Thursday, July 20, 2017

Algebra or Stats?

Apparently, the California community college system is considering allowing students in non-STEM majors to fulfill a math requirement by taking statistics, rather than algebra.

The idea behind the proposal is twofold.  First, algebra generates more student failure and attrition than almost anything else.  (One of the guest speakers at Aspen said that his one piece of advice to any college president looking to improve graduation rates would be to fire the math department.  We laughed, but he didn’t seem to be kidding.)  Second, in many fields, algebra is less useful than statistics.  

The objections are obvious.  Most basically, it looks like watering-down.  If the solution to increased college completion is to get rid of anything difficult, then college completion itself becomes meaningless.  There’s an “exposure” argument, too, that says that many students don’t know they like math or STEM until they’ve found themselves wrestling with it; deprive them of that exposure, even “for their own good,” and the downstream effects are predictable.  Pragmatically, there’s an argument from transfer; many four-year colleges won’t take math courses that don’t have an algebra prerequisite.  And from within, there’s a valid argument to the effect that if you don’t have basic algebra, you won’t be able to generate most statistics; at most, you might be able to consume them.  

For example, when I took stats, I was captivated by the idea of controlling for a variable.  (“You can DO that?”) But the idea of a variable came from algebra.  If you don’t have some level of algebra, I’m not sure how much sense the concept of controlling for one would make.  Correlations and standard deviations also rely on some knowledge of algebra.  “Base” and “rate” make sense algebraically.  I’m not sure how the course would work.

It’s true that drop/fail rates for algebra courses tend to be higher than for stats courses.  It’s also true that in my own scholarly discipline, and in my line of work, I use stats far more than I use algebra.  I find the “median” of a distribution on a regular basis, but I don’t remember the last time I used the quadratic formula.  It just doesn’t come up.  

But the argument from usefulness is stronger against many other fields, and it doesn’t get deployed against those.  We have a history requirement for A.A. degrees, for example.  From a pure ‘usefulness’ standpoint, that’s hard to justify.  But there’s a general consensus that the skills students develop through the study of history are valuable, even if it can be hard to demonstrate in as linear a way.  (Knowing the future would be far more useful, but it’s hard to find good materials.)  We have a humanities requirement that’s entirely independent of usefulness.  Honestly, if we want to argue usefulness, I could imagine a compelling argument that history and literature majors shouldn’t have to take lab sciences.  The usefulness argument is a slippery slope.

Stats courses tend to lend themselves to “general education” kinds of applications very well.  I’m a fan of questions based on epistemology: “what statistical evidence would prove this claim?”  Political journalism offers no shortage of “how to lie with statistics,” which can be excellent fodder for sharpening students’ critical thinking.  Just being able to distinguish between correlation and causation is valuable.  

I’d be curious to hear from folks who’ve taught a stats class that didn’t assume any previous knowledge of algebra.  Can you sneak the relevant algebra in through the stats?  Are the students able to grasp concepts like “control for a variable” without knowing what a variable is?  If the students are able to get the critical thinking and quantitative reasoning skills from a stats class without an algebra prereq, I’m on board.  I just don’t know if they can.