Re: Pedagogy

[John Denker <jsd@AV8N.COM>]

Wolfgang Rueckner wrote:
> Why not just answer the student's question without value judgements?
> Why make any comments about how easy or hard the problem is?

Because a crucial part of the teacher's job is to
motivate the students.  It's usually not the first
thing I say, but I frequently do comment on the
difficulty-level.
 -- In a few cases, reassuring the student that it's
an easy problem is helpful.
 -- In a few other cases, warning the student that it's
a hard problem (so they shouldn't feel dumb if they
have to struggle with it) is helpful.
 -- In the majority of cases, I tend to say something
like "It's easy if you know the trick;  let me show
you the trick."

====

Commenting on the difficulty is not necessarily the right
place to start.  When folks ask me for help with a
problem, my instinctive reaction is come back with
questions, so I can find out where they're coming from.

BTW that's one reason why email is generally a pain;
it's not interactive enough.  Usually I have to guess
where the question is coming from.  A few folks on
this list have got a really good technique:  as part
of the question they *say* where it's coming from.
They say "I tried xxx and I got as far as yyy but
now I think I'm stuck because of zzz" ... which I
reeeeally appreciate.

===============

I learned a thing or two about teaching by watching
Richard Feynman interacting with undergraduates.  He
was known for being a bit gruff with colleagues who
didn't know what was going on, but he was more than
patient with freshmen and sophomores who didn't know
what was going on.

When he was working problems at the blackboard, he
didn't just show the solution.  He commented on the
method of solution as he went along, which is where
this story makes contact with the subject of this
message.  He would often say "At this point, you
may be tempted to try XXX, but that's a trap.  You
can recognize traps of this sort by noticing ....."

I was quite struck by that.  It was not even a case
of RPF "remembering" what it was like to be a student,
because he was so $#@! smart that he had probably
never in his life fallen into the sort of trap he was
discussing.  The point is that he took his job as
teacher very seriously, and he was discussing things
at the students' level.  He made it his business to
find out what the students found easy and what they
found hard and confusing.  He did this partly by just
plain talking to students, and partly by looking at
their homework papers (even though he had graders who
did most of the grading).

At the opposite extreme, I once asked a professor to
explain something he'd written:

       <j1  =  1j2  =  1m1  =  0m2  =  0|JM>    [1]

He rolled his eyes and said "It's completely standard
notation."  And he stopped there!  I replied "But I'm
a student.  I wasn't born knowing the standard notation.
Would you please teach it to me?"

It turns out that it was just a badly-typeset Clebsch-
Gordon coefficient:

       <j1=1, j2=1, m1=0, m2=0 |J, M>           [2]

And I still I had every right to be confused by version
[1], especially since it was the first time anything
like that had been presented.  I could have tolerated
the eye-rolling if he had at least answered the question
without making me ask twice.