Practical Rationality, the disciplinary obligation, and authentic mathematical work: A Look at Geometry

Grossman and McDonald (2008) recently argued that the research community needs to move its “attention beyond the cognitive demands of teaching ... to an expanded view of teaching that focuses on teaching as a practice (p. 185).” Building on the work of Bourdieu (Bourdieu and Wacquent, 1992; Bourdieu, 1985, 1998), Herbst and Chazan (2003, 2006) have written about mathematics teaching as a practice, just as law and medicine are considered practices, in an attempt to better understand the rationality that produces, regulates, and sustains mathematics instruction. This practical rationality is the commonly held system of dispositions or the “feel for the game” (Bourdieu, 1998, p. 25) that influences practitioners as to those actions that are appropriate in the classroom. It is practical rationality that: not only enables practices to reproduce themselves over time as the people who are the practitioners change, but also regulates how