I recently read Paul Lockhart's essay "A Mathematician's Lament" that was published at The Mathematical Association of America Online. It is the best description of the issues that many see in math education that I have come across. On the surface I agree with much of what he discusses. I absolutely agree that discovering math is better than being told it. I believe that the current "ladder" curriculum is weird and disjointed and I agree that most math teachers(me included) are not really qualified to teach math.
But here is the rub and there is really no way to get around this. This essay is idealistic to a point that it is never going to be applicable in any mass educational system. There is one question I have for the author. Why, when I was actually taught by mathematicians, did they teach their class exactly opposite to what you are describing? I understand that I couldn't expect this type of teaching in my K-12 classes and maybe not even in undergraduate, but when I entered graduate school the teaching and lecturing was worse than anything I had experienced up to that point.
With that in mind, I still think it is an excellent read for any math teacher/aspiring math teacher. Found within the idealism are some very good points about teaching math. The most important, though not explicitly mentioned, is that the goal of a math teacher should be to teach students how to learn math, not to teach the math itself.
I will continue my grading systems series this weekend. I wanted to comment on the essay while it was still fresh in my mind.
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I'll spend my time reading this later on. I'll save it in my computer first. Anyway, there's someone I know who had this experience in teaching Math. He taught Math the usual way, and he always found a group lagging behind. He said he wants to deviate from his usual style, just to cater to this group. I hope this essay would help him understand how to teach Math in a way that everyone would understand.
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