TITLE: To Solve Or Not To Solve
AUTHOR: Eugene Wallingford
DATE: April 07, 2013  2:23 PM
DESC: 
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BODY:
This week I bumped into a familiar tension that arises whenever
I assign a new homework problem to students.

<B>Path 1</B>.  I assign a new problem before I solve it myself.
The problem turns out to too difficult, or includes a complication
or two that I didn't anticipate.  Students become frustrated,
especially the weaker ones.  Because of the distraction, most
everyone misses the goal of the assignment.

<B>Path 2</B>.  I solve a new problem before I assign it.  I run
into a couple of unexpected wrinkles, things that make the problem
less straightforward than I had planned.  "This will distract my
students," I think, so I iron out a wrinkle here and eliminate a
distraction there.  Then I assign the problem to my students.  The
result feels antiseptic, unchallenging.  Some students are bored
with the problem, especially the stronger ones.

In this week's case, I followed the second path.  I assigned a new
problem in my Programming Languages course before solving it myself.
When I sat down to whip up my solutions, I realized the problem
held a couple of surprises for me.  I had a lot of fun with those
surprises and was happy with the code that resulted.  But I also
realized that my students will have to do more fancy thinking than
I had planned on.  Nothing too tricky, just a couple of non-obvious
steps along the way to an obvious solution.

Will that defeat the point of assigning the problem?  Will my
stronger students be happy for the challenge?  Will my weaker
students be frustrated, or angry at their inability to solve a
problem that looks so much like another they have already solved?
Will the problem help students learn something new about the topic
at hand?

I ultimately believe that students benefit strongly from the challenge
of problems that have not been pre-digested for them by the instructor
or textbook.  When we take too much care in preparing assignments
ahead of time, we rob students of the joy of solving a problem that
has rough edges.

Joy, and the sense of accomplishment that comes from taking on a
<EM>real</EM> challenge.  Problems in the world typically have rough
edges, or throw wrinkles at us when we aren't looking for them.

Affording students the joy of solving a real problem is perhaps
especially important for the stronger students, who often have to
live with a course aimed at the middle of the curve.  But it's just
as important for the rest of the class.  Skill and confidence grow
out of doing something worth doing, even if it takes a little help
from the professor.

I continue to use both approaches when I create assignments,
sometimes solving a new problem first and sometimes trusting my
instinct.  The blend keeps assignments from veering too far in one
direction or the other, I think, which gives students some balance.

However, I am usually most happy when I let a new problem surprise
us all.  I try to keep these problems on track by paying closer
attention to students as they begin to work on them.  When we run
into an unexpected rough edge, I try to intervene with just enough
assistance to get them over the complexity, but not so much as to
sterilize the problem.

Finding the right balance between too clean and too rough is a
tough problem for a teacher to solve.  It is a problem worth
solving, and a source of both disappointment and joy.
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