by Gordon Honerkamp-Smith

        The strength of the Moore Method lies in the fact that students create, rather than absorb, mathematical concepts. As evidenced in part by the success of the more than 50 doctoral students whom Moore supervised (among them members of the National Academy of Sciences and several presidents of both the American Mathematical Society and the Mathematical Association of America), this type of learning can be highly effective. However, the Moore Method is by no means an effortless path to mathematical understanding. Indeed, only the most enthusiastic, diligent pupils will succeed in an environment where the path to understanding is paved with will power and personal commitment.
        Given the unique character of the Moore style of teaching, it's entirely appropriate to ponder its place in today's universities. Here, we will conclude with such a consideration from the undergraduate perspective. To be sure, the Moore Method would be unsuitable for much of the undergraduate mathematical curriculum, especially in the lower division courses. Students have been trained to expect a thorough presentation of theory followed by an appeal to solve problems through direct application of that theory. And not all students study math with the goal of utter and absolute comprehension in mind. Moreover, considering the demands placed on the learner in a Moore-style classroom, even the brightest, most dedicated students simply will not have time to learn all mathematics in this way. However, with the appropriate conditions, invaluable experiences can likely be gleaned from the Moore Method. Perhaps most important to the serious undergraduate mathematician, the Moore Method can teach one the difference between reading about math and doing it, and it is this distinction which will determine whether a career in mathematics is really the correct path to pursue.

        The Lone Star state is probably best known for the rugged, cowboy lifestyle with which it is often associated; certainly Texas seems more a breeding ground for cattle than for pedagogical theory in mathematics. Despite this Hollywood romanticism, Texas was, in fact, the locus of Robert Leeoore's life--and continues to be the home of his legacy. Born in Dallas in 1882, Moore attended the University of Texas in Austin (UT), where he earned his Bachelor's degree around the age of 19. Moore lectured at UT and also taught high school mathematics for several years before enrolling in the graduate mathematics program at the University of Chicago. In 1905, Moore had earned his doctorate in point-set topology, and he began teaching at various universities including the University of Tennessee, Princeton, Northwestern, and the University of Pennsylvania. However, by 1920 he had returned to UT; where he would work for almost half a century before retiring in 1969. True to his Texan roots, Moore died in Austin in 1974.
        It was during these nearly fifty years as a professor at the University of Texas that Moore cultivated what is known today as the Moore Method of teaching. The crux of his didactic philosophy is perhaps best summarized by a quote he gave in a 1965 film by the American Mathematical Association about his teaching methods: "That student is taught the best who is told the least." This is certainly a far cry from the format of the average university lecture, in which it almost seems a daily contest to see just how much instruction can be crowded into a 50-minute time span. The format of Moore's classes was simple. He would begin by giving the students a few basic definitions and axioms. From these, concepts would be developed almost entirely by the students, who would then be asked to construct examples and proofs and solve problems. Most learning was done outside of class; however, there were no textbooks--in fact, students were required to stay out of the library or any place with potential to expose them to outside knowledge on the subject. Even student collaboration was discouraged--the principle being that effective learning would come from one's own invention and discovery. The classroom environment was quite unique; instead of lecturing, Moore would ask individual students to approach the blackboard and present a previously assigned proof or problem. The rest of the class would follow and scrutinize the material; when one student could not complete a proof or explanation, another would supplant him or her at the blackboard and perhaps present a different solution.