It was clear that my instructor loved teaching it and that it was his favorite class. He was a retired military (colonel) and certainly didn’t need the money. His 1977-1978 calculus class gave him a plaque. In fact, for some months I’ve felt I owed him a blog post and I will write one up now. (For quite some time I’d lost the above link.)
Later when I taught calculus at college, I loved teaching it, and it was pretty obvious to me that a fairly large number of my students enjoyed the subject. What they didn’t like was getting graded on it, and I tried to make this as fair as possible. One of them thanked me because he had never realized before that he was smart enough to pass that class, much less get a good grade in it.
Calculus is not a matter of memorization. Or at least it shouldn’t be. My learning it was not any sort of a chore. It was more like being reminded of things I had always known but had somehow forgotten. Nor have I forgotten much of it despite having learned it over 30 years ago.
For me it was never about memorization. From the beginning, the rules that they teach you were very obvious to me. All I ever had to “memorize” was that the derivative of sin is cos and the deriviative of cos is -sin. The rest you can quickly derive from these if you learned algebra correctly. I believe that this experience is shared with most others who end up using calculus in their lives.
Different students have different minds and have to use different techniques to solve problems. I tried to teach so that as many students as possible would be able to make it through to the end. I think it would be sad to be reduced to memorization of calculus.
I think you have been lucky with your teachers. Your experience may be an exception. I had to make a choice after junior high between science and social science and I chose the latter and never studied calculus or physics. Only later I discovered that math was beautiful and it was not about memorizing ugly notation. In science though as you mentioned previously in a comment, the only method is curve fitting. And that can be done with computers. I also object to the way calculus and physics is taught. These are taught as if they were a monolith. So students must suspend doing “real” research while they master 4 years of calculus.