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Re: Teaching Problem Solving - Moore Method



Please excuse this cross posting, in the interests of
interdisciplinary synergy to discussion lists with archives at:

Phys-L <http://lists.nau.edu/archives/phys-l.html>,

PhysLrnR <http://listserv.boisestate.edu/archives/physlrnr.html>,

Math-Learn <http://groups.yahoo.com/group/math-learn/>.

In his PhysLrnR post of 21 Oct 2002 15:37:31-0500, titled "Re:
Teaching Problem Solving," Laurent Hodges wrote:

HODGES-HODGES-HODGES-HODGES-HODGES-HODGES-HODGES-HODGES
"> Does anyone have an answer to my question, or better yet, an
effective way of teaching problem solving that doesn't require TAs?
Well, there are the methods of R.L. Moore in mathematics! Pretty
drastic, but produced only great students."
HODGES-HODGES-HODGES-HODGES-HODGES-HODGES-HODGES-HODGES

To which Larry Smith responded on 21 Oct 2002 15:55:42-0600:

"Please elaborate. I spent 7 yrs in R.L. Moore Hall in Austin without
learning as much about the man whose namesake it was as I'd have
liked. What were his methods?"

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."

The best discussion of the Moore Method that I have found is that by
the redoubtable Paul Halmos (1988, pages 255-265). [See, also Halmos
(1974, 1983, 1988b). Unfortunately Halmos's lively exposition does
not seem to appear at
<http://www.discovery.utexas.edu/rlm/index.html>.

However, the descriptions of the Moore Method by Jones (1974) and by
Dancis & Davidson (1970) at the above site are of interest. Quoting
the latter (EMPHASIS in the original, bracketed by
"DANCIS&DAVIDSON-DANCIS&DAVIDSON-. . ." so as to avoid the use of
quotes within quotes
" ' ' "):

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).

Students sometimes work on a difficult theorem for a week or more
until someone finally proves it. In advanced courses some of the
problems are open questions, and some of their solutions have become
Ph.D. theses. Thus, the Texas method requires and tends to produce
student willingness to work on problems for long periods of time.
Considerable increases in a student's self confidence will result
from his solving difficult problems.

We now present a brief description of blackboard procedures. In
selecting someone to present a solution to the class, the teacher
picks one of the students who claims to have ALREADY solved the
problem by himself outside of class. Some teachers prefer to call on
the weaker students first. (If a student is hot upon the trail of a
theorem and doesn't want to see someone else's proof, he may leave
class during the presentation.)

Suppose a student is presenting a proof to the class, and a mistake
is found in the proof. If the student can repair the damage
immediately - fine; however, the teacher does not permit the student
to flounder at the blackboard while attempting to repair his proof.
If the mistake in the student's proof can be corrected, the student
is permitted to try again, usually the next day. However, if the
student shows little understanding of the problem, the teacher might
choose to send another student to the board to present a solution.

During a weak student's presentation, the instructor SHOULD be
supportive. This includes helping the student clarify HIS [the
student's] ideas and statements. Proper use of this system does NOT
include the teacher embarrassing or actively discouraging the weaker
student; he does not permit other class members to do so either.

One method of grading is for the instructor to give a standard-type
final examination and to use the results of this examination as the
main criteria for grading those students who have presented few
results to the class.

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.

We conclude by noting that the Moore method tends to develop
ambition, a competitive spirit, and perhaps "Texas-style
individualism." Its most striking success has been in the field of
point-set topology. The list of R.L. Moore's doctoral students
includes a sizable number of outstanding researchers in topology.
(Whyburn, L.S. 1970)
DANCIS&DAVIDSON-DANCIS&DAVIDSON-DANCIS&DAVIDSON-DANCIS&DAVIDSON


The fact that the most of the current generation of physicists,
Physics Education Researchers (PER's), and mathematicians (are there
any MER's?) are oblivious of the "Moore Method" {not to mention the
"Benezet Method" (1935/36)} reminds me of my 1980's informal survey
of Indiana University physics faculty. I asked them individually if
they had ever heard of (a) Percy Bridgeman, and (b) R.W. Wood. About
80% of faculty under 40 years of age had never heard of either! The
percentages would probably be even lower today.

I wonder how the survey would go among today's PhysLrnR's,
Phys-L'ers, and Math-Learn'ers?

Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
<rrhake@earthlink.net>
<http://www.physics.indiana.edu/~hake>
<http://www.physics.indiana.edu/~sdi>


"He who knows only his own generation
Remains always a child."
Cicero (in "Orator")


REFERENCES
Benezet, L.P. 1935-1936. The teaching of arithmetic I, II, III: The
story of an experiment, Journal of the National Education Association
24(8), 241-244 (1935); 24(9), 301-303 (1935); 25(1), 7-8 (1936). The
articles were:

(a) reprinted in the Humanistic Mathematics Newsletter #6: 2-14 (May 1991);

(b) placed on the web along with other Benezetia at the Benezet Centre.
online at <http://wol.ra.phy.cam.ac.uk/sanjoy/benezet/>. See also
Mahajan & Hake (2000).

Dancis, J. & N. Davidson. 1970. "The Texas Method and the Small Group
Discovery Method" online at
<http://www.discovery.utexas.edu/rlm/reference/dancis_davidson.html>.

Jones, F.B. 1974. "The Moore Method," American Mathematical Monthly
84: 273-277; online at
<http://www.discovery.utexas.edu/rlm/reference/burton_jones.html>.

Halmos, P.R. 1974."Measure Theory." Springer Verlag.

Halmos, P.R. 1983. "Selecta: Expository Writing" Springer Verlag.
From the forward: "Paul Halmos has been famous for several decades as
a past master in all forms of mathematical exposition: articles,
books, lectures."

Halmos, P.R. 1988a. "I Want to be a Mathematician: An Automathography
in Three Parts," Mathematical Association of America, p. 258: "Some
say that the only possible effect of the Moore method is to produce
research mathematicians, but I don't agree. The Moore method is, I am
convinced the right way to teach anything and everything. It produces
students who can understand and use what they have learned. It does,
to be sure, instill the research attitude in the student -- the
attitude of questioning everything and wanting to learn answers
actively -- but that's a good thing in every human endeavor, not only
in mathematical research. There is an old Chinese proverb that I
learned from Moore himself:
'I hear, I forget; I see, I remember. I do, I understand.' "

Halmos, P.R. 1988b. "I Have a Photographic Memory. Mathematical
Association of America. Contains a nice photo of Magnus R. Hestenes.
Halmos's caption reads: "Magnus was a part of the Chicago crowd when
I first met him, but he has been at UCLA for a long time. I associate
his name with the calculus of variations, the old Bliss school."
Magnus was also co-producer of that well-known geometric-calculus
variant David Hestenes (2001).

Hestenes, D. 2001. "Oersted Medal Lecture: Reforming the Mathematical
Language of Physics," AAPT Announcer 31 (4): 64: online as a pdf at
<http://modelingnts.la.asu.edu/> / "Overview of GC" where "/" means
"click on." See also "Spacetime Physics with Geometric Algebra" loc.
cit.

Mahajan, S. & R.R. Hake. 2000. "Is it finally time for a physics
counterpart of the Benezet/Berman math experiment of the 1930's?"
Physics Education Research Conference 2000: Teacher Education; online
as ref. 6 at the Benezet Centre
<http://wol.ra.phy.cam.ac.uk/sanjoy/benezet/>.

NSF. 1996. "Shaping the future: new expectations for undergraduate
education in science, mathematics, engineering, and technology;
online at <http://www.nsf.gov/cgi-bin/getpub?nsf96139>. See also NSF
(1998).

NSF. 1998. "Shaping the future, volume II: perspectives on
undergraduate education in science, mathematics, engineering, and
technology; online at
<http://www.nsf.gov/cgi-bin/getpub?nsf98128>.

Whyburn, L.S. 1970. "Student Oriented Teaching - The Moore Method,"
American Math. Monthly 77 (1970) 351-359.

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