The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 1/20 Contents 1.Robert

The Moore MethodA Tradition of Active Student Learning in Mathematics

“That student is taught the best who is told the least.”

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Contents

1. Robert Lee Moore – The Mathematician2. The Classical Moore Method3. Intermission: Video4. Experiences with the Moore Method at UTEP5. Discussion

March 4, 2005



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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; retired at age 87 after teaching for 64 years!

• 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. Moore’s Method of Teaching I

– Used in Moore’s Calculus classes all the way to graduate research courses in topology

– Students present solutions in front of the class– 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



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• R.L. Moore’s Method of Teaching II

– Competitive classroom atmosphere• No cooperation between students, in class or in

preparation for class• R.L. Moore usually called on the weakest students first

– 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. Moore’s Method of Teaching III

– Emphasis on student’s self-reliance• Students were not allowed to use books, or ask other

students/instructors for help– Built on R.L. Moore’s ability to carefully gauge each

student’s 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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• Other Practitioners of The “Texas Method” at UT Austin

Hyman J. Ettlinger(At UT 1913-1969)

Hubert S. Wall(At UT 1946-1966)



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Intermission:Video



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• The Moore Method at UTEP– Michael O’Neill (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• Principles of Mathematics, Introduction to Analysis

(junior level), Real Analysis (senior/beginning graduate level)

– Art Duval• Principles of Mathematics, Introduction to Analysis

(junior level)



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• Principles of Mathematics– Uses a Moore-style textbook – Students are called on or volunteer to

present material in class– Students are encouraged to cooperate in

preparation for class.– Class time management: about 65% of the

time is spent on student presentations, about 35% of the time the instructor stands at the blackboard and teaches.



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An excerpt from…

C. S. Schumacher:Chapter Zero



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• Introduction to Analysis

– Uses a theorem-sequence text (without any proofs) – Students are called “at random” or volunteer to present

material in class– Students are encouraged to cooperate in preparation for

class.– Class time management: about 75% of the time is spent on

student presentations, about 25% of the time the instructor teaches.



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• An excerpt from the theorem-sequence text I use in Math 3341



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• Student comments*

* Course Evaluation, Math 3341, Spring 2001

“It forces students to be ready for class and doesn’t allow for people to slack off eternally and then catch up at the end.”

“At first I thought Dr. Knaust’s class was insane to have students everyday going to the board.

However Dr. Knaust’s 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!”

“…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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• 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?



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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)

– John Parker, R. L. Moore: Mathematician & Teacher, MAA 2004

Documents

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 1/20 Contents 1.Robert