A recent article "ACC may buy aid for remedial programs" in the Austin American-Statesman, Dec. 9, 1997, discussed the issue of ACC hiring Kaplan Educational Centers to help us improve the performance of our remedial students.

I was especially struck by the last two paragraphs, in which Dr. Friedman stated (in part) that "although the college doesn't want to force students to take classes they don't need, it stresses the need for a basic education."  I believe that he has magnificently summed up the crux of the problem, at least with respect to mathematics education.

I have only the greatest of admiration for our students at ACC. Some are college age, many are older adults, and most have families and/or jobs. Unlike the majority of students at many four-year colleges, many of these students are sacrificing their life-styles on the altar of education. I have had students that religiously came to class after work; not very notable in itself, except that this was a class that met at 7:00 AM! Our students deserve the very best we have to offer.

Back to Dr. Friedman's statement, and a couple of questions leading from it, that I will answer (my opinion, of course):

Question #1: Are we forcing students to take classes they don't need?
Answer:         Yes.

In the days before community colleges, the "academically gifted" were, early on in their high school careers, put on track in a "college preparatory" curriculum. They took language, science, English, history, and for math, the usual algebra, trigonometry, geometry, and probably a taste of calculus. The other students, many of them gifted in other ways, took a less demanding academic curriculum, graduated, and went on to "non-professional" but fulfilling careers.

Today, the same philosophy with regard to "college prep" is, unfortunately, being misapplied to the community college student. Basically, a student is deemed not to have fulfilled a high school education in mathematics unless he or she has successfully completed "Algebra II" (second year high school algebra). For those students, the community college provides "remedial education" in the form of Intermediate Algebra. About 50% of the students that take Intermediate Algebra either fail or drop out.

What's wrong here? Are the teachers bad? Are these students being misplaced? Are the students not studying hard enough? Maybe some or all of these to a lesser or greater degree. But the basic problem has to do with the premise:
 

Balderdash!

I am not for weakening the math requirement for students still in high-school.  They are still in their formative years, and may have hidden talents yet to be uncovered by exposure to the rigorous beauty of algebra.

But when students reach college age, the die is cast, for the most part. For most students, if their talents did not extend in the direction of algebra in high school (and they probably didn't, if they are in a remedial math program), there will be no sudden awakening of hidden powers in the college classroom. It is this phenomenon that accounts in large part for the truly appalling rate of failure in Intermediate Algebra in all of our community colleges.

In my opinion, we are doing our students a great disservice by trying to mold them in a direction toward which they are not naturally inclined.

I do not blame community college math departments for this state of affairs. I do blame a philosophy and system based on traditional thought with regard to mathematics education that does not apply to most of our community college population. It is up to the educational administrators and agencies that set philosophy and policy to update their thinking on these matters.

Bringing in curriculum vendors such as Kaplan, either for consultation or as educational hot-dog stands, amounts to putting a band-aid on the problem. It won't work, because the problem is not a surface one to be cured by tinkering with what we have now.

Question #2:  Is there an alternative to algebra as a basic education in mathematics?
Answer:         Yes.

First of all, I am not addressing the teaching of those students who are technically inclined and are going into science, math, or a business curriculum that requires higher-level mathematical skills and knowledge. I am addressing the teaching of the great majority of community college students who are enrolled in non-technical disciplines.

The question has two sub-questions:

What math skills should a non-technical major have on entry to college?

This is a large subject with many answers, none of which is algebra. If I had to give a one-word answer to the above question, I would use the word Numeracy. What does this mean?

Numeracy means having a whole array of more-or-less practical and common-sense mathematical skills, ranging from being able to compute a discount (both approximately without the aid of a calculator, and exactly, with a calculator), to being able to construct a logical argument from a set of premises, to being able to understand, interpret, and critique the vast amounts of numerical and statistical material with which we are bombarded every day in the media. Much has been written about this, notably in two books by John Allen Paulos: Innumeracy, and A Mathematician Reads the Newspaper.

I believe that community college remedial math programs should concentrate their efforts in the direction of numeracy by constructing a comprehensive list of learning outcomes with these kinds of objectives in mind, and designing a graded curriculum around those outcomes. In fact, I believe that these elements already exist in many places in the lower-level remedial courses at ACC.

What should be required of non-technical students in order to fulfill their college mathematics requirement?

Again, the answer is not algebra. Most lay-persons (and unfortunately, many educators), because of their contact with traditional school mathematics, equate mathematics with algebra.  Nothing could be further from the truth!  Algebra is merely a tool that is used in other, more interesting, branches of mathematics, and has no inherent educational value as a separate entity!  It should be taught only to the extent that it is needed by curricula with inherent educational value.

What is the answer? On a positive note, the answer is already in-place and well-established at Austin Community College! It's called MATH 1513, Mathematics: Its Spirit and Use.

Spirit and Use is a wonderful blend of some practical mathematics, numbers sense stuff, history and philosophy of mathematics, and an exploration into some of the many areas of applied mathematics never seen by algebra (or even calculus) students, but whose ideas and concepts are accessible to lay-persons. And best of all, for most topics, no algebra is required! Can you teach group theory and graph theory and gnomons to the mathematically uninitiated? You betcha!

Spirit and Use is just right for that student whose self-description is "I was never good at math in high school. I hate math. And I'm extremely anxious about it."  One of my students appended a nice note to her final examination: "Coming into this class I had a severe case of math phobia - it is now cured! Thank you!"

Unfortunately, many students think that College Algebra is the "right choice" to fulfill their college math requirement, and end up extremely disappointed and disheartened. The failure rate in College Algebra is also around the 50% mark. But that's another story.

To sum up:

Our challenge lies in Dr. Friedman’s assertions that "the college doesn't want to force students to take classes they don't need" and that we should "stress the need for a basic education."  The policy-makers need to be led to formulate a clear and sensible definition of what a "basic mathematics education" is with regard to what it is and what it's not.