Creative Teaching: Heritage of R. L. Moore

Creative Teaching: Heritage of R. L. Moore by D. Reginald Traylor With: William Bane Madieline Jones c D. Reginald Traylor, 1993 Contents I 5 1 The Early Years 7 2 The Graduate and Post Graduate Years 45 3 The Formative Years 63 4 Return to Texas 85 5 The Mature Years: 1930-1953 103 6 The Years of \Modified Service" 125 II 171 7 The Doctoral Students of Robert Lee Moore. 173 8 Publications of Robert Lee Moore 175 9 Academic Descendants of R. L. Moore and Individual Pub- lications 181 i ii PREFACE The motives underlying an undertaking resulting in such a compilation as included herein were of a mixed variety. There definitely is represented a deep respect for the genius of Robert Lee Moore and information, as offered, testifies in part to that genius. Beyond that, some distinct feeling has been developing that far too many teaching techniques have been assigned the label \The Moore Method." Thus, some effort is made to describe that method, as Moore employed it. Of fundamental concern has been those circumstances which led to Moore's retirement at the University of Texas. Is it true that certain meth- ods of teaching, no matter how effective, simply can not exist in today's major universities? Is it true that university enrollments can climb to such a number that certain teaching practices simply must be discarded, no matter how effective they may be? Is it rue that friction between faculty members is assured once one of them begins teaching effectively by the Moore method and the other does not teach after that fashion? Is there any realistic way to expose the Moore method to a non-mathematical administrator so that he can sense its worth without having actually experienced it himself? For these reasons, and others, an attempt is made to present some display of Moore's teaching, along with a description of the settings and times of his efforts. Hopefully, those, who never experienced such teaching, might gain some appreciation for its worth. This treatise is in two parts. The first deals with a chronological treat- ment of Moore's academic activities. Robert Lee Moore is thought by some to be a teacher whose effectiveness has been exceeded by no other. He taught the \doing" of mathematics; he caused students to develop their powers of rational thought. The method of teaching which he developed has come to be known as \The Moore Method." A description of that method is offered herein by way of comments of his students, comments of others who knew of that method, and by a rather complete listing of those people who earned doctorates in mathematics and who are among his academic descendants, along with a bibliography for each. It is hoped 1 2 that such evidence, as provided in this treatise will offer some support to those who can teach effectively by the Moore method. Simultaneously, those students who disparage that approach should have some opportunity to grasp the effectiveness offered by that method. To those who wish to teach after that fashion, perhaps it will be suggested herein that this is a very difficult manner with which to teach. A person employing the Moore method must spend extreme amounts of time pondering his class, fitting his subject matter to his students and them to it, so that their growth in rational power will be successful. Particular attention is given to Moore's teaching and academic philosophies in the last two chapters of the first sec- tion. Any university teacher is herewith invited to compare his own worth and academic values with those of Professor Moore. It should be rather clear that those, who argue that a researcher can not be a good teacher, must contemplate the example of Robert Lee Moore. Moreover, those who argue that they are good teachers, though they have no research interests or accomplishments, should feel honor bound to offer, as an example, at least one of their past students about whom, it very probably is true, did realize success in some substantial endeavor but very probably would not have if deprived of that particular teacher. The second part of the treatise resulted from a Master's thesis effort of W. Bane. Just as one might argue that Robert Lee Moore may have made substantial contribution, though perhaps not as he did, had he not been influenced by E. H. Moore or G. B. Halsted, so might one say that many mathematicians and their mathematics would not have occurred had Robert Lee Moore not functioned as he did. W. Bane began an undertaking of identifying academic descendants of Robert Lee Moore, along with their publications. This effort was continued by M. Jones, resulting in an extensive list of mathematicians with individual bibliographies. Over five hundred academic descendants were identified. Extreme care was taken to assure accuracy. Much information was gained by conversation and by correspondence. In some instances there was real question as to who actually performed the direction of a student. Infrequently there were those who perhaps directed doctoral students, and were themselves \descendants" of Moore, who failed to indicate their own students. Apology is tendered to those omitted. Publications included in the bibliography are from two sources: The author and The Mathematical Reviews. An astounding wealth of mathematical capability and contributions, stemming from Moore is displayed. Of much concern in this writing has been the awareness of demands made by Robert Lee Moore on himself and others regarding exactness and integrity of statements. In no sense is it suggested that the statements included are of the sense of exactness which would have been demanded by 3 Robert Lee Moore of himself, else the activity yet would remain unfinished. However, much, much effort has been made to assure the accuracy of statements included. Repetition does occur from one chapter to another. Some of this is purposeful, anticipating that \assigned readings" might extract those sections of most interest to the audience. Conviction has grown, throughout the preparation of this material, that not enough recognition has been given George Bruce Halsted | for his own teaching and mathematics. He must have carried with him contagious inspiration. Throughout, much dependence on others is admitted and appreciated. Indeed, the undertaking would never have occurred without the assistance of friends and former students of Robert Lee Moore. D. R. Traylor University of Houston 1972 Part I 5 Chapter 1 The Early Years By the fall of 1882, the opening of the Civil War was barely more than twenty years ago and the close of that terrible war between the states was barely more than fifteen years ago. The Alamo had fallen only 46 years earlier and Texas had been a state for only 37 years. Sam Bass, the leg- endary \Robin Hood" train robber had been shot down in the dusty street of Round Rock, Texas only five years ago. Carrie Nation was still operating a hotel in Richmond, Texas and yet was to make her way to Kansas and prohibition fame. The University of Texas had not yet experienced its first class. Dallas, a leading Texas city was indeed still only a frontier town. Open saloons were still in business in Dallas in 1882. Buttermilk had become a very popular drink and was available in the saloons. During the decade from 1880-1890, the population of Dallas had more than doubled and by 1900, Dallas County exceeded any other county in the state in population. In the twenty year period from 1880 to 1900, the city built its first reservoir for fresh water. Communications were improved when the Dallas Telephone Exchange was established in June 1881. It would accommodate 1200 phones and about 260 hand operated phones were immediately put to use. In 1882 the first electric light plant was put into operation. Railroad facilities serving the city were greatly expanded and electric street cars appeared on Dallas streets, although transportation was still horse dominated at that time. The first paving of any Dallas street appeared in 1882 when two main streets, Elm and Main, were paved with bois d'arc blocks. The first traffic arrest was made in early 1886. The charge was driving too fast down Main Street and the fine was $1.00. The prices of goods of that period are suggested by Sanger Brothers offering men's worsted suits for $10.50 each. Whiskey could be purchased for $1.00 per gallon. The year 1882 was unusually dry since only 25,900 bales of cotton were received in 7 8 CHAPTER 1. THE EARLY YEARS Dallas, down from 47,600 of the year before. In 1885 the Dallas Morning News began publication, as did the Herald, the forerunner of the Dallas Daily Times Herald. In 1886 patrons at the Dallas Opera House thrilled to James O'Neill in \The Count of Monte Cristo" and in 1887 paid $15.00 each for seats when Edwin Booth reenacted the role of Hamlet. The Dallas City Hospital was opened and the first public schools were opened to the children of Dallas, though there were many private schools and academies. Such was the setting into which Robert Lee Moore was born. He was the fifth of six children born to Charles J. Moore and Louisa Ann (Moore) Moore. He was to be raised in a home which honored the Southern attitudes, stressing gentlemanliness, honor, integrity, and independence. Charles J. Moore was an independent, strong-willed man who had come from New England, near Hartford, Connecticut. He had followed a brother to Kentucky before the beginning of the Civil War, leaving his northern home and two other brothers behind.

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