Date: Sep 21, 2004 11:26 AM
Author: nstahl@uwcmail.uwc.edu
Subject: Algebra: How Much is Enough?
Ok, let's back off a little. I'm not advocating not using CAS's in calculus

class. I use them there myself and wouldn't give them up. I am saying we

shouldn't use them as an excuse to give up teaching a lot of the algebra (see

footnote for my working definition) that's now taught.

I like the idea of people learning to think more graphically. Surely that can

complement thinking algebraically, but we don't know that it can replace

thinking algebraically.

I like the idea of people learning more problem solving skills and I use CAS's

to give them opportunities to do so. But these are people with fair algebra

knowledge. I personally doubt that people with a lot less algebra knowledge

would be able to make as good use of the CAS's to solve problems.

Unquestionalby a lot of our citizens don't know much algebra now, but many

(enough?) do know it reasonably well and use it in their work.

I fear some of you are willing to let the level of algebra knowledge among

Americans go down a lot. That could be a big mistake. My concern is that we

may underestimate the importance of educating enough of our citizens in

algebra and fail to teach a generation things they turn out to need.

We have stuffed math knowledge into black boxes like Mathematica, and use the

boxes to do some valuable things. In the work place so far, these black boxes

are used by people who know something about math. How well can people do real

work with them who know very little about math? The jury is out on that one.

We don't yet know how much experience and knowledge needs to be in the head in

order to use the CAS on the desk well.

Neil Stahl

Algebra: The level one needs depends on the class and or job, but for the

people who take a calculus class (for business calculus take ~75% of what

follows) I'd want them to be able to work with polynomials and rational

expressions (though not as complex as the ones I did as a kid) and have a good

idea of when to do what. For instance they should appreciate factoring as a

step in solving an equation or inequality.

I'd want them to know exponents and logarithms and their properties very

well. I'd want them to understand the idea of one variable determining

another (i.e. functions) and also use of function notation and inverse

functions.

I'd want them to know the graphs of several basic functions and be able to

use those graphs in thinking about the solution of problems.