Examining Social and Sociomathematical Norms in Different Classroom Microcultures: Mathematics Teacher Education Perspective

Abstract

Doing mathematics is not only an individual construction activity but also a social one (Bowers, Cobb, & McClain, 1999; Hershkowitz & Schwarz, 1999). Highly complex human interactions occur in mathematics classrooms. Furthermore, the process of teaching and learning mathematics involves a kind of collective and interactive relation (Bauersfeld, 1980). Investigating how math is learned and taught from a sociological perspective by generally analyzing classroom culture in general and mathematical culture in particular, scholars have drawn on some concepts such as classroom microculture and mathematical classroom traditions (i.e., Cobb, 1999; Cobb, Stephan, McClain, & Gravemeijer, 2001; Cobb, Wood, Yackel, & McNeal, 1992). Cultural constitution, which appears in a small group and makes more interactions possible among participants, can be defined as the system of knowledge, belief, behavior, and tradition shared by the members of a group (Fine, 1987, as cited in Fine, 2003). Like every community, each classroom establishes, sustains, modifies or eliminates various patterns such as norms, standards, obligations, rules, and routines (Sekiguchi, 2005). This process is called culture building (Fine, 2003). From this perspective, this study focuses on the social and sociomathematical norms embedded in the culture building process.A norm is an important element of classroom microculture that is established by the teacher and students (Cobb, 1999). Norms can be defined as ideas that determine manners; what is expected to be done by a group member, or a person under prescribed conditions (Homans, 1951, p. 123). Similarly, Cobb et al. (1992) and Cobb and Yackel (1996a) use the concept of norm in the meaning of specifying and meeting the mutual expectations that arise in the classroom through the interaction between teacher and students. Norms characterize regularities in individual or collective classroom activities (Cobb et al., 2001). Norms are established and developed through constant student-teacher interactions and thus may differ significantly from one classroom to another (Cobb & Yackel, 1996b). This study, with prospective teachers as participants, thus aims to investigate which social and sociomathematical norms exist in different classroom microcultures.Theoretical FrameworkClassroom MicrocultureA classroom is defined as a complex environment that accommodates individuals who come together with the aim of constructing a learning community (Levenson, Tirosh, & Tsamir, 2009). Like every community, a classroom constitutes and develops an association of social relations and its own microculture (Gallego, Cole, & The Laboratory of Comparative Human Cognition, 2001; Lopez & Allal, 2007). The microculture of a mathematics classroom contains social interactions and the construction of mathematical meaning (Voigt, 1995). It does not exist separate from the mathematical activities of a classroom community (Cobb et al., 1992). Its characteristics depend on norms, patterns, and regulations that are difficult to change, such as students' attitudes (Voigt, 1995). Social and sociomathematical norms, together with a classroom's mathematical practices, constitute the classroom microculture where individual and collective mathematical learning occurs (Cobb et al., 2001).Social and Sociomathematical NormsCobb and Yackel (1996a), who extended their studies from general classroom norms to the normative aspects of mathematical arguments regarding student activities, distinguished norms as social and sociomathematical. Social norms express the social-interaction aspects of a classroom that become normative (Yackel, Rasmussen, & King, 2000). These norms are common norms that can be enacted in any field (Cobb & Yackel, 1996b). For example, explaining and justifying solutions, identifying and stating agreement, trying to make sense of others' explanations, expressing disagreement on ideas, and so forth are social norms for discussions where the whole class participates (Cobb & Yackel, 1996a). …