Categories:

Moore Method

Course Resources

Personal Experiences

History

Mathematics

Biography

Mentions

Issues in Education

Moore Method

• Backlund, Ulf, and Leif Persson, "Moore's teaching method," Normat 41, 1996, 145-149. (In Swedish)
• Barrett, Lida K., and Long, B. Vena, "The Moore Method and the Constructivist Theory of Learning: Was R. L. Moore a Constructivist?" PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(2012), 75-84.
  "... many mathematicians, including those who criticize constructivism, revere R. L. Moore as an outstanding teacher of mathematics.... The goal of this article is to show that Moore's method aligned with a constructivist approach."
• Brown, Stephen I., Reconstructing School Mathematics: Problems with Problems and the Real World (Peter Lang, 2001).
  "What might be viewed as highly suspect (if not downright immoral and debilitating) in the light of present-day prizing of cooperative learning, was a life-enhancing source for an unusually large number of students. In fact, R.L. Moore single-handedly turned out this century's leading set-theoretic topologists." (p. 42) The author was a student of E.E. Moise (Moore PhD, 1947) at the Harvard Graduate School of Education.
• Buck, Robert E., "Conjecturing," PRIMUS; 16(June 2006), 97-104.
  A seminar course for junior-senior mathematics majors is described. The topic is continued fractions, taught by a modified Moore Method, where the focus is on students creating their own mathematics.
• Chalice, D., "How to teach a class by the modified Moore method," Amer. Math. Monthly 102, 1995, 317-321. On CD.
• Clark, David M., "R.L. Moore and the learning curve." On CD.
  
• ______, "The teaching of geometry," 2016.
  "[I]mplementation of the Common Core State Standards for geometry cannot be successful until our teachers themselves gain a modern mastery of the subject that is consistent with these standards."
  
• Cohen, D.W. "A modified Moore method for teaching undergraduate mathematics," Amer. Math. Monthly 89, 1982.
• Coppin, Charles A.; Mahavier, W. Ted; May, E. Lee; and Parker, G. Edgar, The Moore Method: A Pathway to Learner-Centered Instruction, Mathematical Association of America, 2009.
• Dancis, Jerome and Davidson, Neil, "The Texas Method and the Small Group Discovery Method." (1970). Also on CD
• Devlin, Keith, "The greatest math teacher ever," Devlin's Angle blog at MAA Online.
• Eyles, Joseph, Introduction to Ph.D. thesis, R.L. Moore's Calculus Course, (The University of Texas at Austin,1998). Also on CD.
• ______, "Discovering R.L. Moore's calculus class," talk at the International Congress of Mathematicians 1998. On CD.
• Fitzpatrick, B. "The teaching method of R.L. Moore," (in Chinese, translated by Yang Shoulian) Higher Mathematics 1, 1985, 41-45.
• Forbes, D.R. The Texas System: R.L. Moore's Original Edition, Ph.D. thesis, University of Wisconsin, 1971.
• Garrigus, David. "Creativity in Mathematics." 2009.Video available in three parts on YouTube and with additional material on DVD.
  More than twenty-five influential teachers, top researchers, inventors, and leaders of industry attest to the life changing rewards that began for them in a classroom taught by IBL and the Moore Method.
• Halmos, Paul R., "How to Teach," I Want to be a Mathematician. (SpringerVerlag, 1985). pp. 254-264. Also on CD.
• ______., "What is teaching?" Amer. Math. Monthly 101 (1994): 848-855.
  "I will not, I told them, lecture to you .... They stared at me, bewildered and upset--perhaps even hostile. ... They suspected that I was trying to get away with something, that I was trying to get out of the work I was paid to do. I told them about R.L. Moore, and they liked that, that was interesting. Then I gave them the basic definitions they needed to understand the statements of the first two or three theorems, and said 'class dismissed'. It worked."
• ______., & Moise, Edwin E. "The problem of learning how to teach," Amer. Math. Monthly 82 (1975): 466-474. On CD.
• Halmos, Paul R., with Renz, Peter, I Want To Be A Mathematician: A Conversation with Paul Halmos. Film by George Csicsery. 2009. Available through the Mathematical Association of America. Description and trailer from Zala Films.
  "The 1999 interview with Paul Halmos (1916-2006) that forms the backbone of I Want To Be A Mathematician was initiated to gather some comments from Halmos about R.L. Moore for the Educational Advancement Foundation’s R.L Moore Legacy Project."
• Jones, F. Burton, "The Moore Method," Amer. Math. Monthly 84 (Apr. 1977): 273-277. Also on CD.
• Kapur, J.N., "Moore method of teaching," in Current Issues in Higher Education in India, (S. Chand, 1975), pp. 203-205.
  "Today's world needs creative minds and in India the need for such minds is desperate. We should experiment with any method which has a promise of enabling the students to face unfamiliar situations with confidence. The world is so dynamic today that mastery of facts has become secondary to mastery of techniques of acquiring knowledge." Kapur was a professor at Indian Institute of Technology, Kanpur, and Vice-Chancellor of Meerut University.
• Kauffman, Robert M., "Some remarks on the Socratic method in mathematics." On CD.
• ______. et al., "A Demonstration of the Moore Method", Quicktime movie.
• Legacy of R.L. Moore Project, "Master of the Game," 10-minute video. Available through the EAF.
  This is a sample reel, prepared by George Paul Csicsery, for a proposed new video on Dr. Moore and the Moore Method. It includes excerpts from interviews with mathematician Paul Halmos and theologian James W. McClendon.
• Mahavier, William S., "What Is the Moore Method?" Primus, 9 (December 1999): 339-254. Also on CD.
• Mahavier, W. Ted, "A gentle discovery method (the modified Moore method)," College Teaching 45, 1997, 132-135. On CD.
• ______, et al., "A Demonstration of the Moore Method", Quicktime movie.
• ______, E. Lee May, and G. Edgar Parker, A Quick-Start Guide to the Moore Method.
• Moise, E.E. "Activity and motivation in mathematics," Amer. Math. Monthly 72, 1965, 407-412. Also on CD.
• Moore, R.L. "Challenge in the Classroom." Video. (Mathematical Association of America, 1967). Available through the EAF in VHS or DVD format. Transcript.
  This film features interviews with Moore and shows him in the classroom. It is the only attempt he made to publicize his teaching method.
• ______,. Notes for the MAA film, "Challenge in the Classroom." Also on CD.
• ______. (1948, May 17). Letter to Miss Hamstrom, a prospective student. Published in A Century of Mathematical Meetings (American Mathematical Society, 1996), pp. 295-300. Also on CD.
• Parker, G.E. "Getting more from Moore." Primus, vol. 2 (September 1992): 235-246. Also on CD.
• Renz, Peter, The Moore Method: What discovery learning is and how it works. FOCUS: Newsletter of the Mathematical Association of America. (1999, August/September). PDF Version (37KB).
• Spresser, Diane, "The Moore Method: Viewpoint of a Department Chair," 2008.
• Whyburn, Lucille S., "Student-oriented teaching - the Moore method," Amer. Math. Monthly 77, 1970, 351-359. On CD.
• Wilder, Raymond L., "Axiomatics and the development of creative talent," The Axiomatic Method with Special Reference to Geometry and Physics, L. Henken, P. Suppes, and A. Tarski (eds), North-Holland, (1959), 474-488. Also on CD.
• ______., "Material and method," Undergraduate Research in Mathematics: A Report of a Conference Held at Carleton College, Northfield, Minnesota, June 16 to 23, 1961, Edited by Kenneth O. May and Seymour Schuster, pp. 9-27.
• Yorke, J.A., and Hartl, M.D. "Efficient methods for covering material and Keys to Infinity," Notices of the AMS (June/July 1997): 685-687. PDF version on the AMS web.
  “Since the roots of the problems described above run so deep, it is imperative that potential solutions (such as the Moore method) be implemented early in students’ careers—and not just for students planning to become mathematicians” (p. 686).

Course Resources
(See also the Journal of Inquiry-Based Learning in Mathematics which publishes university-level course notes that are freely downloadable, professionally refereed, and classroom-tested.)

• Adamson, I., A General Topology Workbook, ( Springer, 1996).
  “Highly influenced by the legendary ideas of R. L. Moore, the author has taught several generations of mathematics students with these materials, proving again the usefulness and stimulation of the Moore method” (cover). The author was a student at Princeton 1949-52 (Ph.D. under Emil Artin) and was introduced to the Moore method there by Ralph Fox.
• ______, A Set Theory Workbook, (Springer, 1997).
  “The main purpose of this approach is to encourage readers, in the well known educational method of R.L. Moore, to try hard to prove results for themselves” (cover). Review in American Mathematical Monthly on JSTOR.
• Asghari, Amir, "Moore and less!," PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(2012), 509–524.
  "The Moore Method ... implicitly supported me to put into practice an extremely non-traditional approach [in a multivariable calculus course] where traditions are highly ubiquitous. However, I changed the method to such a great extent that one can hardly recognize Moore anymore." The author is at Shahid Behesti University, Tehran.
• Bhushan, Shantha, D. Divakaran, and Tulsi Srinivasan, "Inquiry-based learning in an Indian context," Blackboard. Bulletin of the Mathematics Teachers' Association (India), January 2022, Issue 4: 63-75.
  
  “For Calculus 1, we drew heavily upon existing IBL courses by CA Coppin [Linear point set theory, Journal of Inquiry-Based Learning, No 14, 2009] and WT Ingram [WT Ingram, Foundations of Calculus: Properties of the Real Numbers, Functions and Continuity, Journal of Inquiry-Based Learning, No 11, 2009.], which are closer to Moore's approach of starting with definitions and axioms.” (65)
• Burger, Edward B., Extending the Frontiers of Mathematics, (Key College Publications, 2006).
  An inquiry-based introduction to mathematical proof echoing the Moore style. Online review by William J. Satzer.
• Clark, David M., Euclidean Geometry: A Guided Inquiry Approach, (American Mathematical Society and Mathematical Sciences Research Institute, 2012).
  Makes use of a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory. Written for an undergraduate axiomatic geometry course, the book is particularly well suited for future secondary school teachers. It covers all the topics listed in the Common Core State Standards for high school synthetic geometry.
• Clark, David M., and Xiao, Xiao, The Number Line through Guided Inquiry, (American Mathematical Society, 2021).
  "We describe here some sample formats that GIL [guided inquiry learning] courses at colleges and universities have used. During the twentieth centrury GIL was developed as a distinctive pedagogy at the UNiversity of Texas with a focus on training research mathematicians. At this time Ph.D.s in mathematics were scarce and demands for their skills were growing. Hyman Ettlinger, R. L. Moore, and H. S. Wall formulated a particularly rigorous version of GIL to meet these needs" (p. 117).
• Donnell, William, "Discovering Divisibility Tests," Mathematics in School (May 2008), 14-15.
• ______, "Elementary theory of factoring trinomials with integer coefficients over the integers," International Journal of Mathematical Education in Science and Technology 41(2010): 1114-1121.
  Includes a suggestion for an inquiry-based learning project.
• ______, "Slip and Slide Method of factoring trinomials with integer coefficients over the integers", International Journal of Mathematics Education in Science and Technology, 43(2012): 548-553.
  Includes a suggestion for an inquiry-based learning project.
• Dydak, Jerzy, and Feldman, Nathan, "Major Theorems on Compactness: a Unified Exposition," Amer. Math. Monthly 99(1992), 220-227. On JSTOR.
  "[O]ne can easily convert this text to a collection of problems in classes where the Moore Method is used."
• Hale, Margie, Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture, (Mathematical Association of America, 2003).
  From review by Marion Cohen: "I also thoroughly approve of her format, which is consistent with the Moore Method...."
  
• Halmos, Paul, Linear Algebra Problem Book, (Mathematical Association of America, 1997).
• Henle, James, An Outline of Set Theory, (Springer, 1986).
  "[T]his is a Moore-style text whose proper use depends on the confluence of a patient instructor open to the Moore technique ... with motivated and intelligent students. ... Highly recommended." (Judith Roitman, from review in The Journal of Symbolic Logic, 52(1987), 1048-1049. JSTOR link.) See also The American Mathematical Monthly, 95, 1988, p. 844 (on JSTOR) for Roitman's response to the "vituperative review" by C. Smorynski.
• Hodge, Jonathan, and Klima, Richard E., The Mathematics of Voting and Elections: A Hands-On Approach, (American Mathematical Society, 2005).
  “From a pedagogical standpoint this book was inspired by our involvement in the Legacy of R.L. Moore Project …. When we set out to write this book, we wanted to capture the spirit of a Moore method course, but we also wanted to make sure that the resulting text was accessible to a non-mathematical audience.” (p. x) Online review by Raymond N. Greenwell.
• Horton, Nicholas J., "I hear, I forget. I do, I understand: A modified Moore-Method mathematical statistics course," The American Statistician 67(2013): 219-228.
• Jolly, R.F., Synthetic Geometry, (Holt, Rinehart and Winston, 1969).
  Dedicated to R.L. Moore, this text follows a "developmental" course which "entails letting the student develop a body of mathematical material under the guidance of the professor."
• Levine, Alan L., Discovering higher mathematics: four habits of highly effective mathematicians, Harcourt Academic Press, 2000.
"In an effort to show prospective mathematics majors that mathematics is a vital and beautiful subject, Levine organizes his book around active participation by students in a four-stage scheme for doing mathematics: experimentation, conjecture, proof, and generalization." -- Review by Robert A. Fontenot. American Mathematical Monthly 108, 2001, 179-182 (on JSTOR).
• Mahavier, Wm.Ted, "Interactive Numerical Analysis," Creative Math Teaching 3, 1-2.
• Marshall, David C.; Odell, Edward; Starbird, Michael, Number Theory Through Inquiry, Mathematical Association of America, 2007.
  A text "designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). The result of this approach will be that students:
  • Learn to think independently
  • Learn to depend on their own reasoning to determine right from wrong
  • Develop the central, important ideas of introductory number theory on their own."
  "An extremely ambitious and attractive new textbook." –Review by John J. Watkins, The Mathematical Intelligencer 31, 2009, 82-83.
• McLoughlin, P., "A Modified Moore approach to teaching probability and mathematical statistics: An inquiry based learning technique," ASA Proceedings of the Joint Statistical Meetings, 2008.
• Moise, Edwin E., Introductory Problem Courses in Analysis and Topology, (Springer, 1982).
  "The Moore Method is an idea with many fruitful aspects. Let us not throw out the whole idea because it has some difficult points, rather let us search for a wider application of the good aspects. Moise has written an excellent book; it should make it easier for the problem course approach to find a larger place in the undergraduate curriculum." (From the review by Carl C. Cowen in the Amer. Math. Monthly, 91(1984): 528-530.)
• Nanzetta, Philip, and Strecker, George E., Set Theory and Topology, (Bogden & Quigley, 1971).
  "Those experienced in the Moore method, I believe, will appreciate and be able to use this book just on the basis of the first two chapters on set theory, but they write their own sets of notes for topology and won't need this one. To those not experienced in the Moore method, I recommend this book as a means of introduction to the method and say, 'try it, you'll like it.'" (R.R. FitzGerald, from review in Amer. Math. Monthly 79(1972), 920-921.)
• Schumacher, Carol, Chapter Zero: Fundamental Notions of Abstract Mathematics (Addison-Wesley, 1996).
  From the blurb: "Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups." Reviewed by Robert A. Fontenot. American Mathematical Monthly 108, 2001, 179-182 (on JSTOR).
• Starbird, Michael, and Su, Francis, Topology Through Inquiry (MAA Press, American Mathematical Society, 2019).
  A text "designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students."
• Taylor, Ron, and Rault, Patrick X., A TeXas Style Introduction to Proof, Mathematical Association of America, 2017.
  
• Terry, Lawson, Topology: A Geometric Approach, (Oxford University Press, 2003).
  "These chapters are written in a very different style, which is motivated in part by the ideal of the Moore method of teaching topology combined with ideas of VIGRE programs in the US which advocate earlier introduction of seminar and research activities in the advanced undergraduate and graduate curricula" (p. vi).

Personal Experiences as Students and Teachers

• Avers, Paul W., "A unit in high school geometry without the textbook," in Mathematics in the Secondary School Classroom: Selected Readings, ed. by G.R. Rising and R.A. Wiesen. (Thomas Y. Crowell, 1972), pp. 231-234.
  "Avers' instructional program parallels the work of the nationally known R.L. Moore of the University of Texas. Both are able to get their students emotionally involved with their subject by taking away their textbooks." (From the editorial introduction, p. 227.)
• Brown, J., "My Experiences with the Various 'Texas Styles' of Teaching," 1996. Also on CD.
• Daniel, Dale; Eyles, Joseph W.; Mahavier, Wm.Ted; Pember, J.Craig, "On using the discovery method in the distance-education setting," 2001. Handout.
• Foster, James A., and Barnett, M., “Moore formal methods in the classroom: A how-to manual,” in Teaching and Learning Formal Methods, ed. by M. Hinchey, C. N. Dean. (Morgan Kaufmann, 1996), pp. 79-98.
  “One of us (Barnett) took courses taught using the method in the departments both of mathematics and of computer sciences while in Austin in the 1980s. We describe the method as it was experienced at that time” (p. 85).
• Foster, James A.; Barnett, M.;Van Houten, K.; Sheneman, "(In)Formal Methods: Teaching Program Derivation via the Moore Method," Computer Science Education, 6(1), 1995, pp. 67-91.
  "[T]he students learned the underlying mathematics of program derivation and learned to apply it, by presenting proofs and derivations on a daily basis. Professorial intervention in the classroom was minimal. Our experience has been that students learn otherwise difficult material better, and are better able to put it into practice, with this teaching technique than they would have been able to do in the typical classroom."
• Good, Chris, "Teaching by the Moore Method," MSOR Connections 6 No. 2(2006), 34-38.
  The author, professor of mathematics at the University of Birmingham in England, describes a first-year course, "Development of Mathematical Reasoning," which has proven popular and effective for mathematics students entering the university.
• Green, John W., Interview with Ben Fitzpatrick. 1999. On CD.
• Heath, J., "The Discovery Method." Also on CD.
• Heath, R.W., "The discovery method of teaching mathematics." On CD.
• Ingram, W.T., and Hall, L.M., "Report on the Faculty Mentoring Project: Foundations of Mathematics Course (Math 209)," 2002. On CD.
• Kauffman, Robert, "Three variations on a theme." On CD.
• Kennedy, Judy, "My Experiences with the Moore Method." 1996. Also on CD.
• Lemke, James, "Discovery Learning." 1996. An expanded version is on CD as "The Moore Method."
• Mahavier, Lee, "On three crucial elements of Texas-style teaching as shown to be successful in the secondary mathematics classroom," 1999. Handout.
• McClendon James W., On R.L. Moore.
  A prominent theologian recalls his experience as a calculus student with Dr. Moore in 1943.
• Neuberger, J. W., "Academic Freedom," 2014.
  "This note concerns the increasing pressure felt by students to climb the academic ladder."
• Ormes, N., "A beginner's guide to the Moore Method," 1999. On CD.
• Reagan, Becky, "Testimonial on the influences of R. L. Moore." On CD.
• Reed, M., "Comments on Moore-method teaching." 1996. Also on CD.
• Selden, Annie, 40+ Years of Teaching and Thinking about University Mathematics Students, Proofs, and Proving: An Abbreviated Academic Memoir, Technical Report No. 2017-2, Department of Mathematics, Tennessee Technological University, 2017.
  "Before [my husband John and I] got interested in mathematics education as a research subject, we were mathematicians teaching at least some upper-division and graduate mathematics courses using the Moore Method."
• Siegel, Martha J., “Teaching mathematics as a service subject,” in A. G. Howson, et al., eds., Mathematics as a Service Subject, ICMI Study Series, (Cambridge University Press, 1988), pp. 75-89.
  “I have taught, or rather the students have taught themselves, a full syllabus of the course … using a small group discovery method. … In a sort of Moore method approach, the students are given examples to work out with guidance, a form of programmed prodding towards a solution.” (p. 85)
• Smith, M., "Learning and Teaching Mathematics via Discovery," 1996. On CD.
• Stallman, C., "What I learned from my semester with William S. Mahavier," and W.S. Mahavier, "Mentoring the Moore Method," 2001. On CD.
• Steenrod, N., Letter to R.L. Wilder, 1937, regarding Lefschetz's trying out the Moore Method at Princeton University.
• Suppes, P., “Uses of artificial intelligence in computer based instruction,” in Artificial Intelligence in Higher Education: International Symposium Proceedings, eds. V. Marik, O. Stepankova, Z. Zdrahal, (Springer, 1991).
  “We adopted a computer version, so to speak, of the famous R.L. Moore method of teaching. ... It is easy to implement such a method in a computer framework. A typical example would be a presentation of fifteen elementary statements about the geometrical relation of betweenness among three points. Students are asked to select no more than five of the statements as axioms and to prove the rest as theorems” (p. 208).
• Transue, W.R.R., "Thoughts on 'Discovery' Type Teaching." 1996. Also on CD.
• Vick, James W., Review of two topology texts, Amer. Math. Monthly 116(2009): 373-375.
  "The evidence is clear that the discipline and rigor learned through [the Moore method] have lasting effects. I can still remember the thrill of discovery and the triumph of presentation of a basic theorem as a freshman 47 years ago. ... I will fashion a course [from the text] in which I will include as many of the applications as possible, and on Fridays I will convert the class into a Moore method setting, with students proving theorems from a separate list I have generated." Vick, a professor at the University of Texas at Austin, is a third generation doctoral descendant of Moore.
• Wadle, L., "My experience with the R.L. Moore teaching method," 2001. On CD.
• Woodruff, Edythe, "My experiences with the Moore Method," 2005.
• Young, S.W., "Christmas in Big Lake." 1998. Also on CD.
• Zenor, P., "Personal essay on the Moore Method," 1996. On CD.

History

• Bing, RH, "Notes for R H Bing's Plane Topology Course." On CD.
  A one-semester undergraduate course started by Bing at Wisconsin and continued by R.E. Fullerton, S.C. Kleene, and R.F. Williams. The notes were used by C.B. Allendoerfer at the University of Washington and by W.L. Duren, Jr., at Tulane University.
• Center for American History Archives. Collection Description. R.L. Moore Archives.
• Fitzpatrick, B., "Some aspects of the work and influence of R.L. Moore," Handbook of the History of General Topology, Vol. 1. C.Aull and R. Lowen (eds), Kluwer Academic 1997, 41-61. On CD.
• Frantz, J.B., "The Moore Method," The Forty Acres Follies, Texas Monthly Press, 1983, 111-122. On CD.
• ______., "One-of-a-kind alumni," Alcalde 7(1984), 20-24. On CD.
• Jones, F. Burton, "The Beginning of Topology in the United States and The Moore School," in C.E. Aull & R. Lowen eds., Handbook of the History of General Topology, Volume 1. Kluwer Academic Publishers: 97-103 (1997). Also on CD.
• Lewis, Albert C., "The beginnings of the R. L. Moore school of topology," Historia Mathematica, 31, 2004, 279-295. Preprint (240 KB PDF file).
• ______., "Reform and Tradition in Mathematics Education: The Example of R.L. Moore." April 1998.
• Moore, R.L., (1930, May 22-23). Letter to G.T. Whyburn concerning the axioms of Foundations of Plane Analysis Situs. Also on CD.
• Starbird, Michael , "Inquiry-Based Learning Through the Life of the MAA,"
in A Century of Advancing Mathematics, Stephen F. Kennedy, et al., (eds), Mathematical Association of America 2015, 239-252.
"Perhaps because of the distinctiveness of the teaching methods that Moore’s students had experienced in his classes, many of his students were active in educational issues. Specifically, many of them became leaders in the MAA, participating actively in the educational issues of their day."
• Whyburn, Lucille S., "Letters from the R.L. Moore Papers", Proceedings of the 1977 Topology Conference I, Topology Proc. 2 (1) (1977): 323-338.
• Wilder, Raymond L., "The mathematical work of R.L. Moore: its background, nature, and influence," Arch. History Exact Sci. 26 (1982): 73-97.
• Zitarelli, David, "Towering figures in American mathematics," Amer. Math. Monthly 108(2001): 606-635. On CD. On JSTOR.
• ______, "The Origin and Early Impact of the Moore Method", Amer. Math. Monthly 111(2004): 465-486.

Mathematics - Sample Work of Some Who have Experienced the Moore Method

• Bing, RH, "Metrization of topological spaces," Canadian Journal of Mathematics 3(1951), 175-186. On CD.
• Eaton, William T., "The sum of solid spheres," Michigan Mathematical Journal 19(1972), 193-207. On CD.
  Awarded the 1976 R.L. Moore - H.S. Wall prize.
• Kennedy, Judy, "How indecomposable continua arise in dynamical systems," Annals of the New York Academy of Science 704(1993), 180-201. On CD.
• Kuperberg, Krystyna, "A smooth counterexample to the Seifert Conjecture," Annals of Mathematics 140(1994), 723-732. On CD.
• Lax, Peter, "Change of variables in multiple integrals," Amer. Math. Monthly 106(1999), 497-501 (on CD and JSTOR), and "Change of variables in multiple integrals II," Amer. Math. Monthly 108(2001), 115-119. On JSTOR.
  Dedicated to Moore's student E.C. Klipple "who taught me real variables by the R.L. Moore method at Texas A&M in 1944."
• Zettl, Anton, Sturm-Liouville Theory, (American Mathematical Society, 2005).
  Quotes R.L. Moore in the epigram to Chapter 2: "That student is taught the best who is told the least."

Biography of Moore and His Students

• Bart, Jody, Mary Ellen Rudin is mentioned in Women Succeeding in the Sciences: Theories and Practices across Disciplines, (Purdue University Press, 2000).
• Albers, D. and Reid, C., "An interview with Mary Ellen Rudin," More Mathematical People, D.Albers, G.Alexanderson, C.Reid (eds) (Harcourt Brace Jovanovich, 1990), pp. 283-303.
• Anderson, Richard D., "I Led Three Lives in Mathematics", MER Newsletter, (MER Forum, Fall 1998), 3-11. On CD.
• Armentrout, Steve, and Kirby, Rob, (eds) Robert Lee Moore. Celebratio Mathematica(msp, 2011).
• Bing, RH, (1973, October 5). Remarks at the Dedication of R.L. Moore Hall.
• ______, et al., (1976, January 24). Remarks at The University of Texas at Austin Mathematics Award Honoring the Memory of Professor Robert Lee Moore and Professor Hubert Stanley Wall. Also on CD.
• Corry, Leo, "A Clash of Mathematical Titans in Austin: Harry S. Vandiver and Robert Lee Moore," The Mathematical Intelligencer 29(2007), 62-74. (First page preview from the publisher.)
• Fitzpatrick, B., "The Students of R.L. Moore". Also on CD.
• ______., and Sher, R.B. "B.J. Ball: An appreciation," Topology and Its Applications 94(1999), 3-6. On CD.
• Green, John W., Presentation at the 2001 Legacy of RL Moore Conference.
  A principal research biostatistician with DuPont corporation talks about how he went from topology to statistics and "how Dr. Moore’s influence continues in this new career." In the course of a challenging and politically sensitive research position Dr. Green shows how important qualities such as persistence, self-reliance, and clear thinking, as well as a sense of humor, have proven to be valuable lessons he took from Dr. Moore’s classes. (See also his interview with B. Fitzpatrick above.)
• Hennon, Claudia, "Mary Ellen Rudin," in Women in Mathematics: The Addition of Difference (Indiana University Press, 1997). Reprinted in Celebratio Mathematica.
  
• Kenschaft, Patricia C., Change is Possible: Stories of Women and Minorities in Mathematics, American Mathematical Society, 2005.
  Accounts of Mary Ellen Rudin, Lida Barrett, and Lucille Whyburn are included.
• Lewis, Albert C., R.L. Moore entry in The New Handbook of Texas.
• ______., R.L. Moore entry in the Dictionary of Scientific Biography, (Charles Scribner's Sons, 1990): vol. 18, 651-653.
• McAuley, L., Dedication to F.B. Jones, Proceedings of the Auburn Topology Conference, March 1969. On CD.
• Moore, R.L., "A lineage of R.L. Moore." On CD.
  Moore's genealogical notes on his paternal grandmother's family.
• ______, "Genealogy research of R.L. Moore." Moore's notes. On CD.
• Murray, Margaret A.M., Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America,MIT Press, 2000.
  Interviews are included with Mary Ellen Rudin and Lida Barrett.
• Parker, J., R. L. Moore: Mathematician and Teacher (Mathematical Association of America, 2005).
  This is the most comprehensive biography to date and, in contrast to D. R. Traylor’s 1972 account, it was able to make extensive use of Dr. Moore's papers and the oral history resource in the Archives of American Mathematics.
• Rogers, J.T., "F.B. Jones -- An appreciation," 1999. On CD.
• Rudin, Mary Ellen, "The early works of F.B. Jones," Handbook of the History of General Topology, Vol. 1. C.Aull and R. Lowen (eds), Kluwer Academic 1997, 85-96. On CD.
• Stephan, F.F., Tukey, J.W., et al.,, "Samuel S. Wilks" Journal of the American Statistical Association 60(1965).
  Wilks's first advanced mathematics course was under R.L. Moore.
• Traylor, D.R., Creative Teaching: The Heritage of R.L. Moore, University of Houston, 1972.
  Written during Dr. Moore’s lifetime but not authorized by him, this account by a member of the Moore school of mathematics is a major resource for information about his life and career. The author interviewed early students and colleagues. Chapters by W. Bane and M. Jones list publications by Moore and his mathematical descendants.(See Paul Halmos's review in Historia Mathematica 1(1974), 188-192.) His audio recordings of interviews with Anna Mullikin, Blanche Bennett Grove, F. Burton Jones, George Hallett, and others, can be accessed at the Archives of American Mathematics website.
• Wilder, Raymond L., "Robert Lee Moore 1882-1974," Bull. AMS 82, 1976, 417-427. Also on CD.
• Young, G.S., "Being a student of R.L. Moore," 1938-42, A Century of Mathematics Meetings, AMS, 1996, 285-293.
• Zettl, A., "Research on differential equations." On CD.
  Zettl describes his research but includes a brief biographical account of his family's harrowing escape from a Yugoslavian concentration camp and eventual immigration to the US. Thanks to the Moore Method used in classes that he took, he found his weak mathematics background to be no great disadvantage since he was on the same initial footing as everyone else.
• Zitarelli, David, and Bartlow, Thomas L.,"Who was Miss Mullikin?" American Mathematical Monthly 116(2009): 99-114. See The Mathematical Tourist synopsis by Ivars Peterson.
  Little had been known about Moore's third PhD student Anna Mullikin (1922) who published only one research paper, her dissertation, and became a high school teacher. This article sheds new light on her life and shows how influential her mathematics and her teaching were. For a demonstration of Mullikin's Nautilus, see Demo Collection..

Mentions of Moore and the Moore Method

• Ager, Tryg, A., “From interactive instruction to interactive testing,” in Artificial Intelligence and the Future of Testing ed. Roy O. Freedle, (Lawrence Erlbaum Associates, 1990).
  From the section “Example of finding-axioms: mathematical conjecture”: “VALID has one other exercise type that I would like to discuss. This is by far the most complex type of problem in the course. Based on an idea of R. L. Moore and modified for interactive use in VALID, there are seven ‘finding-axioms’ exercises, of which the following is the simplest” (p. 40).
• Dreyfus, T., and Eisenberg, T., "On different facets of mathematical thinking," in The Nature of Mathematical Thinking, eds. R. J. Sternberg, T. Ben-Zeev (Lawrence Erlbaum Associates, 1996), pp. 253-284.
  Includes a basically sympathetic account of the Moore Method but finds cooperative learning, viewed as "humanizing Moore," to be more congenial, especially for less motivated students.
• Dutilh Novaes, Catarina. The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning. (India: Cambridge University Press, 2020).
  
  "An influential 'dialogical' approach to teaching the technique of mathematical proof dates back to the early twentieth century: the so-called Moore method (Jones, 1977). The method is named after its creator ..." (p. 181).
• Eisenberg, Theodore. “Some of My Pet-Peeves with Mathematics Education,” Mathematics & Mathematics Education: Searching for Common Ground, Michael N. Fried, Tommy Dreyfus (eds.), Springer (2014), 35-44.
  "My heroes in those days were mathematicians who had a sincere interest in teaching ... [including] R.L. Moore who had this new (to me) way of teaching by pitting student against student in competitive situations. (I did not like the competitive part of Moore's teaching, but one certainly could not argue with his success. And so in mathematics education classes we talked about how to humanize Moore's method.)"
• Garrity, T.A. All the Mathematics You Missed: But Need to Know for Graduate School, (Cambridge University Press, 2002), pp. 77-78.
  Discusses significance of point-set topology and its changing role in the curriculum over the last 70 years with a special mention of its use by Dr. Moore at the University of Texas.
• Hersh, Reuben, and John-Steiner, Vera, Loving + Hating Mathematics, (Princeton University Press, 2011).
  "The stories of Clarence Stephens and Robert Lee Moore embody two different, opposed strains in American education .... full integration of previously excluded groups ... requires more than mere legal equality, it demands transformative teaching methods." (p. 299)
• Knuth, Eric J., " Secondary School Mathematics Teachers' Conceptions of Proof," Journal for Research in Mathematics Education 33, 2002, 379-405.
  "As undergraduates, do prospective teachers have opportunities to experience and discuss these roles of proof? The Moore Method of teaching, for example, which is used by some mathematicians, provides undergraduate students with just such an experience." (p. 400)
• Laursen, Sandra L., and Rasmussen, Chris, "I on the Prize: Inquiry Approaches in Undergraduate Mathematics," International Journal of Research in Undergraduate Mathematics Education 5, 2019, 129-146.
  Mentions the historical role of the Moore Method and the Educational Advancement Foundation.
• Lucas, J.R. The Conceptual Roots of Mathematics: An Essay on the Philosophy of Mathematics. (Routledge, 2000).
  The author, a Fellow of Merton College, Oxford, argues for a form of logicism in which much of mathematics is grounded in transitive relations instead of natural numbers or set theory. After looking at Alfred North Whitehead’s failed attempt to found geometry and topology on a mereological basis, i.e. a theory of whole and part, he considers the transitive relation of ‘being embedded in’ as utilized by R.L. Moore.
• Milnor, John, “Growing up in the old Fine Hall,” in Prospects in Mathematics
  ed. Hugo Rossi (American Mathematical Society, 1999), p. 3
  “The person who was closest to me in the early years [at Princeton University] was Ralph Fox. … I particularly enjoyed the course in point set topology which he taught by a form of the R. L. Moore method: He told us the theorems and we had to produce the proofs. I can’t think of a better way of learning how to make proofs and how to learn the basic facts of topology – it was a marvelous education.”
• Morrel, J.H. “Why lecture? Using alternatives to teach college mathematics,” in Teaching in the 21st Century: Adapting Writing Pedagogies to the College Curriculum, (Routledge (UK), 1999), pp. 29-48. Online purchase http://www.questia.com/
  “In order to adapt this [the Moore method where students ‘understood the topics extremely well and had a lot of practice in writing and explaining mathematics’] to an undergraduate setting, in which the time constraints and required syllabi mitigate against the use of such a method, I have used a modification of this approach … ” (p. 38).
• Palombi, Fabrizio, and Rota, Gian-Carlo, Indiscrete Thoughts, (Birkhäuser, 1997).
  "The core of graduate education in mathematics was Dunford's course in linear operators. Everyone who was interested in mathematics at Yale eventually went through the experience, even such brilliant undergraduates as Andy Gleason, McGeorge Bundy, and Murray Gell-Mann. The course was taught in the style of R.L. Moore ..." (p. 29).
• Raiffa, H. “Game theory at the University of Michigan, 1948-1952,” in Toward a History of Game Theory ed. E. Roy Weintraub, (Duke University Press, 1993).
  “I took a course called ‘Foundations of Mathematics’ with Professor Copeland, who taught in the R. L. Moore style: students are challenged to act like mathematicians, to convince themselves and others of the veracity of some plausible conjectures, to concoct starkly simple illuminating counterexamples, to generalize, to speculate, to abstract. No books were used. All the results were proved by the students. … I became hooked. Even though I didn’t know Leonard J. (Jimmy) Savage at the time, he also became enthralled in the same type of teaching program by being forced to act like a mathematician. I decided to become a pure mathematician and pursue a Ph.D. degree” (p. 166).
• Ross, Arnold E., "Creativity: Nature or Nurture? A View in Retrospect," in N. Fisher, et al., eds., Mathematicians and Education Reform, 1989-1990, (American Mathematical Society, 1991), pp. 39-84.
  Ross's early education in the USSR he likens to the Moore Method. Its spirit of “explanation and justification” continued to characterize his own approach to teaching mathematics. However, he mistakenly attributes its origins in the USA to E.H. Moore. (More on this misunderstanding can be found in the 1999 videotaped interview with Ross available at the Archives of American Mathematics.)
• Samuelson, Paul A., Inside the Economist's Mind: Conversations with Eminent Economists, (Blackwell, 2006).
  Robert Aumann on taking real variables from the logician Emil Post at City College in the 1940s: "It's called the Moore method—no lectures, only exercises. It was a very good course." (p. 329)
• Schmitz, S., and East, K. “Using proof pedagogy to scaffold pre-service teachers' application of child development,”Teacher Education & Practice, 31(2018), 63–80.
  “After learning about the Moore method, it occurred to us that this kind of thinking was exactly what we wanted pre-service teachers to do with development. We wanted our students to apply knowledge of development rather than simply learn about development.” (65)
• Selden, A., and Selden, J. “Tertiary mathematics education research and its future,” in Teaching and Learning of Mathematics at University Level: An ICMI Study, ed. Derek Holton, (Springer, 2001), pp. 255-274.
  A section on the Moore Method suggests that courses making use of it “could provide interesting opportunities for research in mathematics education.”
• Shier, D.R., and Wallenius, K.T. Applied Mathematical Modeling: A Multidisciplinary Approach, (CRC Press, 1999).
  “The modeling approach in applied mathematics has much in common with the discovery methods used in pure mathematics, such as the famous R. L. Moore approach” (p. 14).
• Szenberg, M., and Ramrattan, L.B.,eds., Collaborative Research in Economics: The Wisdom of Working Together, (Springer, 2017).
  “Collaboration is formed from the desire to follow or imitate the leader. ... The mathematic discipline provides such an example in regard to the Moore method.” (Introduction by the editors, pp. 15-16.)
• Winkler, P. Mathematical Puzzles: A Connoisseur's Collection, (A K Peters, Ltd., 2004).
  The author comments on the “figure 8s in the plane puzzle" that he “heard it attributed to the late, great topologist R. L. Moore.”

Related Issues in Education

• Bagnato, Robert A., "Teaching College Mathematics by Question-and-Answer," Educational Studies in Mathematics 5(Jun., 1973), 185-192. On JSTOR.
• Finkel, Donald L., Teaching with Your Mouth Shut, (Boynton/Cook, 2000).
  "The teacher, then, attempts to create a blueprint for learning by keeping her mouth shut and instead designing an environment for her students with the following three features: (1) The teacher presents an overall problem-to-be-solved, which is broken down into smaller problems that build on each other …. (2) The teacher creates a blueprint for a ‘whole’ experience …. (3) She reconfigures the classroom so that she is ‘out of the middle’ ….” (p. 108).
  "In sum, the teacher refuses to govern the students in their inquiry because he wants the students to learn how to govern themselves” (p.115).
• Kilpatrick, Jeremy, "Confronting reform." Amer. Math. Monthly 104 (1997): 955-962. Also on CD.
• John Selden, and Selden, Annie, "Unpacking the Logic of Mathematical Statements," Educational Studies in Mathematics, 29 (Sep., 1995), 123-151. On JSTOR.
• Wilder, Raymond L., "The Role of Intuition," Science, NS 156(1967), 605-610. On JSTOR.
  "Intuition plays a basic and indispensable role in mathematical research and in modern teaching methods."
• Woodruff, Paul, Reverence: Renewing a Forgotten Virtue, (Oxford University Press, 2001).
  "A silent teacher need not treat lofty subjects. You think it a trivial fact that seven plus five equals twelve, but one may stand in awe of it nevertheless (as has more than one great philosopher). With awe or without, a teacher is well advised to be quiet from time to time about even the most ordinary facts, so that students may have the freedom to make those facts their own." (On "The Silent Teacher," p. 189.)