College Algebra is Still Not Pre-Calculus :(

My colleagues at the college are having discussions about what the nature of a good precalculus course is; their discussions are interesting, though little consensus seems to be emerging. I’ve posted on this before College Algebra is Not Pre-Calculus, and Neither is Pre-calc, so I am not going to repeat much of that.

I have also posted previously about some great data reported by David Bressoud, namely “The Pitfalls of Precalculus” (http://launchings.blogspot.com/2014/10/the-pitfalls-of-precalculus.html). The basic message of that report is that precalculus does not help the students who really needed it, and actually caused harm to students who had little need. This data, in fact, is less positive than the reviews of remedial mathematics.

The mess and dysfunctional curriculum in STEM mathematics seems to continue due to:

The acceptance of a procedurally-bound preparation course or courses (college algebra, pre-calculus), without any design basis or data to support this arrangement.
The rigidity of the calculus curriculum itself, which as resisted modernization for 3 decades (see http://launchings.blogspot.com/2017/05/re-imagining-calculus-curriculum-i.html)

Sure, we have made some progress in pedagogy; the recent MAA “Instructional Practices” guide outlines a bit of the progress (though without much consensus on ‘best’ practices); see https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide. The content — that which justifies the existence of a course — is horribly out of date, with a focus on symbolic manipulation and memorization that has caused our courses to not have respect within our partner disciplines.

My colleagues discussion does not generally include what to teach in calculus; that content is taken as a given, like a poorly written play for which our troupe must still put on a show. No, the discussions generally turns on whether pre-calculus needs to serve the preparation needs for all calculus courses in the sequence or to focus on the first course in calculus. I am hoping that the conversation will evolve to include the fundamental questions that determine whether calculus courses are STEM-encouraging or merely obstacles the ablest students need to overcome.

One of my colleagues refers to our pre-calculus course as “death by algebra”; I would put it a bit differently:

The precalculus content is a mixture of excessive algebraic procedure combined with a dysfunctional obsession with trigonometric formulae and identities; those who survive algebra are likely to meet their doom in the trig.

Our curriculum is all about serving the important goals. We want more students to pursue STEM paths and dreams, and for most of them to be successful if they are willing to work. Our current precalculus and calculus curriculum is an anthropological artifact worthy of study to help people understand how bad stuff can continue for decades; other than that, this curriculum is not worthy of any additional effort. We need to create a better curriculum — SOON — so that we stop doing damage to the very students who could achieve success in STEM programs.

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