Good questions?

The hardest part of teaching may be finding good questions to ask.

This time of year our tutor is working mainly with Advanced Placement students, those looking to get college credit by taking a nationwide exam.  In principle it’s a good idea; the students don’t have to sit through material they’ve already mastered and also get a bit ahead of their required coursework.  And introductory college courses can be dire.  The college doesn’t need to put as much time and effort into those courses.  In general, matching students’ abilities to courses is a good thing.

But, as we’ve noted before, having an important standardized test means there will be teaching to the test: concentrating on strategies and tricks useful only for the test, rather than mastering content.  Part of that, our tutor noticed particularly this year, has Physics, Chemistry and Calculus students pushing through great piles of practice problems.  One unstated hope of this sort of thing is that on the real test the student will see a problem just like one he or she has seen before, and can use the earlier one as a template.  We’d really like to test the student’s ability to apply principles and analyze the situation, rather than simply use brute memory.

But there are only so many ways to set up an inclined-plane problem, only so many elements to specify electronic configurations for, only so many integrals that a student can be expected to do.  Details can be varied almost infinitely, but the template remains the same.  How can we come up with a fresh approach?

Our tutor thinks he’s seeing an attempt at that.  Some of the practice questions a student has shown him for the AP Precalculus exam are very complicated or asked in a backwards or inside-out way.  A situation was declared to be exponential, but the student was required to treat it as linear.  The multiple-choice answers were all intermediate steps in solving another problem, but in a way no student would actually do it.  The wording was so convoluted in some places that it took our tutor a long time and much concentration to work out just what it was asking for.  These were all new ways of dealing with the subject, but actually only tested the student’s ability to penetrate a badly-stated situation.  We think that’s not what an AP Precalc test should really be doing.

We don’t really have an answer.  Coming up with questions that test only what we want to test, rather than something else, is hard.  Doing it in a nationwide standardized test may be impossible.  But we’d like to see it done.