Art Duval and Helmut Knaust

The Moore MethodA Tradition of Active Student Learning in Mathematics

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

Department of Mathematical SciencesThe University of Texas at El Paso

March 8, 2002

Art Duval Art Duval and and Helmut KnaustHelmut Knaust



Contents

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



• 1882– Born in Dallas, Texas

• 1898 - 1901– B.A. and M.A.,

The University of Texas• 1902 - 1903

– High School Teacher in Marshall, Texas



• 1903 - 1905– Ph. D., University of Chicago, – Advisors: E.H. Moore & O. Veblen

• 1905 - 1920– Teaching at various universities

1904



• 1920 - 1969– Professor at The University

of Texas • 1974

– Died in Austin, Texas

1937

1969



• 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.



• R.L. Moore’s 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



• R.L. Moore’s Method of Teaching (cont’d)– 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 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



An excerpt from …

W.S. Mahavier and W.T. Mahavier:Analysis

N.B.: This text for a whole semester is 12 pages long.



Intermission:Video



• 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• Introduction to Analysis (junior level), Real Analysis

(senior/beginning graduate level)– Art Duval

• Principles of Mathematics (junior level)



• 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.



An excerpt from…

C. S. Schumacher:Chapter Zero



• Student comments*

* Course Evaluation, Math 3325, Fall 2001

“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 enjoyedthe class :)”

“At first I did not like that we would be graded on presentations. But I see where it has been helpful.”



• The Student Perspective

– Cristina TorresPrinciples of Mathematics, Fall 2001



• 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.


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



• The Student Perspective

– Susan ArrietaIntroduction to Analysis, Spring 2001Real Variables, Fall 2001



• 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



• 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



• 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



All Questions Answered,All Answers Questioned*

* Borrowed from Donald Knuth



• 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 [email protected] Knaust [email protected]

http://www.discovery.utexas.edu/index.html

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Art Duval and Helmut Knaust