Re: what is understanding

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

Ludwik raises important issues here, worthy of further discussion.

On Sat, 12 Jul 1997, LUDWIK KOWALSKI wrote:

[snip]

> Some people were trained "never to push that button" without knowing what
> the consequences would be. They have a hard time with computers where the 
> "try it and learn from what you see" attitude prevails. In the same way 
> some people were trained not to accept scientific knowledge without 
> understanding. They usually have a hard time in situations in which vague 
> terms are used instead of clear-cut justifications (experimental, logical, 
> axiomatic). 

I've just sat through interviews with several applicants for a teching job
at our University. They conducted a class (non-calculus intro physics).
All had had teaching experience (their resumes proclaimed that). All
could write most impressive essays about their teaching philosophy.

Yet I heard these people using simple terms in vague manner, taling about
"currents" without specifying AC or DC, even discussing the charging of a
a capacitor with "electricity flows...", then later "...current flows" 
then (once) "charge goes..." (I was taking notes.) Did any student ask for
clarifying definitions of these three words? No. Did the students
understand the "explanation"? Doubtful. One of these people even slipped
when discussing a transformer and referred to voltage when he meant
current. He did this several times before I asked about it, since no
student had complained. 

Now these people had done supposedly good quality research in high level
experimental physics (as attested by lengthy publications lists). Yet they
could not discuss physics with clarity. I have no doubt they could *think*
physics quite well. A psychologist once said that physicists communicate
in careless and sloppy manner. They continually leave out important steps,
use vague language, and even incorrect language. Yet they can understand
*each other* in technical conversation because each participant mentally
(and very promptly) corrects these mistakes as the conversation goes on.
This works because the participants share a common base of understanding.
(That word again.) But teacher and student do not share a common base of
understanding, so in this setting one should use a far more careful form
of discourse.

As I think back on my past experience I wonder... Isn't it the *best*
students who can learn in spite of crummy textbooks and poor instruction? 
These students mentally correct the deficiencies of their instruction. The
poorer students can't do this. Someone else once remarked that "Physics is
one of the worst-taught subjects. But that's ok, because those who have
what it takes to become physicists will be those able to overcome
poor instruction." So careless instruction may serve as a subtle way of
weeding out the "unfit", at least those unfit for careers in physics
research. I have had physics profs say this openly and without apology.
I'm not necessarily condoning this, but I have to admit some validity
to it. 

[So the ability to correct mistakes in explanations represents one test of
understanding.]

Good preparation for careers in physics teaching may require a different
approach than preparation for careers in physics research. Few schools
have intelligently implemented this. Most schools take the attitude that
preparation for physics teaching simply means taking fewer courses, and
easier courses in college than those that research physicists take. And
then they look at those who take the "education" track as "second class
citizens" in the physics community. Universities have created that
caste distinction. 

> A lagrangian in the text of an explanation, or a reference to a gluon
> should, ideally, cause a highschooler to suspend the process of reading 
> and direct him to further studying. In real life we do take shortcuts 
> (accepting some science without understanding) but this is nothing to be 
> proud about. Do you agree? 

A very useful exercise: Give a printed text discussion to students and
have them circle each term or phrase they don't precisely understand. 
Better yet, have them write their best guess of the meaning of the circled
terms. You will find the results interesting. Hand them a transcript of
one of your lectures (transcribed from a tape recording of it), to do the
same. 

One may compare this to learning other things. I learned arithmetic
before being introduced to the laws of algebra. We learned to count before
any exposure to theories of countability. The "new math" tried to invert
this sequence. Did that work?

> Yes, understanding does depend on the persistence of people trying to 
> make sense of information. Long reasoning chains should be recognized
> as obstacles to understanding. Teaching should reward students with the 
> pleasure of understanding as often as possible. The nearly instant 
> gratification can be useful, sometimes. 
>                                                    Ludwik Kowalski

	-- Donald (Another e' posting.)

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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