The latest Ask a Science Blogger Question is:
What makes a good science teacher?
My fellow SB’ers have already unloaded a wealth of good answers.
In one of his essays for Fantasy and Science Fiction Magazine, Isaac Asimov relates the story of the famous chemist who was discussing the nature of fire with an audience of ten year olds. After the presentation the chemist was stopped cold when a student asked him, “Why are they called matches?” Asimov was especially amused by this anecdote, because on the very day the presentation took place his latest essay had hit the newsstands. He was also discussing certain questions related to fire, but he had thought to explain the origin of that term. (As I recall, the answer had something to do with the name of a part of a lantern).
Asimov pointed out the importance of anticipating questions that people would ask when learning about something new. I believe this is especially important in mathematics teaching. The key to good teaching is an ability to put yourself in the position of someobody learning the material for the first time.
Sadly, mathematicians seem to find this difficult to do. That is why math textbooks are, almost without exception, terrible. They are written like reference books; adequate if you want to look up a theorem but almost worthless if you’re new to the subject. Mathematicians have a way of talking to one another that is utterly foreign to students. For example, a calculus teacher will ask a question like, “What properties does this function have?” He has in mind things like: Is the function continuous? Is it differentiable? Does it have asymptotes? Are there points where the function is undefined? That sort of thing. But for a student the whole idea that a function is the sort of thing that has properties is strange. To them a function is just some expression like f(x)=x+1.
As a fellow mathematician pointed out to me, it’s not that students hate mathematics. They just don’t like feeling confused.