Re: [MATHEDCC] RE: Developmental Math Labs

Rob Kimball (rlkimbal@WTCC-GW.WAKE.TEC.NC.US)
Mon, 24 Nov 1997 12:03:36 -0500 (EST)

Here is a real story to go along with Taylor's "piano analogy" (see
below).
A friend of mine has a beautiful daughter who has entered several
"beauty contests" over the last few years. She always does very
well, except in talent. This year, she decided to learn to play
one piece on the piano (a classical work that was somewhat demanding).
She had never taken piano. Six months ago she began practicing
under the tutorlidge of a piano instructor. One week before the
contest (which was last week) she decided to change her talent to
a poetry reading. It seemed that even with all the practice, the
attempt to learn piano "out of context" was not possible.

PS: She didn't win this year either.

Rob Kimball

On Thu, 20 Nov 1997, RWW Taylor wrote:

> Perhaps I can contribute some historical perspective on the issue of
> learning math by independent study. During the 70's and 80's we
> ran a large "Math Learning Center" through which we delivered all of
> our mathematics instruction at NTID (NTID is roughly the equivalent
> of a small community college in many respects). At times we had
> enrollments of over 500 students in our learning center, all being
> taught out of a single large room with instruction being provided on
> a shared basis by a cadre of trained faculty, augmented by student
> assistants. The basic arrangement was for students to study provided
> materials on their own until they could pass a test, then move on.
>
> Ten years ago we dropped this idea entirely in favor of classroom
> instruction. In retrospect I would have to call our efforts during the
> learning-center years, however earnest and well-intentioned, essentially
> a disservice to the students that we worked with. Our whole faculty is
> much happier with the relationships that can be developed in the small-class
> model we follow now. Whether we would be sufficiently happy with a
> large-class model I don't know.
>
> The basic point at stake is the view of what needs to be learned.
> If one views mathematics as just a collection of techniques to be
> mastered (as many of our colleagues in the technical departments
> our courses serve did) then there might be some argument for
> simply providing access to methods for learning to apply these
> techniques to standard problems, and call that mathematics
> education. If, on the other hand, one wants to view mathematics
> as a _process_, as a way of looking at and understanding the world,
> as a way of coping with the non-standard problems that really
> make up life, then mastering a collection of canned techniques
> is a sterile exercise and of little use to students in the long run
> (especially as it is clear that the standard techniques can better
> be applied by using technology).
>
> The actual thinking and recognition of pattern that make up what we call
> "mathematical modelling", as well as appreciation of the subtle points
> that lead one to deeper levels of understanding and provide the real basis
> for further learning, cannot be addressed in a situation where the
> responsibility posed to the student is simply to learn how to solve a given
> set of problems of a particular type. I would pose an analogy to piano
> playing here. You have to learn how to position your hands at
> the keyboard, and to build up strength and dexterity by pursuing
> finger exercises. But all of this will buy you nothing if you are
> not paying attention to the _music_.
>
> RWW Taylor
> National Technical Institute for the Deaf
> Rochester Institute of Technology
> Rochester NY 14623
>
> >>>> The plural of mongoose begins with p. <<<<
>
>
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