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Re: Teaching Problem Solving - Moore Method



On Tue, 22 Oct 2002 10:02:56 -0700, Richard Hake said:

Information regarding the famous mathematician R.L. Moore and his
"Moore Method" are at the Univ. of Texas's "The Legacy of R.L. Moore"
at <http://www.discovery.utexas.edu/rlm/index.html>:

"Professor Moore's method of teaching at The University of Texas was
a forerunner of inquiry-based learning, a method which has been
recommended in the report of a review of undergraduate education made
to the National Science Foundation in 1996. . . .(NSF 1996). . . .
entitled 'Shaping the Future.' What has become known as the 'Moore
Method' provides an example worth studying by anyone interested in
teaching and, in particular, provides an opportunity to learn how
teaching and research need not be separate, competing enterprises.
R.L. Moore, together with the community of his fellow teachers of
mathematics at The University of Texas, and their students and
students of students, form an historically significant and
influential group in American mathematics."


(extensive material deleted)


DANCIS&DAVIDSON-DANCIS&DAVIDSON-DANCIS&DAVIDSON-DANCIS&DAVIDSON
Under this method each student proves as many theorems and solves as
many problems as possible by himself outside of class. For each
theorem or problem, one student presents, at the blackboard, a proof
or a solution that he devised by himself. Students are not permitted
to discuss mathematics outside of class. The Texas method makes use
of a competitive atmosphere. There is competition among students to
impress the teacher and to solve more of the difficult problems than
their classmates. Friendly competition spurs many students to work
harder than they would otherwise, and occasionally to work above and
beyond reasonable limits (i.e., to the detriment of other courses).



(more material delete)



The Texas method does a spectacular job of differentiating between
the stronger and the weaker students. This method has been used as a
filtering device to identify mathematical talent. The filter has also
convinced other students that they do not really want to become
mathematicians.

The Moore method is well suited for courses at the senior and first
year graduate level and for some research courses. A senior level
course in topology or complex variables is a good course for a
teacher to first try out the Moore method. The authors have no
experience and some apprehension about using the Moore method in
isolated freshman or sophomore courses which are part of a standard
curriculum.

As a staff scientist from 1972-1981 in the Department of
Astronomy at the University of Texas at Austin and as an aspiring
instructor, I learned of R.L. Moore because I attended UT-Austin's
"Teaching Enhancement Center" activities. A baccalaureate
mathematics and philosophy major with an interest in the foundations
of mathematics, I was very interested in Moore being one of the
outstanding "constructivists" of his day. A constructivist is one
who does mathematics research only with what he is capable of proving
himself. Because of this constraint, the constructivist program has
had success in only a few branches of what today we consider modern
mathematics. Had I chosen to become a mathematician rather than an
astronomer, I doubt I would have chosen the constructivist's path.

As an instructor, I am alarmed at the suggestion this method
ought to be emulated widely in a variety of classes. Clearly, the
pedagogy associated with the method selects for a specific kind of
student, so it would be best used for those individuals already
existentially committed (graduate students and the most advanced
undergraduates) to the field of study in which it is used and who
already have developed a clear vision of how to solve problems. The
Moore method does not teach heuristics -- it forces its users to
develop these methods themselves with NO outside intervention. The
method, at worst, filters for the brightest AND most motivated
students; it does not create the conditions for bright students to
FIND motivation for further study or a professional commitment to the
subject being "taught". As such, I find it totally inappropriate for
use in non-science major classes. These classes need to act as
"pumps", not "filters".

Paul
--
Paul M. Rybski, Ph.D., Associate Professor and former Chair,
Dept. of Physics, and
Director, Whitewater Observatory
University of WI-Whitewater
Whitewater, WI 53190-1790

Office FAX: (414) 472-5633
Email address: rybskip@uww.edu

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.