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 Lee Moore – The Mathematician 2.The Classical Moore Method 3.Intermission: Video 4.Experiences with the Moore Method at UTEP 5.Discussion March 4, 2005

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 2/ –Born in Dallas, Texas –B.A. and M.A., The University of Texas –High School Teacher in Marshall, Texas

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 3/ –Ph. D., University of Chicago, –Advisors: E.H. Moore & O. Veblen –Teaching at various universities 1904

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 4/ –Professor at The University of Texas; retired at age 87 after teaching for 64 years! 1974 –Died in Austin, Texas

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 5/20 R.L. Moore was one of the most accomplished mathematicians in the first half of the 20 th century. He was President of the American Mathematical Society from 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.

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 6/20 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

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 7/20 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

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 8/20 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

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 9/20 An excerpt from … W.S. Mahavier and W.T. Mahavier: Analysis N.B.: This text for a whole semester is 12 pages long.

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 10/20 Other Practitioners of The “Texas Method” at UT Austin Hyman J. Ettlinger (At UT ) Hubert S. Wall (At UT )

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 11/20 Intermission: Video

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 12/20 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)

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 13/20 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.

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 14/20 An excerpt from… C. S. Schumacher: Chapter Zero

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 15/20 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.

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 16/20 An excerpt from the theorem-sequence text I use in Math 3341

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 17/20 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 Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 18/20 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

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 19/20 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?

The Moore Method A Tradition of Active Student Learning in Mathematics “That student is taught the best who is told the least.” 20/20 Resources –The R.L. Moore Legacy Project at The Center for American History at The University of Texas at AustinThe R.L. Moore Legacy Project ( –The Texas pages of MathNerdsMathNerds ( –John Parker, R. L. Moore: Mathematician & Teacher, MAA 2004