Re: sketching, qualitative reasoning

[Peter Schoch <pschoch@NAC.NET>]

I will lend my voice to saying that the students should have a good
ability to reason through a problem and understand reasonable vs.
unreasonable answers, etc.  However, my original comment was made with
respect to a pure calculation question, one that did not lend itself to
reasoning (in my opinion) -- so I just suggested using the computer
rather than valuable time.

I guess this is the way I approach teaching mathematics -- yes, here at
the community college I am not only the physics prof., but I also teach
differential equations (and CIS, and astronomy...).  I teach the REASON
for doing an operation, the mechanical mastery of HOW to do it, we do
several examples of this mechanical procedure, and then I show them the
computer and tables.  Finally, I do applications -- giving them the
"closure" as to where this can be used in the real world.

I stress that they must "check" the computer for a reasonable answer,
and that they must also cultivate a "feel" for what they are doing.  By
the end of the semester I am reasonably successful at being able to
engender that ability in the students.

I use the same type of philosophy in my Calculus based Physics classes.
I teach the REASON for doing an operation (history, etc.), the
mechanical mastery of HOW to do it, we do several examples of this
mechanical procedure, and then I show them the computer and tables.  My
focus is on getting them to understand how it is used in the "real
world", and why it is (and MUST be) important to them.  I let the
computer do the integration, systems of equations, least squares
regression, etc.  I stress that we have to check them, and we do, and we
have found some interesting blunders!

I guess my focus is on understanding, rather than on doing hundreds of
problems for sheer drudge work.  The computer is supposed to alleviate
all that drudge work to allow more time to cultivate understanding
and the intuitive feel for the subject.  If I can use IP, Mathcad,
ProSolv, Lotus 1-2-3, Excel, etc. to allow the students to spend more
time on understanding and discussion, and less on calculation, then I
think it is worthwhile.

Peter Schoch




"JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL
60439" wrote:
> Hi all-
>         John Denker sagely says:
> *************************************************************
> We should not under-emphasize sketching in particular, and qualitative
> reasoning in general.  Feynman practically defined "understanding" an
> equation as being able to describe the qualitative properties of the
> solution, without actually grinding out the solution in detail.
>
> Qualitative reasoning should not be taken as a euphemism for doing a sloppy
> job on an intrinsically quantitative question.  Instead, it is the skill of
> giving an appropriately qualitative answer to a qualitative question.
> ***********************************
>         Not only do I agree, but I expect that there will be many such
> questions in the Tartakoff and Uretsky calculus text.
>                                         Regards,
>                                                 Jack
>
>         "I scored the next great triumph for science myself,
> to wit, how the milk gets into the cow.  Both of us
> had marveled over that mystery a long time.  We had
> followed the cows around for years - that is, in the
> daytime - but had never caught them drinking fluid of
> that color."
>                 Mark Twain, Extract from Eve's
>                 Autobiography