
Re: A statement on what is wrong with standard calculus
Posted:
Sep 21, 2004 11:26 AM


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 noone 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.

