Mathematics and Statistics
The Ohio Section: Meetings
One of the best ways to gauge the pulse of an organization is to observe its meetings. This is particularly true of the Ohio Section since, at least in the early years, its principal activities consisted of annual meetings.
Thirty-nine out of the first forty such meetings were held at The Ohio State University. The only exception was the 34th annual meeting, held at Denison University in 1950 with a record 139 persons in attendance. Beginning with a meeting at Oberlin College in 1956, it became customary to vary the location from one year to the next, with efforts being made to include all geographic regions of the Section.
For more than thirty years the typical Ohio Section meeting took place on a Thursday or Friday and consisted of an afternoon session, a dinner, and an evening session. In 1943 it was noted that "contrary to the custom, only an afternoon session was held." This meeting also had the lowest number of persons in attendance (36) since 1926. The following year saw a return to afternoon, dinner and evening sessions, but the 1945 meeting was canceled altogether, due to the exigencies of World War II. Beginning with the 1948 meeting, the time frame was changed to Saturday, with morning and afternoon sessions. This pattern continued through the 50th annual meeting in 1966, after which the present two day (Friday-Saturday) meeting schedule became the norm.
On December 7, 1963, a special meeting of the Section was held at Denison University under the leadership of the Section Chairman, Charles Capel (Miami University). No formal papers were presented at this meeting, but sessions were devoted to discussion of the freshman-level mathematics curriculum, teacher training and certification, and revision of the Ohio Section By-Laws. The outcome of this historic meeting was the formation of standing committees CONTTAC, CONCUR, and COB. (See the chapter on Committees for details.)
The next fall meeting of the Ohio Section was a joint meeting with the MAA Committee on the Undergraduate Program in Mathematics (CUPM), held in Columbus on October 20-21, 1967. Two years later the fall meeting became an annual event in the Ohio Section. For several years each fall meeting program was dedicated to a special topic, including: mathematics for junior colleges, accreditation of mathematics departments, differential geometry, and applications of mathematics. After 1972, however, fall meeting programs no longer centered on a single theme. The spring meeting is still designated as the "annual meeting" because the annual business meeting and election of officers occur then.
The 1915 Constitution of the Ohio Section specified that the annual meeting "shall be held at the same time and place as that of the Ohio College Association," and this practice was observed for many years. The first annual meeting in 1916 was a two-day affair, held on a Friday and Saturday in connection with the meetings of The Ohio College Association, The Ohio Academy of Science, The Ohio Society of College Teachers of Education, and The Association of Ohio Teachers of Mathematics and Science. These same five societies met together in 1917, and the Section continued to schedule its meetings in connection with those of the Ohio College Association through 1931.
In 1922, following the Friday meeting of the Section and the OCA, a joint Saturday meeting was held with the Society for the Promotion of Engineering Education. In more recent times the Section has met jointly with the Ohio Academy of Sciences in May, 1970, the Ohio Mathematics Association of Two-Year Colleges in April, 1979, and the Society for Industrial and Applied Mathematics in the fall of 1982.
In the report of the eighth annual meeting of the Ohio Section, held March 30, 1923, it is noted that "Following an inquiry from the University of West Virginia, it was voted to invite the mathematicians from that state to join in the meetings of the Ohio Section." Ten years later the Allegheny Mountain Section was formed, with the intent of serving mathematicians in Western Pennsylvania, West Virginia, and Eastern Ohio. The latter remained in the Ohio Section, but all of West Virginia, except Cabell County, joined the new Section, a situation that remains to this day.
The fiftieth annual meeting of the Ohio Section was held at Ohio Wesleyan University on April 23, 1966. Celebration of the occasion appears to have been limited to special recognition for A.G. Caris, the only charter member of the MAA in attendance, and Rufus Crane, who had served as Secretary-Treasurer of the Section for 21 years.
The core of every Ohio Section meeting has been its program of papers, mostly contributed by members of the Section. The contents of these papers reflect the mathematical and academic trends of the times. The topics may be broadly characterized as classical mathematics, applied mathematics, statistics, history of mathematics, the undergraduate curriculum, and mathematics education. The small sample that follows can only give the reader a flavor of Ohio Section programs. Those who want a fuller taste are invited to examine the reports in the American Mathematical Monthly (listed in Appendix B) or the list of invited addresses (Appendix F).
At the first annual meeting, Chairman R.B. Allen (Kenyon College) started the tradition of giving a Chairman's Address. His paper was an expository treatment of "Hypercomplex Number Systems." Another 1916 paper on a classical topic was "Divergent Series and Their Applications," by C.N. Moore (University of Cincinnati). R. L. Wilder (Ohio State University) talked about the definition of a continuous curve in 1925, and B. H. Redditt (Kenyon College) discussed the symmetry groups of polyhedra five years later. A talk on the theory of transfinite sets could still be called "Controversial Mathematics," by Henry Blumberg (Ohio State University) in 1926. The 1990 President's Address by Olaf Stackelberg (Kent State University) combined two classical topics in a paper titled "Number Theory and Probability: A Rich Interplay."
Applied mathematics has also been well represented over the years. In 1917, for example, C.J. West (Ohio State University) spoke on "The application of Mathematics to the Biological and Social Sciences," while Paul Biefeld (Denison University) gave a paper on the actual and apparent paths of comets. "The Theory of Relativity" was discussed by A.C. Lunn in 1920, and a certified public accountant from Columbus, W.E. Langdon, spoke on "Mathematics in Accounting" the following year. By the 1950's applied topics included linear programming, electric circuits, and photogrammetry. The 1960's saw a greater emphasis on pure mathematics -- undoubtedly a consequence of the "new math" movement. However, the past two decades have witnessed a renewal of interest in the applications of mathematics, with papers on such topics as error-correcting codes, graph theory, optimization, apportionment of votes, and mathematics for computers.
It is interesting to observe the growing impact of computers on mathematics. In 1930 George W. Spenceley (Miami University) discussed the solution of linear equations by means of a "computing machine" that was actually a Monroe mechanical calculator. Nineteen years later, Edmund Churchill and Herman Berman (Antioch College) described an analog computer used to solve simultaneous linear equations. In 1952 -- a year after UNIVAC's debut -- Eugene R. Epperson (Miami University) reported on "A New 23-Place Logarithm Table" that he and the Spencelys had just completed for the Smithsonian Institution. The following year R.W. House (Wright-Patterson AFB) described "The Air Force's Newest Large-Scale Computer," OARAC, capable of 5000 operations per minute.
By the end of the 1950's there was already talk of the impact of electronic computers on the mathematics curriculum, yet the 1958 meeting included a paper on "advanced slide rule techniques." Ohio State University's computer science curriculum was described in 1965, and the program for the 54th annual meeting in 1970 included eight papers on the theme of computers in the undergraduate curriculum. Five years later "Pocket Calculators in the Classroom" caught the attention of the Section and, by 1978, the question was "What Can a Pocket Programmable Do for You in Numerical Analysis?" In 1989 pocket calculators had graphics, as well as symbolic algebra capabilities, and the Ohio Section fall meeting included a minicourse on "Computer Algebra Systems and their Classroom Use," led by Zaven Karian (Denison University).
The Ohio Section also encouraged papers in the area of statistics. For example, in 1918 H. O. Rugg (University of Chicago) and W. E. Anderson (Wittenberg College) discussed the use of statistical (i.e. standardized) tests in collegiate mathematics. A paper on correlation coefficients was presented by W. E. Cairns (Oberlin College) in 1921 and C. C. Morris (Ohio State University) discussed sampling theory in 1931. Statistical distributions formed the basis of a paper by P. R. Rider (Wright-Patterson A.F.B.) in 1954 and "The Role of a Statistics Laboratory on a College Campus" was the title of a 1959 paper of D. R. Whitney (Ohio State University).
Papers on the history of mathematics often appeal to a wide audience, and the Ohio Section is no exception. A sampling of historical topics at section meetings would include "Chinese Algebra" by Emma L. Konantz (Ohio Wesleyan University) in 1922, "Mathematical Statements in the History of Mathematics" by G.A. Miller (University of Illinois) in 1941, and "Curves of the Calculus" by V. Frederick Rickey (Bowling Green State University) in 1984. Harriet Glazier (Western College for Women) suggested a list of courses for prospective teachers of secondary mathematics in 1916, including a history course "which should give the historical background of the subject and familiarity with the mathematical literature." O.L. Dustheimer (University of Toledo) gave details of such a course in 1949. Thirty years later Fred Rickey spoke on "History of Mathematics as a Pedagogical Tool."
Biographical studies of famous mathematics have also been the subjects of interesting lectures. In 1933 W.G. Simon (Western Reserve University) spoke on the life and work of E.H. Moore, who had once been a student at Woodward High School in Cincinnati. Sir William Rowan Hamilton was the topic of paper by J.L. Synge (Ohio State University) in 1944, and the most recent annual meeting included an invited address by John W. Dawson (Pennsylvania State University) on "The Life and Work of Kurt GKdel."
The undergraduate mathematics curriculum has always been a topic near and dear to the hearts of Ohio Section members. At the first annual meeting, A.E. Young (Miami University) addressed the question of "What Elective Courses Following the Calculus Should the Average College Offer?" and Harriet Glazier (Western College for Women) spoke on "What Courses Should Be Offered for Prospective Teachers of Secondary Mathematics?" The following year Louis Brand (University of Cincinnati) spoke on "Senior Year Mathematics for Engineering Students." In 1923 C.N. Mills, reporting on a survey of 26 colleges and universities in Ohio, noted that the number of semester hours required for a mathematics major ranged from 15 to 38. The following year two papers were presented on "sectionizing" of college freshmen on the basis of prognostic tests.
As early as 1931 W.G. Simon (Western Reserve University) expressed "Some Doubts About the Content of Elementary Courses in Calculus." After World War II, the undergraduate mathematics major was reexamined and became the subject of the 1948 chairman's address by Harry Pollard (Miami University). That same year Wayne Dancer (University of Toledo) reported that the number of semester hours required for such a major in Ohio colleges now ranged from 24 to 36, with the average being slightly more than 28. At the 1958 annual meeting Laurie Snell described "The New Dartmouth Mathematics Curriculum," while Wade Ellis discussed independent studies at Oberlin College, and Gaylord Merriman reported on three experimental courses at the University of Cincinnati.
Major changes in the undergraduate curriculum, prompted by the work of CUPM, began to occur in the sixties. In the fall of 1967, a "Conference on Collegiate Mathematics in Ohio" was held in Columbus, jointly sponsored by the Ohio Section and CUPM. Members of various CUPM panels described the work of this committee and its implications for Ohio colleges and universities. Two years later another fall section meeting was devoted to a discussion of matters related to mathematics for junior colleges. The movement to include some discrete mathematics in the first two years and the call for a "lean and lively calculus" have shared the curriculum spotlight in the 1980's.
Pre-college mathematics education has also been an ongoing concern of the Ohio Section. A round-table discussion in 1920 dealt with "Freshman Mathematics to Meet the Changing High School Mathematics as Presented for Entrance to College." Speakers noted a tendency to minimize the amount of mathematics required for high school graduation, so that "more pupils enter college deficient in mathematics." Two years later Marie Gugle, of the Columbus Public Schools and soon to become President of the National Council of Teachers of Mathematics, spoke on the problem of articulation between high school and college mathematics.
Teacher training also captured its share of attention in the Section. In 1929 M. O. Tripp (Wittenberg College) spoke about "The Teacher's Course in Mathematics," and a 1947 committee chaired by Harold P. Fawcett (Ohio State University), who would also become President of NCTM, recommended a training program for teachers in the elementary schools. That same year the Chairman's Address by S. A. Rowland (Ohio Wesleyan University) was titled, "The Association's Interest in Pre-College Training."
The 1957 annual meeting program included talks by Bernard H. Gundlach (Bowling Green State University) on "A New Approach to the Teaching of Elementary Mathematics," and by Mildred Keiffer (Cincinnati Public Schools) on "Mathematics in the Cincinnati Public High Schools." These dual problems of the pre-college curriculum and the training of teachers run like a bright thread through the programs of the Section and are still common topics for papers at meetings in the 1990's.
Although most papers have been contributed by active members of the Ohio Section, distinguished visitors from outside the state have often been invited to address section meetings. In 1935 Gabriel SzegK (Washington University) spoke on "Some Recent Applications of Sturm's Oscillation Method." Karl Menger (University of Notre Dame) gave a lecture on "The Foundations of Projective and Affine Geometry" in 1938, and Emil Artin (Indiana University) presented an "Introduction of Coordinates in Affine Geometry" three years later. For the 1942 meeting Lester R. Ford (Illinois Institute of Technology) told about "A Million Ways to Solve Equations," and Murray Klamkin (Ford Motor Company) spoke on "Mathematics in Industry" at the fall meeting in 1972.
Invited speakers have sometimes been incumbent officers of the MAA. For example, in 1964 R.H. Bing was President of the Association when he gave an invited address on "Homogeneity." The following year President R.L. Wilder spoke to the Ohio Section on "The Axiomatic Method." R.P. Boas (Northwestern University) was also President of the MAA when he spoke on "Consequences of Continuity" in the fall of 1973. Boas returned in April of 1981 to give a lecture on "The Harmonic Series and the Elephants."
It is interesting to note certain timely topics that have appeared on Ohio Section programs. For example, the general theme of the annual meeting in 1919 was "Mathematics and Warfare." Contributed papers at that meeting included "The Mathematical Features of Navigation" by D.T. Wilson (Case School of Applied Science), "Ballistics as Applied Mathematics" by M.E. Graber (Heidelberg University), and "The Mathematics of Aviation" by S.E. Slocum (University of Cincinnati). During World War II, a 1942 symposium invited those present to compare experiences "as to the effect of the present emergency upon the nature and content of courses offered." The following year H.K. Justice (University of Cincinnati) reported on the results of a questionnaire designed to ascertain the "effects of the war upon mathematics in Ohio," and Henry Blumberg (Ohio State University) responded with an address titled "Whither American Mathematics?"
The Great Depression notwithstanding, the 1930's found the Ohio Section growing in numbers and enthusiastically supporting the annual meetings. Attendance records were set at Section meetings in 1933 and 1938. At the latter, C.C. Morris "analyzed the mathematical aspects of the recovery program of President Roosevelt, showing why he took the steps he did, their result, and prophesying what his future steps [would] be." In 1952 Professor O.L. Dustheimer (then retired), reconsidered one of the most far-reaching of these steps in a paper on "Social Security and College Retirement Programs."
The Ohio Section has not been averse to employing the latest in educational technology. In 1917 for example, three of the papers delivered at the annual meeting were illustrated by "lantern slides." By 1930 Ida M. Baker (Western Reserve University) was involved in an experiment with the Cleveland Public Schools, teaching arithmetic lessons via radio. A later generation of instructors began to replace radio with educational television, and mathematical film festivals were featured at section meetings in 1966, 1972, and 1973. In the seventies and eighties video cassettes, computers, and hand-held calculators appeared in ever-increasing numbers, not only in Ohio classrooms, but in talks presented at section meetings as well.
In the early 1950's J. Sutherland Frame introduced Pi Mu Epsilon student paper sessions at the Joint Summer Mathematics Meetings, and it was inevitable that students would eventually participate in the Ohio Section meetings. The earliest record of student papers occurs in April, 1957, when A. J. Gruber (Kent State University) spoke on "a serial numbering system for permutations." Nearly a decade later, in 1968, G.J. Sherman (Bowling Green State University) and Edward Molnar (Ohio University) spoke on "The Rim of an R-group" and "The History of Ryley's Problem," respectively. Two years later there were three student speakers on the program, followed by two students in 1971 and seven students, representing four universities, in 1972. This began a tradition of student papers at the spring meetings that has grown to rival the contributed papers by faculty in quality as well as in number.
The idea of student paper sessions quickly spread to other sections. By 1982, seventeen sections reported student papers totaling 98 in number, with the Ohio Section leading with 22. Five years later the number of student papers presented at the Ohio Section spring meeting had grown to 31, and nearly half of the persons registered at that meeting were students. For a number of years it was the practice of the Ohio Section to give awards to three students for outstanding papers. Today, however, each student speaker receives a free MAA membership and, along with other students who attend the meeting, is invited to partake of a pizza party and free lodging with students at the host institution.
Ohio Section meetings in the 1990's may seem less formal than those of 75 years ago, but they are certainly as informative and interesting. Section members continue to regard them as an important way of renewing professional friendships, rekindling enthusiasm, and keeping up to date with the latest trends in collegiate mathematics.
Copyright 1990, The Ohio Section, MAA, All rights reserved.