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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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nstahl@uwcmail.uwc.edu wrote:
> 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.
Are you saying that it is a good thing to prevent students with
weak algebra skills from passing calculus on that basis alone,
even if they can demonstrate some ability in calculus? If so, I
disagree. On the other hand, if you are echoing my statement that
students should pay the price for weak algebra to the extent that it
weakens their ability to understand calculus and solve calculus
problems, then of course I agree.
What do you mean by reasonable standards? Do those standards include
a requirement that students demonstrate an understanding of the basic
concepts of calculus? That they be able to solve a problem which is
not based on a template they have studied before? That they be able
to explain their answers? That they be able to deal with real data in
the form that scientists and engineers encounter it? That they be able
to come up with their own formulas modelling that data, rather than
manipulate someone else's? I do not believe that these were included in
the standards of most departments before calculus reform. Calculus
reform, properly applied, raises the standards considerably. Just ask
the students.
> 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.
I wouldn't say not much algebra is needed for teaching calculus, but I
would say that more of the algebra can be done on a computer or
calculator. However, there is one algebraic skill that is important for
calculus and its applications, and that computers cannot do, and that is
the ability to develop formulas which model a given situation, and to
understand the significance of parameters in those formulas. This is an
area where calculus reform has increased the emphasis over traditional
courses.
> 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 agree that this is a problem. Calculus reform itself has the same
problem. As I said above, I believe that calculus reform has raised the
standards. But no-one can guarantee that those standards will continue
to be applied in the classroom. The traditional calculus course suffered
from a steady decline in standards over many years, until all that was
required was facility in algebra. It's up to all of us to prevent this
from happening again.
> For instance, we don't know that someone who doesn't
> know much algebra can learn much science.
Probably not. We should talk and listen to scientists and engineers
about this. I believe the algebraic skill I mentioned above is
important. However, there may be others that are better done on the
computer; symbolic integration, for example.
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