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harvard calc
Posted:
Jun 9, 1997 9:03 PM


Here are some random thoughts about the discussion on the merits of the Harvard Calculus book and other reform texts and reform calculus courses in general.
First of all, I would categorize most calculus students this way:
1) students who intend to concentrate in mathematics  for whom calculus is a first step toward analysis.
2) students who intend to pursue the study of physics or other physical sciences for whom calculus is a first step toward the ability to model the physical world through differential equations.
3) students who intend to use calculus to pursue the study of an increasingly mathdependent world of social sciences.
I suspect it is a safe bet that, when they were students, most college and university math professors fell into the first category. They ended up as professors because they were uncommonly successful at being math majors  most of them in a pretechnology age. They were good at symbol crunching and probably liked it. Maybe they looked at their work graphically  maybe not, but it is unlikely that they spent much time (at least in a pretechnology age) looking at things numerically.
But what about their students? Maybe the mathmajor intenders think a lot like they do which is wonderful, but I'll bet that most of the rest of them, at least those in the 3rd category, think very differently. These may be kids for whom symbol manipulation offers little enlightenment, who desperately need pictures or numbers. These are kids who will need to use calculus and who will need to understand, on an intuitive and gut level, what they are doing and why and, for many of them rigor, at least initially, may be a barrier to this intuition.
Why is this so horrible? Is there something immoral about learning how to use mathematics instead of learning mathematics for its own sake? (and  from my experience in teaching the Harvard book, this is precisely what it offers). It is not a book for everyone but it is a book, IMHO, for a lot of kids and a good one. (Yes they shouldn't have left the MVT out, but every text I have ever taught needs some supplementing). And the tone of scorn that some recent writers have heaped on calculus courses for nonmath majors does not reflect very admirably on the math teaching profession.
Maybe the emotions that underlie the recent discussion about all of this are a reaction to the fear that many of the recent changes in high school math education are calculated to meet the needs of those who are unlikely to go on ultimately in mathematics and that, in the process, the needs of the strongest math students are not being addressed. I don't think there is any doubt that this is happening. I wish that the needs of a greater variety of students were being attended to and, as a teacher of some very strong math students, I find myself increasingly challenged to find good texts and materials for them. But this doesn't mean that the Harvard book and the other reform calculus books are not needed and welcome resources for some of my students. It just means that I have to look elsewhere for a book for the others.
Joan Reinthaler Sidwell Friends School



