Kilpatrick The Development of Mathematics Education as an Academic Field JEREMY KILPATRICK UNIVERSITY OF GEORGIA I trace the development of mathematics education as a field of study and practice distinct from mathematics. After 1908, but especially after 1969, ICMI has been both a mirror of that development and a stimulus for new directions. As the community of people who identify themselves as mathematics educators has grown, it has increased in diversity, in part because of the growing multi-disciplinarity of the field. There is also diversity across countries in the way mathematics education is institutionalized and how it is related to mathematics. How has ICMI dealt with these issues? The International Commission on Mathematical Instruction (ICMI) was established as a commission of the International Mathematical Union (IMU) at the 1952 meeting of the IMU general assembly in Rome. Both organizations were reincarnations: The ICMI was the successor to the Commission internationale de l’enseignement mathématique (CIEM, anglicized as the International Commission on the Teaching of Mathematics), which had been organized at the 1908 international congress in Rome, functioned between congresses until the First World War, was revived in 1928, and then was dissolved in 1939 (although its secretary general, Henri Fehr, claimed it was technically still in existence in 1952, when it became officially attached to the IMU; Lehto, 1998, p. 316). The IMU had been founded in 1920, was suspended in 1932, and then was reconstituted in 1952 (see Figure 1). Before 1952, “the Commission was connected not with the IMU, but with the International Congresses. Each Congress gave it a mandate for the period between two Congresses, i.e., for four years, and appointed a Committee to coordinate its activities” (p. 65). In other words, the subordinate (ICMI) antedated the superordinate (IMU).Kilpatrick 2IMU ICMI 1900 1920 1940 1960 1980 2000Figure 1. Timeline for ICMI and IMU. The idea for an international commission on mathematics education had first been put forward by David Eugene Smith (1905) in an article in L’Enseignement Mathématique. He was one of five respondents to a request expressed at the Third International Congress of Mathematicians in Heidelberg the preceding year for opinions regarding needed reforms in the teaching of mathematics in higher education. Addressing the question of how the teaching of pure mathematics might be improved, Smith argued for the creation of a commission to be named by an international congress to study the problem. At the Fourth International Congress in Rome in April 1908, he made a formal proposal that a commission be established to conduct “a comparative study on the methods and plans of teaching mathematics at secondary schools” (quoted in Lehto, 1998, p. 13). The scope of the study was eventually expanded to all types of schools, including primary schools, vocational schools, and universities. The proposal for a commission was adopted by the Congress, and Felix Klein was appointed the founding president of the CIEM, serving until 1920 and beginning a tradition in which presidents of the commission were research mathematicians with an interest in mathematics education. The one exception was David Eugene Smith, president from the CIEM’s revival in 1928 until 1932. Although a distinguished historian of mathematics and holder of a chair in mathematics education at Teachers College, Columbia University, Smith had studied mathematics only as an undergraduate, obtaining his doctorate in art history. He had studied to become a lawyer before beginning his teaching career (Swetz, 1987, pp. 299–304; Travers, 1983, pp. 381–382). He is credited (Jones & Coxford, 1970, p. 42)Kilpatrick 3with being one of the two principal founders of mathematics education as an academic field in the United States (the other was Jacob William Albert Young of the University of Chicago). Both 1908 and 1952 marked periods when the school mathematics curriculum was being faced with new demands, countries were attempting or about to attempt efforts to reform that curriculum, and an international exchange of views seemed appropriate (Howson, 1984). Before both periods, the gap between the mathematics taught in schools and mathematics as a scientific discipline had widened, and the views of mathematicians on how to close the gap seemed to set the terms of debate (Wheeler, 1989; Wojciechowska, 1989). In each case, activities undertaken by the ICMI were to be decisive, not only in addressing issues of reform but also in shaping the field of mathematics education. In what follows, I discuss the development of mathematics as an academic field over the past century or so, taking the ICMI as both a barometer of that development and a spur to greater change. Mathematics Education Enters the Academy Although mathematics itself as an academic subject can trace its lineage back at least to the quadrivium of Plato’s academy and even to the Sumerian and Babylonian scribal schools (Davis & Hersh, 1981; Høyrup, 1994), the subject of mathematics education is both more recently and less firmly established in the academy. Throughout the 19th century, the modern scientific disciplines were emerging in higher education, beginning with the reforms of the Protestant universities of Prussia (Kilpatrick, 1992, p. 4). During the second half of the 19th century, mathematics succeeded in becoming an autonomous discipline in German universities although not yet in the technical colleges (Schubring, 1989, p. 175). As teacher education began to move into institutions of higher education in various countries during the last decades of the 19th century and early decades of the 20th, education, too, began to beKilpatrick 4treated as a separate academic field. The first seminary for teachers had been established at Halle in 1704 and the first chair of education there in 1779 (Fleming, 1954), but as of 1910, there were only 13 staff members at German universities with teaching responsibilities in education (Husén, 1983). Other pioneering chairs in education were those established at the University of Iowa in 1873, at the University of Edinburgh in 1876, and at the University of Uppsala in 1910. At about the same time, school mathematics was gradually becoming an object of scholarly study and not just a field of practice (Jahnke, 1986; Schubring, 1988). The Reform Program