Art Duval and Helmut Knaust

1. Art Duval and Helmut Knaust Department of Mathematical Sciences The University of Texas at El Paso March 8, 2002

2. Contents • Robert Lee Moore – The Mathematician • The Classical Moore Method • Intermission: Video • Our Experiences with the Moore Method at UTEP • Discussion

3. 1882 • Born in Dallas, Texas • 1898 - 1901 • B.A. and M.A., The University of Texas • 1902 - 1903 • High School Teacher in Marshall, Texas

4. 1903 - 1905 • Ph. D., University of Chicago, • Advisors: E.H. Moore & O. Veblen • 1905 - 1920 • Teaching at various universities 1904

5. 1920 - 1969 • Professor at The University of Texas • 1974 • Died in Austin, Texas 1937 1969

6. 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.

7. 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

8. 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

9. An excerpt from … W.S. Mahavier and W.T. Mahavier: Analysis N.B.: This text for a whole semester is 12 pages long.

10. Intermission: Video

11. 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)

12. 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.

13. An excerpt from… C. S. Schumacher: Chapter Zero

14. 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 :)”

15. The Student Perspective • Cristina Torres Principles of Mathematics, Fall 2001

16. 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.

17. “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!” • “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.” • Student comments* * Course Evaluation, Math 3341, Spring 2001 “…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.”

18. The Student Perspective • Susan Arrieta Introduction to Analysis, Spring 2001 Real Variables, Fall 2001

19. 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

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? • Finding suitable teaching material

21. 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

22. All Questions Answered, All Answers Questioned* * Borrowed from Donald Knuth

23. 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@math.utep.edu Helmut Knaust helmut@math.utep.edu