# David Eugene Smith (1860–1944)

### mathematics education teachers teaching

Professor of mathematics at Teachers College, Columbia University, David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cortland, New York, to Abram P. Smith, attorney and surrogate judge, and Mary Elizabeth Bronson, who taught her young son Latin and Greek. Smith studied at Syracuse University, earning a B.Ph. (1881), M.Ph. (1884), and Ph.D. (1887) with a concentration in aesthetics and the history of fine arts.

In 1881 Smith began to practice law in his father's office, but welcomed a chance opportunity in 1884 to teach mathematics at the local normal school, where he had studied as a boy, embarking upon what would become a forty-two-year career in academia. He left Cortland Normal School in 1891 to head the mathematics department at Michigan State Normal School (later Eastern Michigan University) in Ypsilanti. From 1898 to 1901 Smith served as principal of Brockport (New York) Normal School. In 1901 he accepted the chair in mathematics at Teachers College, Columbia University, where he remained until his retirement in 1926.

During the 1890s and early 1900s, as enrollments in American high schools increased, national committees convened to examine education recommended curricular reform. For mathematics, the curriculum was to decrease emphasis on rule-based learning and "mental discipline" and move toward a more inductive approach, with practical applications that would better prepare students for college. To be effective, this approach would require teachers well-prepared in mathematics and knowledgeable in its instruction.

Smith was a leader in developing programs that combined the study of mathematics and teaching. At Michigan State Normal School he offered one of the earliest courses in methods for teaching algebra and geometry in secondary school. He also offered a course in the history of mathematics–unique at the time–that examined how the subject developed and how it had been taught in the past. Smith's interest in history continued throughout his career, and he made it a hallmark of his programs. In 1900 Smith published *The Teaching of Elementary Mathematics,* a handbook for teachers that would become a seminal work in the field of mathematics education.

At Teachers College Smith developed graduate programs for secondary and postsecondary teachers that included a two-year or three-year sequence of course work in the history of mathematics. In 1906, two of Smith's students were awarded the first American doctorates in mathematics education. All Smith's programs, whether undergraduate or graduate, shared three distinguishing characteristics: They encouraged teachers to take an active role in determining the mathematics curriculum and classroom pedagogy, to gain a historical perspective on teaching their subject, and to consider international viewpoints on education.

From 1908 to 1912 Smith took to the international stage, seeking to establish mathematics education as a field worthy of special study, separate from mathematics or general education alone. He conceived of the International Commission on the Teaching of Mathematics (ICTM), convinced the eminent mathematician Felix Klein to accept the presidency of the commission, and was primarily responsible for the organization of an extensive network of national committees that prepared detailed reports on mathematics instruction in their respective countries. The American commission, with Smith as chair, identified its country's greatest need as the improved preparation of teachers. With the 1912 presentation of the series of ICTM reports to the International Congress of Mathematicians and the decade-long support of Eliakim Hastings Moore, Jacob William Albert Young, and George Myers at the University of Chicago, mathematics education emerged as a distinct field of study. Smith served as ICTM vice president (1908–1920) and later as president (1928–1932).

Smith's concern for history grew out of long-cultivated interests. From boyhood, Smith enjoyed travel and became an avid collector. When he began to teach mathematics, he turned his attention to mathematical artifacts. By the time Smith donated his collection to Columbia in the 1930s, he had gathered more than 3,000 portraits and autographed letters of famous mathematicians, and approximately 300 rare astronomical instruments and ancient counting devices.

Smith enjoyed collecting not only for himself, he also delighted in sharing his broad knowledge and insight with others. Beginning in 1901, Smith advised George A. Plimpton, head of the New York office of the publishing house Ginn and Company, on acquisitions for his mathematical textbook collection. By 1908, Plimpton had assembled the most complete library of arithmetics printed before 1601. Since Plimpton generously permitted Smith's graduate students access to his collection, they had the rare opportunity to study valuable primary sources. To make the collection more widely known, Smith prepared a richly illustrated catalogue, *Rara Arithmetica* (1908).

As a highly regarded historian of mathematics, Smith contributed numerous books, articles, translations of and commentaries on the subject, most notably his two-volume *History of Mathematics* (1923, 1925). In 1924 Smith joined with others to found the History of Science Society, and, subsequently, served as its president (1927). In 1932 he founded the journal *Scripta Mathematica* with Jekuthiel Ginsburg. Smith also took on the role of mathematics editor for a number of encyclopedias, including *Cyclopedia of Education* (1911–1913) and *Encyclopedia Britannica* (1927).

Smith made other significant contributions to the professional mathematics community. From 1902 to 1920 he served as librarian of the American Mathematical Society (AMS) and associate editor of its *Bulletin.* He became a charter member of the Mathematical Association of America (MAA) when it was organized in 1916, served as associate editor for its publication, *The American Mathematical Monthly,* and was elected president for the term 1920 to 1921.

A significant portion of Smith's writings dealt with issues relating to the newly developing field of mathematics education. *The Teaching of Arithmetic* appeared in 1909, followed by *The Teaching of Geometry* in 1911. These works were complemented by Smith's prodigious production of textbooks, often in collaboration with others. Smith-Wentworth textbooks in arithmetic, algebra, and geometry were dominant during the 1910s. Smith also helped to organize associations for mathematics teachers. In 1903, together with Thomas Fiske, a Columbia mathematics professor who had founded AMS in 1888, Smith convened an organizational meeting for the Association of Teachers of Mathematics in the Middle States and Maryland and was elected its first president.

Major national committees concerned with educational reform invited Smith to join their ranks. The National Committee of Fifteen on the Geometry Syllabus, appointed by the National Educational Association, included Smith as a member. It issued its report in 1911. In 1920 the MAA appointed Smith to the National Committee on Mathematical Requirements, which issued its influential report in 1923.

Smith combined his interests in teaching, mathematics, history, travel, and collecting to support the development of new programs to prepare mathematics teachers for the nation's schools. His vision, efforts, and accomplishments left a rich legacy to mathematics education, a field of study he pioneered in the early twentieth century.

## BIBLIOGRAPHY

DONOGHUE, EILEEN F. 1998. "In Search of Mathematical Treasures: David Eugene Smith and George Arthur Plimpton." *Historia Mathematica* 25:359–365.

DONOGHUE, EILEEN F. 2001. "Mathematics Education in the United States: Origins of the Field and the Development of Early Graduate Programs." In *One Field, Many Paths: U. S. Doctoral Programs in Mathematics Education,* ed. Robert E. Reys and Jeremy Kilpatrick. Washington, DC: American Mathematical Society/Mathematical Association of America.

SMITH, DAVID EUGENE. 1900. *The Teaching of Elementary Mathematics. Teachers' Professional Library,* ed. Nicholas Murray Butler. New York: Macmillan.

SMITH, DAVID EUGENE. 1908. *Rara Arithmetica.* Boston: Ginn.

SMITH, DAVID EUGENE. 1912. *Report of the American Commissioners of the International Commission on the Teaching of Mathematics.* Washington, DC: Government Printing Office.

SMITH, DAVID EUGENE. 1923, 1925. *History of Mathematics,* 2 vols. Boston: Ginn.

EILEEN F. DONOGHUE

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