Math and Short-Term Memory

My calculus students have an exam tomorrow on max-min.

They are freaking out, for good reason.

I suspect that the class average is at an absolute max. As of right now the median grade in the class is a B+. This is because my teaching style in calculus is to do about a bazillion routine examples in class, assign a zillion routine examples for homework, and then have the exam be mostly routine examples. It's freakin' business calculus. If you have a deep understanding, that's great. If not, then follow the recipe. Add two cups of derivative and bake at 350 for 40 minutes.

In the past week I've spent many, many hours in my office helping my students with calculus. They are unable to do anything with fractions (not even able to see that 2x/2 = x). One claims to have never heard of the quadratic formula. Apparently they have no awareness of anything -- aside from factoring pleasant, monic trinomials -- from life before calculus.

This semester I've started putting review questions on every exam (all exams are cumulative) in hopes of my students remembering some of the material in the course long enough to pass the final. For most of them this is a terminal course required by popular majors trying to cull the herd. They just need to remember calculus until December.