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Re: A statement on what is wrong with standard calculus
Posted:
Sep 21, 2004 11:26 AM
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I'm sorry, but I find the response below too glib. Yes, no doubt some
people did pass calculus with poor algebra skills before reform
calculus, but many of us tried to keep that from happening, and in
a department with reasonable standards it didn't happen all that much.
Now there seems to be a growing feeling that not much algebra is needed
for calculus, so less algebra will be learned in calculus and no doubt
less algebra will be learned in algebra classes since one can't use
calculus to justify the effort of learning algebra.
Given the speed with which some people will give up teaching a hard
topic, I can forsee that soon not many students will learn much
algebra.
I have no problem with individuals, or individual departments, trying
that as an experiment: not teaching or demanding much algebra then
following their students for the next several years and seeing if,
in fact, they didn't need much algebra.
I object to such an experiment being conducted on a national scale,
which is what this could become. We don't know that a nation with
almost no citizens who know algebra well can thrive in the competitive
world out there. For instance, we don't know that someone who doesn't
know much algebra can learn much science.
Let's be slow about jumping on that bandwagon. We can downplay "hard"
algebra some, and certainly teach more problem solving skills, while
still insuring that those we pass know a lot of algebra.
Neil Stahl
------------- Begin Original Message -------------
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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