Art Duval and Helmut Knaust

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Art Duval and Helmut Knaust
Department of Mathematical Sciences The
University of Texas at El Paso March 8, 2002
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• Contents
• Robert Lee Moore The Mathematician
• The Classical Moore Method
• Intermission Video
• Our Experiences with the Moore Method at UTEP
• Discussion

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• 1882
• Born in Dallas, Texas
• 1898 - 1901
• B.A. and M.A.,
• The University of Texas
• 1902 - 1903
• High School Teacher in Marshall, Texas

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• 1903 - 1905
• Ph. D., University of Chicago,
• Advisors E.H. Moore O. Veblen
• 1905 - 1920
• Teaching at various universities

1904
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• 1920 - 1969
• Professor at The University
• of Texas
• 1974
• Died in Austin, Texas

1937
1969
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• R.L. Moore was one of the most accomplished
  mathematicians in the first half of the 20th
  century.
• He was President of the American Mathematical
  Society from 1936-1938.
• He had more than 50 Ph.D. students.
• Three of his students became Presidents of the
  American Mathematical Society.
• Six students served as Presidents of the
  Mathematical Association of America.
• A sour note R.L. Moore never let black students
  take his classes, even after UT Austin was
  desegregated.

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• R.L. Moores Method of Teaching
• Only the class framework is provided by the
  instructor
• The instructor assigns problems to the class, but
  does not teach
• Students work on assigned problems outside of
  class
• Students present solutions in front of the class
• The students in the audience act as a jury for
  the validity of the presentations
• The instructor insures the correctness of the
  mathematical content both on the board and in the
  student discussions

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• R.L. Moores Method of Teaching (contd)
• Competitive classroom atmosphere
• No cooperation between students, in class or in
  preparation for class
• R.L. Moore usually called on the weakest students
  first
• Emphasis on students self-reliance
• Students were not allowed to use books, or ask
  other students/instructors for help
• Built on R.L. Moores ability to carefully gauge
  each students capabilities and her progress
  throughout the semester

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An excerpt from W.S. Mahavier and W.T.
Mahavier Analysis N.B. This text for a whole
semester is 12 pages long.
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• Intermission
• Video

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• The Moore Method at UTEP
• Michael ONeill (now at Claremont-McKenna)
• Principles of Mathematics, Introduction to
  Analysis (both junior level), Real Analysis
  (senior/beginning graduate level), Real Variables
  (graduate level)
• Helmut Knaust
• Introduction to Analysis (junior level), Real
  Analysis (senior/beginning graduate level)
• Art Duval
• Principles of Mathematics (junior level)

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• Principles of Mathematics
• Uses a Moore-style textbook
• Students volunteer to present material in class
• Students are encouraged to cooperate in
  preparation for class.
• Class time management about 70 of the time is
  spent on student presentations, about 30 of the
  time the instructor teaches.

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An excerpt from C. S. Schumacher Chapter Zero
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• Student comments
• 
  Course Evaluation, Math 3325,
  Fall 2001

At first I did not like that we would be graded
on presentations. But I see where it has been
helpful.
I am ... appreciative for your patience and
nice constructive criticism. I think that you
never made anyone feel inadequate or ignorant no
matter how far off they were.
I took this course before with another
instructor and ... the students didn't know what
the instructor was talking about. ... this
instructor made it easier for the student to
understand.
Difficult - but challenging. I felt I learned a
lot. I truly enjoyed the class )
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• The Student Perspective
• Cristina Torres
• Principles of Mathematics, Fall 2001

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• Introduction to Analysis
• and Real Analysis
• Uses textbooks with proofs and exercises (without
  proofs)
• Students are called at random to present
  material in class
• Students are encouraged to cooperate in
  preparation for class.
• Class time management about 70 of the time is
  spent on student presentations, about 30 of the
  time the instructor teaches.

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• Student comments
• 
  Course Evaluation, Math 3341,
  Spring 2001

At first I thought Dr. Knausts class was insane
to have students everyday going to the board.
However Dr. Knausts method of having the
students do the board work was unique and helped
me to learn. This was the toughest class I
have ever taken!
It forces students to be ready for class and
doesnt allow for people to slack off eternally
and then catch up at the end.
Presenting the material studied in front of
your peers really makes you study hard and it is
a very good way to learn the material.
His technique is unorthodox, but extremely
helpful.
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• The Student Perspective
• Susan Arrieta
• Introduction to Analysis, Spring 2001
• Real Variables, Fall 2001

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• Lessons Learned
• It is crucial to create the right class
  atmosphere
• Works best when all students have similar
  mathematical backgrounds and abilities.
• Optimal class size 4-12 students

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• Challenges
• What to do when none of the students is willing
  to step up to the blackboard?
• What to do if no student finds the error on the
  blackboard?
• Finding suitable teaching material

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• Can the Moore Method work in other disciplines?
• We think it will work in classes
• where the main objective is for students to
  build their abilities rather than for the
  instructor to disseminate knowledge

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• All Questions Answered,
• All Answers Questioned
• Borrowed from Donald Knuth

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• Resources
• The R.L. Moore Legacy Project at The Center for
  American History at The University of Texas at
  Austin
• (http//www.discovery.utexas.edu/index.html)
• The Texas pages of MathNerds
• (http//www.mathnerds.com/texan/index.asp)
• Art Duval artduval_at_math.utep.edu
• Helmut Knaust helmut_at_math.utep.edu