Characteristics of Classroom Mathematics Traditions: An Interactional Analysis

Understanding the Cultural Construction of School Mathematics

“…Wherever they are located, lessons "have a routineness about them that ensures a degree of consistency and predictability" (Kawanaka et al, 1999, p. 91). This sense of routine predictability has been variously described as the traditions of classroom mathematics (Cobb et al, 1992), the characteristic pedagogical flow of a lesson (Schmidt et al, 1996), the cultural script and the lesson signature (Hiebert et al, 2003). Such descriptions allude to repeatedly enacted pedagogical strategies typical of a country's lesson (Cogan & Schmidt 1999).…”

Ecologies of participation in school classrooms

“…Usual school mathematics refers to the pervasive form in which mathematics has been and continues to be taught in schools in the UK (Boaler, 1997a(Boaler, ,1999(Boaler, , 2000Boaler & Greeno, 2002;Boaler, Wiliam & Zevenbergen, 2000;Boylan, 2004;Cotton, 1998;Ernest, 1998;Mendick, 2006;Nardi & Steward, 2003) and, in spite of the recent reform movement, in the US (Anderson, 1997;Cobb, Wood, Yackel, & McNeal, 1992;Gregg, 1995;Stigler & Hiebert, 1997). Many aspects of usual school mathematics are common features of the way mathematics is taught in schools elsewhere.…”

“…Teachers" power to significantly shape or change specific mathematical practices (as understood as curriculum content) is limited, bound as they are into regulatory assessment regimes. Nevertheless, where approaches to learning mathematics are enacted that allow students to engage with mathematical problems and also with each other in more meaningful ways, the meaning of the mathematical practices and mathematical objects also changes (Cobb et al, 1992). To give an example, using fractions as a means to investigate infinity gives a different relationship to the mathematical content and can engage learners in ways that practicing algorithms does not (Povey, Burton, Angier, & Boylan, 1999).…”

Editorial Introduction

“…Wherever they are located, lessons "have a routineness about them that ensures a degree of consistency and predictability" (Kawanaka et al 1999, p. 91). This sense of routine predictability has been variously described as the traditions of classroom mathematics (Cobb et al 1992), the characteristic pedagogical flow of a lesson (Schmidt et al 1996), the cultural script and the lesson signature (Hiebert et al 2003). Such descriptions allude to repeatedly enacted pedagogical strategies typical of a country's lesson (Cogan and Schmidt 1999).…”