The answer or the process?

When there’s more than one way to get there, you have to choose.  This can be confusing or useful.

A couple of weeks ago, our tutor found himself working with an autistic student.  The young man is intelligent and capable, but to make the most of his potential requires a teacher with special training, which our tutor (to his regret) does not have.  However, he did learn some things from working with this student.

The problem set consisted of various configurations of parallel lines, transversals, triangles and the like.  One or two angles were given, and the task was to work across the diagram to find out what something on the far side had to be.  There were several ways to do each problem, depending on which route one took and how one put the various equations together.  When our tutor said, “Here is one way to do it–” the student broke in with, “But what’s the right way?”  Autistic students are uncomfortable with having to choose among many options.

And not only autistic students.  In the unfamiliar wilderness of mathematics, many students get confused with possible ways of doing things.  They want just one clear path to follow; other things are distractions.  So our tutor tries to work out what they already know how to do and what they’re comfortable with.  He can suggest easier or faster ways of working a problem (especially on timed tests), but most important is something the student understands and can apply reliably.

It’s somewhat later that students begin to appreciate alternatives in mathematics.  When the answer is difficult or not available, finding the same result two different ways gives confidence.  And when you’re actually doing research, alternate methods are invaluable.  Not only do they reveal any mistakes you make, they can show (if they agree) that what you’re working with actually exists, even if only within a theory.  At the highest level, two different groups using entirely different ways to calculate (say) the Hubble constant can give an invaluable estimate of how well you actually know something.

Well, at least in science and math there is (most of the time) a right answer.  In literature the picture is not so clear.  Our tutor remarked that, in this era of the widespread Faustian Bargain, the students would benefit from an acquaintence with Marlowe’s Faust.  That inspired our writer to do some research, reading through a version of the play with many pages of attached literary criticism.  He concluded that such criticism tells you much more about the critic than the play itself.  Which is true: a work of literature only provides the starting-point, something to examine from different angles and looking at different themes.  There is no “right answer” to Moby Dick.  Which is, again, frustrating to students.

Our tutor learned another lesson from our autistic student.  After he had found the desired angle by his method or our tutor’s, he went back and calculated all the other angles and details of the figures.  It was gratifying to see his pleasure when when everything came out right.  This is not recommended procedure for a standardized test, where wasting time like this would greatly lower his score.  But it’s excellent training for a scientist.