By Jeremy Kilpatrick

NCTM’s Mathematics Education Trust (MET) relies on contributions from Council members and other individuals, Affiliates, and corporations. Gifts to the Edward G. Begle Fund help support the Pre-K–6 Classroom Research Grant (up to $6,000). The purpose of this grant is to support and encourage classroom-based research in precollege mathematics education in collaboration with college or university mathematics educators.

**Edward G. Begle: Pioneering Topologist and Mathematics Educator**

Edward Griffith Begle was born November 27, 1914, in Saginaw, Michigan. He attended the University of Michigan, where he studied under the topologist Raymond L. Wilder—the first doctoral student at the University of Texas of Robert Lee Moore, the founder of topology in the United States, and the inventor of the Moore method for teaching mathematical proof. Begle received a bachelor’s degree in mathematics from Michigan in 1936 and a master’s in 1937. Not surprisingly, given that Wilder was his mentor, Begle pursued the study of topology, going to Princeton University, where he obtained a PhD in 1940 under the direction of Solomon Lefschetz. Begle’s dissertation was on locally connected spaces and generalized manifolds.

After teaching mathematics at Princeton in 1940–41 and spending a year at Michigan as a National Research Council Fellow, Begle accepted a position in the mathematics department at Yale University in 1942 and taught there until 1961, rising through the ranks from instructor to associate professor. While on the Yale faculty, he continued his research on generalized manifolds, publishing several important results, such as a proof of the Vietoris-Begle mapping theorem. During this period, Begle also took an interest in the improvement of undergraduate teaching, publishing an introductory calculus textbook in 1954. Unlike most such textbooks, *Introductory Calculus, with Analytic Geometry *is addressed to the students themselves and not to their instructors. It emphasizes the basic concepts of the subject, attempting to show students the logical structure of calculus and not simply to acquaint them with techniques.

In 1951, Begle was elected secretary of the American Mathematical Society (AMS), a position that brought him into the mainstream of the American mathematics community. He held the position for six years during a time when AMS was coping with problems brought on by the postwar expansion of interest and activity in mathematics. In 1958, concern over the increased need for mathematicians led to two conferences sponsored by the National Science Foundation, both of which called for a project to revamp the school mathematics curriculum. Begle was offered and accepted the post of director of the resulting project: the School Mathematics Study Group (SMSG). He served as director for the duration of the project, from 1958 to 1972.

SMSG was the largest and most influential of the so-called new math curriculum projects in the United States. As its director, Begle organized teams of school teachers and mathematicians to write textbooks that would more effectively reflect and prepare students for the mathematics of the university, taking advantage of concepts such as set, relation, and function to provide not only a more coherent discourse in the mathematics classroom but also a more meaningful structure for learning. Students would be drawn to mathematics by seeing how it fit together and, in particular, how the great ideas of modern mathematics brought order into a curriculum that was riddled with errors and imprecise language. Begle’s view of the school mathematics curriculum, as expressed in the first SMSG newsletter, reflected the goal of teaching for understanding that he had sought in his calculus textbook:

Since no one can predict with certainty his future profession, much less foretell which mathematical skills will be required in the future by a given profession, it is important that mathematics be so taught that students will be able in later life to learn the new mathematical skills which the future will surely demand of many of them. (Begle, 1968, p. 239)

In 1961, SMSG moved from Yale to Stanford University, where Begle was given a joint appointment as professor in the department of mathematics and the school of education. Ultimately, however, his appointment was shifted entirely to the school of education, a move that reflected his growing interest in educational topics such as curriculum development and evaluation, teacher education, and research in mathematics education.

Begle’s 1969 address, “The Role of Research in the Improvement of Mathematics Education,” at the First International Congress on Mathematics Education in Lyon, France, was influential in putting research on the agenda of mathematics education internationally. He sought to give research an empirical footing:

I see little hope for any further substantial improvements in mathematics education until we turn mathematics education into an experimental science…. We need to start with extensive, careful, empirical observations of mathematics learning. Any regularities noted in these observations will lead to the formulation of hypotheses. These hypotheses can then be checked against further observations, and refined and sharpened, and so on. To slight either the empirical observations or the theory building would be folly. They must be intertwined at all times. (Begle, 1969, p. 242)

After conducting the National Longitudinal Study of Mathematical Abilities—the largest study of factors affecting the learning of mathematics—Begle began a series of reviews of the empirical literature and with his students developed well-structured teaching units so that they could conduct studies in which a single dimension of instruction was varied and its effects measured. A posthumously published book (Begle, 1979) contains Begle’s review of the research on many facets of mathematics education.

During his career, Begle was active in the National Council of Teachers of Mathematics, serving on the Board of Directors, Finance Committee, and Research Advisory Committee. He was a member of the committee on the undergraduate program of the Mathematical Association of America, chairman of the conference board of the Mathematical Sciences, and trustee of the American Mathematical Society. Begle served two terms on the United States Commission on Mathematical Instruction, from 1962 to 1966 and from 1970 to 1975. He chaired the commission from 1963 to 1966. He served on the executive committee of the International Commission on Mathematical Instruction from 1975 to 1978. In 1960, he was elected a fellow of the American Association for the Advancement of Science. In 1969, he received the Distinguished Service Award of the Mathematical Association of America, and in 1971, he received the Rosenberger Medal from the University of Chicago for his significant contributions to humanity. He remained on the Stanford faculty until his death from emphysema on March 2, 1978. He was survived by his wife, six of his seven children, and seven grandchildren.

**References**

Begle, E. G. (1954). *Introductory calculus, with analytic geometry.* New York, NY: Holt, Rinehart & Winston.

Begle, E. G. (1968). SMSG: The first decade. *Mathematics Teacher, 61,* 239–245.

Begle, E. G. (1969). The role of research in the improvement of mathematics education. *Educational Studies in Mathematics, 2,* 232–244.

Begle, E. G. (1979). *Critical variables in mathematics education: Findings from a survey of the empirical literature.* Washington, DC: Mathematical Association of America and National Council of Teachers of Mathematics.

**Recent Grant Recipient**

At the time the grant was awarded, Debbie Short was a fifth-grade teacher at Jeffery Elementary School in Kenosha, Wisconsin. Debbie is currently an instructional coach at Brass Community School (Kenosha). Her efforts are focused on creating curriculum, collecting data, and coaching teachers in the newly adopted Wisconsin Common Core Standards.

**Creating a Classroom of Future Problem Solvers with the Touch of the Promethean World**

Debbie Short collaborated with Prisca R. Moore of Carthage College (Kenosha, Wisconsin) on a study to examine the impact of a technology-enhanced math problem-solving program and technology tools on instruction and the learning environment. They examined the knowledge, skills, and attitudes of fifth-grade students and collaborated with college faculty and classroom teachers to develop problem-solving teaching resources using Hot Math, the research-based mathematical problem-solving program. Promethean interactive whiteboard and ActivExpressions were used to increase student engagement and to facilitate understanding by incorporating interactive math applets and other online teaching resources.

For more information about Edward G. Begle, including supporting resources, click here.