Are we serving STEM students well?

Here is a question for us to ponder deeply:  Does the traditional curriculum (starting with developmental mathematics and including a pre-calculus/college algebra course) serve STEM students well?  There seems to be some consensus that the traditional curriculum does not serve other students well, those not going in to a STEM field.  We seem to lack a cohesive view of what it even means to prepare students for calculus.

I do have a judgment on this issue, though I want to explain the context first.  Over my time in this profession, I have specialized in developmental mathematics and (more recently) general education mathematics (such as quantitative reasoning).  I have not taught calculus, nor pre-calculus.  This combination makes me quite dependent upon others for information and points of view.  Fortunately, many colleagues have been generous over the years in talking with a person like me.

No, absolutely not … that is my conclusion about our courses serving STEM students well.  If I had to boil down everything people have told me over the years about what students need to succeed in calculus, and in engineering, and in sciences, it would be this:

STEM-bound students need to develop perceptual abilities, flexible and adaptive reasoning, and a work ethic that allows them to acquire needed resources (such as procedural skills and technology usage).

Our current pre-calculus track (beginning with developmental courses but continuing throughout) is an anvil of symbolic procedures with occasional taps of reasoning.  Students will encounter roughly 400 discrete learning outcomes in approximately 20 containers in their experience, none of which prepares them for the cognitive challenges of calculus.  The occasional need to reason (we don’t want to make it ‘too hard’, apparently) are clearly less important to our students; they focus on what we focus on — procedures and correct answers.  As in Lockhart’s Lament, we submerge and disguise the beautiful … the exciting … and the real challenge.

Take a look at the Calculus Readiness (CR)  Test from the MAA (see http://www.maa.org/pubs/FOCUSFeb-Mar11_ccr.html) .  The items on this assessment are far more about perception and reasoning than the rational root theorem; the items are more about strong reasoning than they are about formulas for sum & products in trig functions.

Some people might be thinking that there may be some validity for my point of view if we are talking about a reform calculus curriculum (which is the framework that created the MAA CR test).  However, I see this is our fundamental flaw about STEM preparation:

STEM-bound students will eventually have to apply their mathematics within a content area.

I do not really see a reason to use a traditional calculus program as an excuse to avoid fixing the pre-calculus problem.  Both areas need work, so start somewhere.  Our good students consistently report that they did fine in our calculus courses but then really hit problems when they were required to apply those concepts within their program … whether this happens in the junior/senior courses in their major, or in their graduate courses.  One of my respected colleagues says:

We don’t know what a good pre-calculus course should be, but it is certainly not Pre-Calculus.

Developmental mathematics is in the current ‘hot seat’, in the target, on the radar, whatever your metaphor might be.  That’s fine, as the traditional courses are in severe need of renewal so that they actually help students.  However, the big difference maker will be when we extend the reform work into the pre-calculus and calculus courses.  For too long, we have meekly accepted the role handed to us … a role that places a high priority on ‘weeding out’ those not deemed good enough, by any means necessary.  This is our time to reclaim mathematics, to show all students the core ideas and provide experiences which expand their perceptual skills and reasoning abilities.  Math can be an a magnet, an attractor to STEM fields.

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