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Topic: A statement on what is wrong with standard calculus
Replies: 15   Last Post: Sep 21, 2004 11:26 AM

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William McCallum

Posts: 26
Registered: 12/8/04
Re: A statement on what is wrong with standard calculus
Posted: Feb 21, 1996 6:27 PM
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Diana Watson wrote:

> Questions. When are people supposed to learn algebra?

In an algebra course.

> Or,
> are they supposed to learn algebra at all?


Yes. However, the ability of computers and calculators to perform
algebraic calculations, and the fact that students will use that
ability whether we like it or not, may mean we need to rethink
what we teach in algebra. Perhaps we should concentrate more on
teaching students to judge output from an algebraic calculation,
and less on teaching them to produce it.

> Are we advocating passing students through calculus with at
> best a rudimentary knowledge of algebra.


As far as I remember, we were doing this long before calculus
reform.

In both traditional and reform calculus, students with poor algebra
don't do very well. However, in a reform course they have the chance
to use other skills, such as geometric intuition, or problem-solving
skills. These skills are not irrelevant to calculus, and students
who have and demonstrate them should get credit for them. Presumably
the lack of algebraic skills will cost them a grade point or two,
as it should.

> Isn't this (or is this) the
> equivalent of passing students who can't read at grade level?


You are comparing passing individual courses with passing a
whole year of school. I would have no objection to a student
who can't read at grade level but who is good at mathematics
being given a pass in mathematics and a fail in reading. But
it doesn't work that way at school; either you go on to the
next year or you don't. So I don't see how the analogy works.


Hope you find this enlightening,

Bill McCallum





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