The Unit of Analysis in Mathematics Education: Bridging the Political-Technical Divide?

Mathematics education is a complex, multi-disciplinary field of study which treats a wide range of diverse but interrelated areas. These include the nature of mathematics, the learning of mathematics, its teaching, and the social context surrounding both the discipline and applications of mathematics itself, and as well as its teaching and learning. But research and researchers in mathematics education fall loosely into two camps: On the one hand there is technical research, drawing on mathematics, psychology and pedagogy, concerned with narrow questions about the teaching and learning of mathematics. On the other hand there is political and social research drawing on sociology and philosophy, addressing large scale problems of social consequence. These two camps tend to draw on different theoretical underpinnings as well as having different interests. Is it possible to find a shared theoretical element, a single unit of analysis for mathematics education which provides a unified approach to both analysing and explaining all of these diverse aspects? Can such a unit provide a bridge across the technical-political divide? Before these questions are addressed the meaning of the term „unit of analysis‟ is clarified. After distinguishing between methodological and ontological senses, I propose units of analysis within each of the four listed subdomains of mathematics education. Then drawing on Blunden's (2009, 2010) interdisciplinary version of cultural historical activity theory I propose a single over-arching unit of analysis, the collaborative project, for the whole field, thus potentially bridging the technical-political divide. Mathematics Education What makes up the field of mathematics education as a research domain? A good starting point is Joseph Schwab's (1961) four commonplaces of teaching. These include the subject taught, the learner, the teacher, and the milieu of teaching, comprising the relationship of the subject, and its teaching and learning aims, to society in general. Applying these four commonplaces of teaching to the field of mathematics education results in the specification of four domains of theory that mathematics education as a research field must accommodate. These are: 1. An account of the nature of mathematics (philosophy of mathematics), 2. A theory of learning mathematics (psychology of learning mathematics), 3. A theory of teaching mathematics (mathematical pedagogy), 4. A theory of the social context of mathematics education, incorporating the interpersonal, cultural, social, societal and political milieu of mathematics education in its theoretical and practical forms (sociology of mathematics). This is a tentative listing because there might well be further subdomains of mathematics education beyond those identified here. However, many of the issues not explicitly mentioned, such as the aims of teaching and learning of mathematics, the mathematics curriculum and its assessment systems, and issues of diversity defined in terms of class, 1 The (first) definite article in this title is intended to designate the topic of discussion as specific singular area, and is not intended to imply that the unit (or units) of analysis proposed are unique or constitute the only viable