I think this is an interesting article and it makes a lot of good points, but it skims over a very real problem: most adults are not developmentally ready for calculus. A currriculum path that prepares students for a science major will not work for most students. As long as we try to find a one-size-fits-all approach, we are going to fail. This article advocates a developmentally appropriate curriculum. Developmentally appropriate for whom? If we design a curriculum that is appropriate for most students it will fail to adequately prepare those with math talent.
It is true that some people confuse rigor with difficulty, but the real problem illustrated by the author's anecdotes is that the teachers were not capable of understanding the material themselves! How does he expect bright students to be prepared for calculus if they can't do rate problems in eighth grade? Or understand what an identity is? These concepts are developmentally appropriate for eighth graders on the track for scientific careers.
Yes, the focus on testing is counterproductive. But it exists because we perceive that there is a real deficiency in the ability of teachers to actually teach math! To fix this problem, we need to pay math teachers enough to buy competence for our public schools. And we need to provide developmentally appropriate curricula for different ability groups.
Of course you can't instruct students by assigning material that they aren't prepared for. I don't think that necessarily means that the material is inappropriate, but that the lack of preparation is systemic. Ganem doesn't address that. He seems to excuse teachers from knowing the material by saying that he himself found it difficult.
Articles like this are used as support for those who want to dumb down the curriculum. I don't think that's the right approach. I think we need to stop expecting to prepare everyone for calculus. I don't think that's a realistic expectation.
Last edited by Cathy A; 10/19/09 05:52 PM.
