Saturday, April 28, 2012

My thoughts on College Algebra

I'm 24 and have taught College Algebra 9 times.

I realize that's not some kind of record.  But it is a lot.

When I first started teaching it, I was so excited:  How could anyone possibly find any of this boring?!

I'm finally starting to understand my students' frustrations.  Don't get me wrong, I still love math, and I love teaching College Algebra.  But I'm starting to wonder if it's really accomplishing what it set out to do.

I know this isn't the case everywhere, but in the part of the country where I live (the great Midwest), College Algebra is the peak of most college students' mathematical career.  Any previous or remedial work is a build-up to help students succeed in College Algebra.

But what is College Algebra?

It was designed to help students succeed in calculus.

The problem is that only one in ten students enrolled in a College Algebra class will end up taking a full-length calculus sequence.

So what's the point in preparing students for calculus if very few of them will end up taking it?

I believe College Algebra needs to be revamped (and kudos to the schools who are already working on this).  I'm not one to jump on the "Math education has to be applicable to real-world situations" bandwagon; although I'm not at all opposed to this approach.  What I am opposed to is giving pure math a bad rap.  Pure math can be just as fun as applied math.  The thing is, in a typical College Algebra course, we teach very little of the fun stuff in pure math.  Call me crazy, but I'd love to see a beginning college course that showcases the best of the world of pure mathematics.  I truly believe every college student can do a bit of abstract algebra, a little number theory, a piece of combinatorics, and a snippet of analysis/calculus.

How encouraging would it be for a student to finish her final mathematics course and be able to say, "I can do calculus!"  As opposed to what several of our current students end up saying:  "I barely passed a class that I had already taken in high school."

I currently teach high school seniors who are taking College Algebra for both high school and college credit.  I teach them nothing new.  Nothing.  I've compared the topics I have to cover to the topics taught in their Algebra 2 curriculum and they're identical.  Do we really want to send the message of This is the end-all of math!  Functions and equations.  That's pretty much all math is.  Specifically, rational, exponential, and logarithmic functions and equations.  The end.  In fact, we think this is so important, we're going to teach it to you again!  And again!

That's really not the message I want to be sending.  But what are students to think if that's what every single math class they've taken (both in high school and in college) focuses on?

At the Conference to Improve College Algebra in 2002, Arnold Packer said the following:
Many would skip College Algebra if they did not have to pass it to get the degree they need to enter their chosen career field. Enrollment in CA tends to fall dramatically when colleges make quantitative reasoning or intermediate algebra the requirement. Finally, a few years after finishing the course, getting their degree, and starting their professional life, they cannot recall anything they learned. Or, equivalently, they have never used anything they learned in College Algebra.
All of this is unfortunate and related. Mathematics courses that seem hard, boring, and irrelevant prior to College Algebra establish the expectation that College Algebra will be more of the same. Moreover, the course – as conventionally taught – does nothing but confirm the foreboding.
That's the sad truth.  But I think things will change.  And I hope to be part of that change in some small way.

This fall I will start an adjunct position at my alma mater, where I will be teaching a Survey of Mathematics course.  My hope (albeit lofty) is to showcase some of the best and most interesting topics of pure mathematics.  We'll see how it goes.

In conclusion to this rant, a final plea...

To high school teachers:  Encourage all your students to take their required college math classes ASAP (i.e., discourage them from waiting until their senior year of college).  I've taught too many amazing individuals that were--and probably always will be--one class short of a bachelor's degree:  College Algebra.  Oftentimes this is due to a prolonged break in their mathematics education.  Also, encourage your bright students to test out of College Algebra (CLEP it if allowed) and move on to Calculus or take some other math elective, lest we produce a generation that thinks polynomial functions are the epitome of mathematics.

To College Algebra teachers:  Let's try to make this class as engaging as possible.  It will be more enjoyable for both ourselves and our students if we challenge ourselves in this way.  Also, I try to remember:  my students have seen all of this before.  That doesn't mean they remember it all, but they have seen it.  Thus, according to the law of diminishing marginal utility, we'll have to work harder to sell it the second (or third) time around.  (That's right, my husband's a CPA.  I know my economics talk.  Sort of.)

To college administrators:  Decide who really needs to take this class and who might benefit from a different kind of mathematics course.


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