Re: Pedagogy

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 13:46 -0500 5/6/04, Vickie Frohne wrote:

> One thing that helps is to tell students, explicitly, that they are expected
> to figure things out. Nobody "automagically" knows the answers, although
> sometimes it can seem that way.

I found, quite by accident, that if I clearly didn't know how to
solve a problem once it was raised, and the students got to watch my
thought processes as I worked through it, it helped them. Once I
stumbled on to this, I would try to get a problem or two tossed out
each week that I didn't know how to solve before-hand, and then as I
worked through the problem, I would point out explicitly what I was
doing and why. If I had to flail a bit to find a method, I pointed
that out. If I was trying a couple of different approaches to see
which one worked, or worked better, they were told that, too.

This way, they got to watch the process work, and could get some idea
of what approaches an "expert" problem solver might follow in solving
a particular problem for the first time. They saw that I tried to
categorize the problem not by the context, but by the physical
principle(s) involved, and then they saw how I applied the principles
to the problem, and when I reached a dead end they would see that,
and realize that it happens to everyone and not to beat their heads
against them, but go back and try a different approach.

They saw that I kept track of units throughout, so that I could pick
up errors early on, and that I would also keep an order of magnitude
estimate of the answer in my head, so I would know if I had made a
calculational error.

All of these things (and more) are the things we tell the students to
do every day, but it seems to mean a bit more to them if they see
someone actually using these techniques to solve problems that they
haven't done before.

I also liked to show them particular problems where the "usual"
techniques aren't necessarily the best approach. That way they can be
encouraged to think outside the box when it is appropriate.

Lest they get the false notion that because I can solve these
problems and they can't, that I am some sort of flippin' genius, I
freely give credit to the (mostly) students who taught me some of
these unusual approaches to problems. Every so often, I get stuck,
and one of the students then bails me out. *That* really helps them
build confidence. I learned early on that knowing the answer to every
question is not always the best pedagogical technique. Especially if
a student can bail me out. Then they know that they haven't lost
hope. Not everyone has to know all the answers, and help can come
from any quarter.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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