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. <<<<
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************