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Topic: harvard calc
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Joan Reinthaler

Posts: 110
Registered: 12/6/04
harvard calc
Posted: Jun 9, 1997 9:03 PM
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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 math-dependent 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 pre-technology 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
pre-technology age) looking at things numerically.

But what about their students? Maybe the math-major 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
non-math majors does not reflect very admirably on the math teaching

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

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