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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."
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).
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.