Re: what is understanding

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

On Wed, 9 Jul 1997 Hugh Haskell <hhaskell@mindspring.com> wrote:

> It seems to me that Leigh has put his finger on an important aspect of
> understanding that has not come up in this thread (at least I haven't
> noticed it). We keep thinking of understanding as a binary quantity-either
> you have it or you don't. This is clearly not true. Understanding is a
> continuum ranging from little or none to truly profound. Most physics
> teachers are somewhere in the middle and the question we need to address is
> what level of understanding is appropriate for students at various levels,
> and should it be evenly spread across the spectrum of topics we deal with
> or is is acceptable if the depth varies from topic to topic, and if so,
> which topics are the most important to put our effort into to make sure
> that the understanding has passed beyond the little or none stage?

> I've seen a dozen different definitions of understanding in this thread,
> some better than others, but none that satisfy me. Unfortunately, I haven't
> got any improvements to offer. It begins to seem to me that understanding
> may be one of those words like art-we may not be able to define it but we
> usually know it when we see it.

Understanding is a mental process that students of physics and mathematics
should be able to generate in themselves while studying. It is a high level 
part of knowing, a "cognitive grasp" with subjective and objective components.
It has many "shades of gray". Understanding is a methaphysical category (not 
part of physics). It enables us to enjoy learning, be creative, discuss 
subjects with more knowledgeable people, be good teachers, apply knowledge 
in new situations successfully, recognize errors, know what is impossible,
etc. etc. 

Fortunately we already have an intuitive grasp of what understanding is.
We also know that some explanations are productive, in terms of leading
to understanding, while others are not. Should we expect the moments of 
understanding occur during each teaching activity, once a week or "much 
later"? Sounds like the old dilemma of "love and marriage". The question
was already addressed by Hugh (see below); do we agree with his earlier 
observation? Is it OK "to teach without blaiming ourselves for the lack 
of expected understanding"?
                                                         Ludwik Kowalski
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    Date: Sun, 6 Jul 1997 From: Hugh Haskell <hhaskell@mindspring.com>

> > Students are expected to understand physics. But what is understanding?
> > It is state of mind, with respect to a topic or a set of topics. ...
> >
> > > UNDERSTANDING is attained when a student can confront a novel situation
> > > and validly discuss it (at length) with an expert.
>
> If understanding is not a state of mind then what is it? Students of 
> physics are expected to develop that state of mind in the process of 
> self-explanation based on what they observe, do, read about, etc. Can 
> this process be imposed by force? Or should we, teachers, wait for it 
> to occur spontaneously? The term "wait" stands for "teach without 
> blaiming ourselves for the lack of understanding".
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If my own experience is any indication, understanding came very late in
the process. Much of what I now understand about physics I gained after I
started teaching. Perhaps understanding is more than we should reasonably
expect of students, esp. at the introductory level. A successful teacher
friend of mine, Pat Canaan of Corvallis, OR, has, for many years held that
students should learn how to solve the problems first, understanding will
come later. While I don't teach based on that proposition, I often think
that I ought to. Every year, it seems to me that I end up understanding
more new things than my students ever do, and maybe that is the way it
should be.
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