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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