Mathematics & Mathematics Education: Searching for Common Ground

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Mathematics & Mathematics Education: Searching for Common Ground Michael N. Fried

Between these two groups. . . there is little communication and, instead of fellow-feeling, something like hostility. (C.P. Snow, The Two Cultures, p. 59)

Prologue If being mathematically educated could be summed up simply as a familiarity with certain key mathematical ideas—integer, algebraic equation, function, proof—their applications, and a facility in working with them, one could state unequivocally what the interests, foundations, and goals of mathematics education as a field should be. Not too long ago, only the conditional form of this statement would strike one as curious and odd. For what else could one mean by being mathematically educated, and what else could one place higher on the agenda of mathematics education research than the teaching and learning of these key mathematical ideas? And, with that, one could hardly imagine challenging the close and natural alignment between mathematics education and mathematics as academic disciplines. However, over the last quarter century or so, and for better or for worse, this simple notion of where the core of mathematics education lies has been offset by goals and interests allying it, as an academic field, more closely with psychology of learning, cultural differences, and social justice, among others, than with mathematics itself. Thus, while the first two-thirds of the twentieth century could boast of great mathematicians such as Felix Klein, Jacques Hadamard, George Pólya, and Hans Freudenthal making contributions to mathematics education, today, not only are such figures rare in the field, they have also been to an extent alienated by it. In the spring of 2012 a symposium concerning the relationship between mathematics and mathematics education was held at Ben Gurion University of the Negev. The symposium was in honor of Ted Eisenberg, who over the years has lamented profoundly the growing divide between the mathematics community and the mathematics education community. It has always been his opinion, shared by the editors M.N. Fried (B) Science and Technology Education, Ben-Gurion University of the Negev, Beer Sheva, Israel e-mail: [email protected] M.N. Fried, T. Dreyfus (eds.), Mathematics & Mathematics Education: Searching for Common Ground, Advances in Mathematics Education, DOI 10.1007/978-94-007-7473-5_1, © Springer Science+Business Media Dordrecht 2014

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of this volume, that the divide between the two communities is wasteful and unhealthy for both. The work at hand, which grew out of that symposium, confronts this disturbing gap. By examining areas of commonality as well as disagreement we hope to define more clearly the role mathematics as a discipline plays in mathematics education and mathematics education research and will try to establish a basis for fruitful collaboration between these disciplines. We can only hope that in the end readers will be left with a clearer sense of the mutual benefit both communities stand to lose by failing to stren

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