Are Math Courses Worthwhile?

Colleges usually require students to take math courses, whether for an associates degree or a bachelor degree.  The common approach is to identify a level on the “developmental math to calculus” ladder that seems like the best fit.  I believe that this approach is bound to failure, partially because these math courses are normally not worth taking … from the students’ point of view.

Much of the current conversation focuses on developmental mathematics, and whether those courses are worth the investment of institutional resources.  This approach hides the assumption that the gateway college courses are worthwhile for the institution and its students.

During a meeting about general education last week, a comment was made that we all know what college algebra is; to be fair, the speaker meant college algebra as opposed to intermediate algebra.  It’s true that math faculty can tell when they see a college algebra course — because it matches a generic description of college algebra.  The suggestion was also made that a college algebra course includes more demanding problem solving than intermediate algebra.

A student perspective on courses is naturally simpler than ours, but perhaps we need to attend to that perspective to solve our deep-rooted curricular problems.  A course is worthwhile for students when one or more of these conditions is met:

• The content of the course is naturally appealing to a curious mind.
• The abilities developed in the course enable success in other courses (easily seen as such).
• The process of learning in the course is stimulating and/or rewarding (innately).

I’m not describing students who think a course is worthwhile because it was easy, nor those who see primarily value in the social relationships.  I am thinking of students who are looking for an academic reason for taking a course.

A course such as college algebra is doomed to fail all student criteria, at least for most students.  It seems like we, as mathematicians, want students to take these courses so that we can spot the unusual students for whom such an artificial set of content appeals to students via the third condition (the learning is innately stimulating or rewarding).  We seem to take pride in the tidy logic and coherence of the traditional content, forgetting that students might need something different for their needs.

In other disciplines, a gateway course is often seen as an attractor for students — show students how wonderful the discipline is so that they want to see more.  Sociology and french inspire students, sometimes, because wise faculty design such courses to be potentially inspiring to a broad cross-section of students.  When was the last time your college algebra course inspired somebody who was not already STEM-bound?

We would like to have more math and STEM students, but we put courses in front of students that have a strong track record of discouraging student interest in our discipline.  Whether we call it college algebra or pre-calculus, a central goal of the course should be student inspiration.  I do not think our typical courses serve students sufficiently well to be worthwhile.

My concern also applies to other courses besides college algebra or pre-calculus.  We often use statistics as an easier path for students, a sort of “we can’t win anyway, so let’s make it easier” approach.  It’s time for us to re-build our gateway math courses so that they are appropriate introductions into the science called mathematics.  The emerging models of developmental mathematics — AMATYC New Life, Dana Center Mathways, Carnegie Foundations Pathways — can form a foundation for these new gateway math courses.

Our gateway math courses are not usually worthwhile for students, but they can be … and we should make them be worthwhile.

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2 Comments

• 

  By schremmer, March 30, 2013 @ 5:44 pm

  I agree very much with most of the above. (But I don’t see how the “emerging models” are going to work any better than the models that “emerged” for the past forty years.) I would also say that our courses have always been “one size fits all” which was bad enough, but that, in addition, they are now driven by the desire of publishers to “customize”: “Ah, you want a chapter on the Riemann integral in your basic arithmetic, just between addition of fractions and multiplication of integers in that order? Can do. No problem!”.

  On the other hand, given the available technology, it is now quite simple for anyone willing to write a textbook, even with the nowadays required ancillaries, to do so. For more about this–and a couple of examples, see FreeMathTexts.org. (By me)

  Thus, instead of having “Developmental Math 012”, we could have “Prerequisite for Math XXX”, “Prerequisite for Math YYY”, etc. Each one with its own text. One big advantage is that Math XXX and Math YYY could then be tightly integrated with their prerequisites into much shorter sequences. For an example, see “How Content Matters” in the March 2013 Notices of the AMS. (By me).

  Regards
  –schremmer

• 

  By schremmer, March 30, 2013 @ 6:44 pm

  Trying to put in the links:

  FreeMathTexts.org

  March 2013 Notices of the AMS

  –schremmer

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