Learning: Discovery, not Mimicry
Dan Wolaver

Once, when our family was traveling with a real-estate agent in her car, our young son asked, “Hey, what kind of car is this?” I looked over at the steering wheel, saw the Chrysler logo, and waited for her answer.  “Look around you,” she said.  “Do you see any clues?”  Surprised, I asked, “Are you a teacher?”  “I was,” she said.

I think this attitude of encouraging students to discover for themselves best characterizes good teaching.  Polya’s book “How to Solve It” is my favorite text on teaching.  It’s devoted to the idea of letting the student do as much as possible by himself—of coaxing him in a productive direction by asking him carefully balanced questions.  When I help a student one-on-one, we stand at a board to get our ideas down in pictures and equations (in that order).  I find that if I’m the one wielding the chalk, the student feels it’s my show and becomes passive—doesn’t really engage his thinking.  So I’ve adopted the practice of having the student do the writing throughout the session.  It’s slower, but more productive.  I can tell from what the student puts down whether he really understands.

In an unpublished essay I suggest ways to lead the student to discovery though guessing.  Like our real-estate agent, a teacher should lead a student to answer his own question based on what’s already available to him.  The student is reluctant because he feels that he would be merely guessing, whereas he should proceed only from a position of certainty (as teachers and professionals seem to).  I try to disabuse students of this impression by letting them see me guessing—feeling my way from one idea to another. 

These principles aren’t obscure or original with me; most teachers appreciate the importance of engaging the student.  Yet teaching so often falls into one-way lecturing, which really doesn’t foster much engagement.  What pitfalls keep teachers from their highest ideals?  Two stand out:

1) The pressure to move things along (so we can cover the material) doesn’t allow time for the student to explore, go up blind alleys, and ultimately discover.  The time seems best spent if the teacher takes over, laying out the development in a smooth, clear, and logical progression.  Some of this is good, but it’s over-done.  Lecturers sometimes argue that homework and the lab are the places for the student to struggle through things himself.  But the teacher is rarely available for help during the struggle.  So it comes down to man-hours.  Leading the student to discovery is best done in one-on-one sessions, but there aren’t enough teachers to give every student the necessary attention.  One solution is to put time into training teaching assistants to be really effective in the ways described above.  Another is for lecturers to get good at engaging a whole class to participate in discovery.  This will reduce the amount of material covered, but I think we can pare down, trusting the student to extrapolate from a few well-chosen examples that he has really comprehended.

2) The teacher needs to get himself out of the way.  There’s a joy in sharing the insights we’ve discovered as a teacher, and perhaps pride too.  But it’s possible to instead lead the student to make the discovery so he can feel that joy (and pride).  Sometimes the student will take a different tack and surprise us with a different insight.  In any case, we need to listen carefully to understand what’s going on in the student’s mind.  We often uncover unforeseen stumbling blocks to his understanding.  As a teacher thus concentrates more on the students, he is naturally getting himself out of the way.  There’s a joy in this too, because both teacher and students are having an adventure in discovery.