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The Moore Method: A Pathway to Learner-Centered Instruction

The Moore Method: A Pathway to Learner-Centered Instruction

By Charles A. Coppin, W. Ted Mahavier, E. Lee May and G. Edgar Parker

Catalog Code: NTE-75
Print ISBN: 978-0-88385-185-2
Electronic ISBN: 978-0-88385-973-5
260 pp., Paperbound, 2009
List Price: $57.50
MAA Member: $46.00
Series: MAA Notes

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The Moore Method: A Pathway to Learner-Centered Instruction offers a practical overview of the method as practiced by the four co-authors, serving as both a “how to” manual for implementing the method and an answer to the question, “What is the Moore Method?” Moore is well-known as creator of the Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects. Beginning with Moore’s method as practiced by Moore himself, the authors proceed to present their own broader definitions of the method before addressing specific details and mechanics of their individual implementations. Each chapter consists of four essays, one by each author, introduced with the commonality of the authors’ writings. To see a video demonstrating the Moore Method go to www.legacyrlmoore.org/mahavier.

Table of Contents

Dedication 
Acknowledgements
1. Introduction
2. Moore’s Moore Method
3. What is the Moore Method?
4. On Culture
5. Development and Selection of Materials
6. In the Classroom
7. Grading
8. Why Use the Moore Method?
9. Evaluation and Assessment: Effectiveness of the Method
10. Frequently Asked Questions
Appendices
About the Authors
References
Index

Excerpt: Ch. 6 In the Classroom (p.81)

(Parker) A day in a Moore Method classroom. Well, here we are. Class is due to begin in five minutes. I’ve reviewed what happened last class period, slept on it, and thought about it again. Beavis got a nice example that showed that Problem 15 is not a theorem because of the behavior of the function he defined at the boundary of the open interval. Cassie was working on Problem 21 when we ran out of time last class and, from what she’s done so far, it looks like she can make an induction out of what she did when she assumed continuity on two disjoint open intervals. I’ve read the turn-ins that I collected three class periods ago (and am feeling pretty guilty about not having returned them sooner, but that is the way it goes sometimes), made remarks on the four papers, put firmly in mind the neat alternative to Justin’s argument that Bertie found in her proof of Problem 17, and socked away a reminder to look for an opportunity to reinforce the way Justin organized his cases. Ben seems to have had roughly the same idea as Justin, but didn’t sort out the cases effectively in his write-up, so if an opportunity occurs that allows us to recall the structure of Justin’s proof, it will probably help Ben. I have a new sheet containing the next three problems I intended to hand out after Problem 21 got done, plus two problems that Beavis’s example suggests.

SHOWTIME! I return the papers.

“Before we get started today, would you mind, Bertie, if I shared with the class an idea from your proof of Theorem 17? It’s okay if you say ‘no.’ You may not be ready to share your idea yet, but it is awfully pretty.” I mustn’t bully Bertie into giving away her ideas since it may give her an edge in presenting next time her turn comes up. In fact, if I could have thought of a way that she might use what she did to resolve one of the problems that is still unsettled or created a problem that fit the course well on which her idea would work, I wouldn’t be revealing what she did, just congratulating her on that beautiful idea different than Justin’s that she had used in her proof. Bertie seems to be surprised, but gives her assent, and I give a brief description of her argument. After class, she tells me that she thought, since what she had done was different from what Justin presented, that it must have been wrong.

“Does anyone have a question about Beavis’s example from last time or, for that matter, anything else in the course so far?” Harry asks a question about a technical detail in Beavis’s example. Since the point of logic involved has surfaced several times, I answer the question, connecting the point to an earlier theorem and pausing several times to ask Beavis if I am being faithful to his argument. Katie Sue asks a question about the beginning of Cassie’s argument, which I defer, suggesting that she ask it again when Cassie returns to the board.

“If there are no more questions, I have another sheet for you.” I pass out the sheet and make appropriate remarks. In this case, I point out why Problems 25 and 26 are natural conjectures to make in the wake of Beavis’s example, and that if Problem 21 is, indeed a theorem, then Problems 27, 28, and 29 are reasonable questions to ask.

“Cassie, can you finish?” From here, my job becomes wholly reactive, with due attention paid to keeping my peace.

Now that we’ve seen an example of what the beginning of a class might look like, let’s go back and consider an outline of scenarios that are likely to occur on any given class day, and look at some ways to address them.

About the Authors

Charles A. Coppin
I received my baccalaureate from Southwestern University, Georgetown, Texas, and my doctorate in mathematics from the University of Texas, Austin, Texas. I was a student of H.S. Wall, a colleague of R.L. Moore. Having studied Point Set Topology under Moore, I had significant exposure to the Moore method. I was a member of the mathematics faculty at the University of Dallas where I was Chair for several years. I was a Distinguished Visiting Professor of Mathematics at the United States Air Force and Visiting scholar at the Visualization Lab at Texas A&M.

Nothing I have accomplished would have been possible without my wife, Alaine Fay. We have been married 45 very good years. Alaine Fay has been my professional partner. My teaching has been greatly influenced by many years of conversation with her and watching our children grow up. Our family now includes three children, Stephen, Peter, Sarah, and son-in-law Michael.

W. Ted Mahavier
I am a grandson of the Texas Method in two senses. My father, William Mahavier, was a student of Moore, and my advisor, John W. Neuberger, was a student of Wall. Thus, two influential people in my life had considerable exposure to Moore and his colleagues. As a child, I was constantly surrounded by mathematicians and graduate students at departmental social functions at Auburn, Emory, and North Texas. What struck me most as a child growing up around this group of devoted mathematicians was how in one sentence they would be debating properties of indecomposable continua while in the next they would be bragging proudly about how an elementary education major had proved that the square root of two was an irrational number in some particularly interesting way. Their devotion to their research and teaching at every level has stayed with me to this day and my teaching methods are strongly influenced by the courses I took over the years.

In total, I took over 22 courses under nine descendants of either Moore or Wall. Michel Smith’s calculus course at Auburn University caused my change in major from physics to mathematics. My father’s examples, as I sat in on his classes at Emory, stayed with me and eventually led me to teach via Moore’s method. At the University of North Texas, Paul Lewis taught me more about mathematics and teaching mathematics than anyone, and John W. Neuberger, a man whose infinite optimism is an inspiration to all who know him, directed my dissertation. While I am a firm believer in the method and my education was largely guided by mathematical descendants of Moore, H. S. Wall, and H. J. Ettlinger, I remain a strong supporter of other methods, perhaps because the non-Texan Dean Hoffman set the stage for my return to graduate school in a lecture-style class by convincing me that I could prove theorems. I feel deeply indebted to my teachers and I repay them in the only way I can, by carrying their examples into my classroom and passing the time they offered me onto my own students.

E. Lee May
I have been practicing the Moore Method throughout 37 years of teaching. I have taught at Emory University; Kennesaw State University; Wake Forest University; and for most of my career, at Salisbury (Maryland) University. The courses that I have designed bear titles such as “Discovering Affine Transformations,” “Introduction to Abstract Mathematics,” “A History of Mathematics from—through 1600,” and “Statistics through Baseball.” I have received a Maryland Council of Teachers of Mathematics award as an Outstanding College Teacher of Mathematics, and the John M. Smith Award of the Maryland-District of Columbia-Virginia (MD-DC-VA) Section of the Mathematical Association of America (MAA) for Distinguished College or University Teaching. My publications include “Localizing the Spectrum,” “The Local Resolvent Set of a Locally Lipschitzian Transformation is Open,” “Real-Linear (Including Similinear) Operators,” “An Experiment with Mathematical Statistics,” “Are Seven-Game Playoff Series Fairer?”, and “Is the Integral Test Wrong?” A Research Adventure in Calculus,” (My latest two manuscripts are “0 for April, or Are Batting Slumps Inevitable?”, and “The Spectra of Affine Operators.”) I have served as chairman of my department and of my MAA section. I have participated in seven of the eleven Legacy of R.L. Moore Conferences, and chaired or co-chaired three. For ten years I was the founding director of Salisbury University’s Center for Applied Mathematical Sciences, an organization that paired faculty-directed teams of undergraduates with local businesses for the purpose of solving problems for those organizations. I have also spent two years as a fulltime, independent computer-consultant to small businesses.

G. Edgar Parker
I have taught mathematics since 1969 (or since 1963 if you count tutoring I did as a high school student and as an undergraduate college student), settling for this second choice in careers because of an insufficient fastball (or at least that is the reservation the scouts had). My teaching experience includes four years in a public high school; courses at Atlanta Junior College; four years as a teaching assistant during my graduate education at Emory University, by most measures a highly selective university; seven years at what is now University of Texas-Pan American and was, at that time, an open-admission university; and the last twenty-three years at James Madison University. At James Madison, I have taught a full range of the service and pure curriculum, including precalculus, the calculus sequence, math-for-students-who-don’t-want-to-take-math, the mathematics for prospective elementary/middle-school teachers sequence, linear algebra, differential equations, algebraic structures, point-set topology, geometry, analysis, and a course on the structure of the numbers. At both Pan American and James Madison, I have directed undergraduate research projects. The topics for these investigations have ranged through topics as diverse as applications of mathematics to football and basketball, square roots by composition for nonlinear functions, models for the numbers in which numbers are represented by sets of homomorphism and isomorphism. I have taken baby steps into the applied curriculum by teaching the modeling course and developing a version of math-for-students-who-don’t-want-to-take-math that I call The Nature of Applied Mathematics. For the five years that we had it at James Madison, I taught the interdisciplinary freshman seminar. This broad range of curricular content and student audiences has informed my teaching as it has evolved, and continues to evolve, over the course of a career in education.

My baccalaureate degree is from Guilford College where I took courses in the Moore style from J. R. Boyd, Ken Walker, and my older brother, Elwood. I did my graduate work at Emory University, where John W. Neuberger directed my thesis. While at Emory, I took Moore Method courses with David A. Ford, Philip C. Tonne, William S. Mahavier, John W. Neuberger, and Mary Frances Neff. I owe them all big time, mostly for things to emulate, but also, on occasion, for things to avoid. For the past decade, I have been active in the Legacy of R. L. Moore movement through which I began professionally collaborating with Mahavier, co-founder of MathNerds. I have been a career-long colleague and friend of May, whom I met initially at my first AMS meeting in 1977. My published works include nine refereed papers in mathematics journals, three refereed papers in mathematics education journals and two sets of course notes in the Journal of Inquiry-based Learning in Mathematics.

 

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