To Teach or to Learn - the Adult Learner Model

Introduction

Listening | Information Listening | Social Listening | Listening for Appreciation | Critical Listening

Critical ReadingThe SQ3R Reading Method

Reading Material, Journals and References

 

Bloom's Learning:  Benjamin Bloom's Holistic Teaching:  Affective | Psychomotor | Cognitive

 

Education Links

 

Getting to Knowledge

 

Threshold of BIC

 

 

 

 

 

 


 

Introduction

 

What is the difference between teaching and learning?

 

Teaching is passive, whereas learning is active. Never confuse motion with action, says an old adage.  View teaching as motion, whereas learning is motion and action.  Management guru Dr. Henry Mintzberg likes to say that teaching management to the uninformed is a waste of time and diminishes management - referring to full time MBA students with little, to no practical management experience.  Then there are the experienced professionals enrolled in non-traditional universities who complained because they are too busy and need to know exactly what to read, in order to make efficient use of time and complete assignments as quickly as possible." - In this context, "knowledge" as defined in Benjamin Bloom's Holistic Teaching, can best be described as the existing beliefs, context and ideas, whereas in Dr. Bloom's terminology, evaluation is more closely related to the transfer function attempting to overcome the threshold of BIC.

 

To change teaching, counseling, advising, or learning styles, it is necessary to understand adult learning characteristics and their implications" say  Maxine E. Rossman, Mark H. Rossman in their piece titled The Rossman Adult Learning Inventory: Creating Awareness of Adult Development as part of a doctoral dissertation.   Using a sixty-item questionnaire, the Rossman Adult Learning Inventory (RALI), was conceptualized, developed, field-tested, and revised (Rossman, 1977). The purpose of the study was to determine the extent to which community college faculty were aware of adult-learning characteristics. The study concludes that adult learners are better suited for non-traditional universities as:

  • Adults need to know why they are learning.
  • Adults need to be seen as competent.
  • Adults want their knowledge and skills acknowledged in the classroom.
  • Adults need to be self-directed and experientially involved in their learning.
  • Adults want learning to be life-centered and applicable

So, how do we reconcile the apparent paradox?  To teach as Dr.Mintzberg suggests, adapt teaching methods following the RALI guidelines, or?

What Mr. Mintzberg clearly refers to is a student body with little to practical experience in management.  This implies that the BIC (Beliefs, Ideas and Concepts) database is null.  Sort of like elementary school children, or even trying to describe the an elephant to a person who has never had eyesight.  Now compare this to the part-time university student who has plenty of practical experience, who sees himself more than competent, yet when shown flaws in his reasoning, he answers  "no, it is not a flaw in my reasoning, I am just stating my opinion".  Or what about the student who complaints because the questions being asked require him to think, rather than find the answer in a specific page of the assigned reading material?

For these purposes, we make a distinction between data, information and knowledge, where in order for information to become knowledge, it must overcome the threshold of BIC - that is, the information obtained must break through the preconceived notions and ideas, such as the previous example of flawed reasoning.  That is, as long as the student fails to recognize that his reasoning is flawed, the new information he receives, might as well be discarded.

 

Getting from information to knowledge:  Concepts, Beliefs, Ideas

 

Robert Lee Moore (1882-1974) was a towering figure in twentieth century mathematics, internationally recognized as founder of his own school of topology, which produced some of the most significant mathematicians in that field. The  Moore Teaching Method, which he devised virtually prohibit students from using textbooks during the learning process, call for only the briefest of lectures in class and demand no collaboration or conferring between classmates encouraging  students to solve problems using their own skills of critical analysis and creativity. Moore summed it up in just eleven words: 'That student is taught the best who is told the least.'

 St. Augustine provides an excellent illustration of the challenges found in overcoming the threshold of BIC:  "There is no doubt that it is better to communicate knowledge in parables for we appreciate more that which we get from hard work, for the seeking gives greater pleasure in the finding.  For those who seek but do not find, suffer from hunger. Those again who do not seek at all because they have everything, often die.  Either of these two extremes  is to be avoided."

Then there is the old Chinese Proverb:  Tell me, I'll forget, show me, I may remember, involve me, I'll not forget.

The Adult Learner Method is a combination of Moore method, St. Augustine's edict and the Chinese proverb:  Involve the adult learning in the learning process using a minimalist approach, while identifying and overcoming the threshold of BIC (Threshold of BIC

 

 


 

 

Bloom's Learning

Bloom's Taxonomy is considered to be a foundational and an essential element within the education community, consisting of a classification of the different learning objectives that educators set for students, first presented in 1956 through the publication The Taxonomy of Educational Objectives, The Classification of Educational Goals, Handbook I: Cognitive Domain, by Benjamin Bloom (editor), M. D. Englehart, E. J. Furst, W. H. Hill, and David Krathwohl. The Taxonomy divides educational objectives into three domains: Affective, Psychomotor, and Cognitive. Within the taxonomy learning at the higher levels is dependent on having attained prerequisite knowledge and skills at lower levels . A goal of Bloom's Taxonomy is to motivate educators to focus on all three domains:



Affective
Skills in the affective domain describe the way people react emotionally and their ability to feel another living thing's pain or joy. Affective objectives typically target the awareness and growth in attitudes, emotion, and feelings.

There are five levels in the affective domain moving through the lowest order processes to the highest:

Receiving
The lowest level; the student passively pays attention. Without this level no learning can occur.

Responding
The student actively participates in the learning process, not only attends to a stimulus; the student also reacts in some way.

Valuing
The student attaches a value to an object, phenomenon, or piece of information.

Organizing
The student can put together different values, information, and ideas and accommodate them within his/her own schema; comparing, relating and elaborating on what has been learned.

Characterizing
The student holds a particular value or belief that now exerts influence on his/her behaviour so that it becomes a characteristic.

Psychomotor
Skills in the psychomotor domain describe the ability to physically manipulate a tool or instrument like a hand or a hammer. Psychomotor objectives usually focus on change and/or development in behavior and/or skills.
Bloom and his colleagues never created subcategories for skills in the psychomotor domain, but since then other educators have created their own psychomotor taxonomies.

Cognitive

Skills in the cognitive domain revolve around knowledge, comprehension, and critical thinking of a particular topic. Traditional education tends to emphasize the skills in this domain, particularly the lower-order objectives.

There are six levels in the taxonomy, moving through the lowest order processes to the highest:

Knowledge
Exhibit memory of previously-learned materials by recalling facts, terms, basic concepts and answers
· Knowledge of specifics - terminology, specific facts
· Knowledge of ways and means of dealing with specifics - conventions, trends and sequences, classifications and categories, criteria, methodology
· Knowledge of the universals and abstractions in a field - principles and generalizations, theories and structures

Questions like: What are the health benefits of eating apples?

Comprehension

Demonstrative understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas
· Translation
· Interpretation
· Extrapolation

Questions like: Compare the health benefits of eating apples vs. oranges.

Application
Using new knowledge. Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way


Questions like: Which kinds of apples are best for baking a pie, and why?

Analysis
Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations
· Analysis of elements
· Analysis of relationships
· Analysis of organizational principles


Questions like: List four ways of serving foods made with apples and explain which ones have the highest health benefits. Provide references to support your statements.

Synthesis
Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions
· Production of a unique communication
· Production of a plan, or proposed set of operations
· Derivation of a set of abstract relations

Questions like: Convert an "unhealthy" recipe for apple pie to a "healthy" recipe by replacing your choice of ingredients. Explain the health benefits of using the ingredients you chose vs. the original ones.

Evaluation
Present and defend opinions by making judgments about information, validity of ideas or quality of work based on a set of criteria
· Judgments in terms of internal evidence
· Judgments in terms of external criteria

Questions like: Do you feel that serving apple pie for an after school snack for children is healthy? Why or why not?


Some critiques of Bloom's Taxonomy's admit the existence of these six categories, but question the existence of a sequential, hierarchical link.

The revised edition of Bloom's taxonomy has moved Synthesis in higher order than Evaluation, for example, whereas as some consider the three lowest levels as hierarchically ordered, but the three higher levels as parallel. Others say that it is sometimes better to move to Application before introducing concepts.

 


 

Education Links

 

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Reading Material, Journals and References

  • 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.)
  • 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.
  • Bing, RH, (1973, October 5). Remarks at the Dedication of R.L. Moore Hall.
  • Bing, RH, 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.
  • Fitzpatrick, B., 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).
  • 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.
  • Lewis, Albert C., 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.
  • Moore, R.L., "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). On CD.
              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.
  • 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.

 

  • 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.
  • Frantz, J.B., "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).
  • Lewis, Albert C., "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.
  • 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.
  • Zitarelli, David, "The Origin and Early Impact of the Moore Method", Amer. Math. Monthly 111(2004): 465-486.
  • 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.
  • 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.
  • 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" (400).
  • 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)
  • 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).
  • 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.”

 

  • 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.
              The theologian James W. McClendon recalls his experience as a calculus student with Dr. Moore in 1943.
  • 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.
  • 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. On CD.
  • 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.
  • 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.
  • Adamson, I., 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.
  • Burger, Edward B., Extending the Frontiers of Mathematics, (Key College Publications, 2006).
              An inquiry-based introduction to mathematical proof echoing the Moore style.
  • Donnell, William, "Discovering Divisibility Tests," Mathematics in School (May 2008), 14-15.
  • 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."
  • 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)
  • 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."
  • 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).
  • 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).
  • Backlund, Ulf, and Leif Persson, "Moore's teaching method," Normat 41, 1996, 145-149. (In Swedish)
  • 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.
  • 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, K. "The greatest math teacher ever," Devlin's Angle at MAA Online. Also on CD.
  • Eyles, Joseph, Introduction to Ph.D. thesis, R.L. Moore's Calculus Course, (The University of Texas at Austin,1998). Also on CD.
  • Eyles, Joseph, "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.
  • Halmos, Paul R., "How to Teach," I Want to be a Mathematician. (SpringerVerlag, 1985). pp. 254-264. Also on CD.
  • Halmos, Paul R., "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."
  • Halmos, Paul R., & 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.
  • Kauffman, Robert M. 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.
  • Mahavier, W. Ted, et al., "A Demonstration of the Moore Method", Quicktime movie.
  • Mahavier, W.Ted, 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.
  • Moore, R.L. Notes for the MAA film, "Challenge in the Classroom." Also on CD.
  • Moore, R.L. (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.
  • Wilder, R.L., "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).
  • Anderson, L. W.  Sosniak, L. A. (1994) Bloom's Taxonomy: A forty-year retrospective.

  • Krathwohl, D. R, Anderson, L. W. (2001) A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives Learning Domains or Bloom's Taxonomy - Donald R. Clark

  • Paul, R. (1993). Critical thinking: What every person needs to survive in a rapidly changing world (3rd ed.). Rohnert Park, California: Sonoma State University Press.

  • Taxonomy of Educational Objectives: The Classification of Educational Goals; pp. 201–207; B. S. Bloom (Ed.) Susan Fauer Company, Inc. 1956.

  • A Taxonomy for Learning, Teaching, and Assessing — A Revision of Bloom's Taxonomy of Educational Objectives; Lorin W. Anderson, David R. Krathwohl, Peter W. Airasian, Kathleen A. Cruikshank, Richard E. Mayer, Paul R. Pintrich, James Raths and Merlin C. Wittrock (Eds.) Addison Wesley Longman, Inc. 2001

  • "Taxononmy of Educational Objectives. Handbook II: The affective domain; Krathwohl, D. R., Bloom, B. S., Masia, B. B.; 1964.

 

 

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