Abstract
The notion of a classroom mathematical practice was introduced in the reprinted chapter in the last part. It is fair to say in retrospect that my initial use of this construct was largely intuitive: I had not defined a classroom mathematical practice with any precision or clarified how other researchers might identify the mathematical practices interactively constituted by the teacher and students in other classrooms. The primary goal of the chapter reprinted in this part was to overcome some of these limitations. The process of attempting to explicate and refine this notion was lengthy and occurred as Janet Bowers and Michelle Stephan conducted retrospective analyses of two classroom design experiments for their dissertation studies (Bowers, 1996; Stephan, 1998). A report of Bowers’ analysis was subsequently published in Cognition and Instruction (Bowers, Cobb, & McClain, 1999) and a revised version of Stephan’s dissertation was published as a Journal for Research in Mathematics Education monograph (Stephan, Bowers, & Cobb, 2003). The chapter reprinted here framed part of Stephan’s dissertation analysis as a case in which to explicate the process of analyzing the collective mathematical learning of a classroom community.
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Notes
- 1.
Janet Bowers is currently a member of the mathematics education faculty at San Diego State University.
- 2.
Michelle Stephan is currently a middle-school mathematics teacher in Seminole County, Florida, where she recently received the award of teacher of the year.
- 3.
Stephan and Rasmussen (2002) subsequently identified an additional evidentiary criterion for claiming that a particular type of mathematical activity has been constituted as normative in a classroom.
- 4.
This experiment was conducted in collaboration with Beth Estes, a first-grade teacher. The members of the research team in addition to Estes and myself were Koeno Gravemeijer, Michelle Stephan, Kay McClain, and Beth Petty.
- 5.
This characterization of the relation between individual and collective learning makes contact with Sfard’s (2008) recent analysis of mathematical learning from a strong discourse perspective. Sfard stresses the process of both individualizing collective practices and collectivizing novel individual contributions. In addition, it is consistent with the sociologist Anthony Giddens’ (1984) characterization of the relation between social structure and human agency. Giddens argues that social structure both enables and constrains the ways in which agency can be exercised, and that structure is created, reproduced, and potentially transformed as people exercise agency.
- 6.
This approach has much in common with grounded theory as described by Glaser and Strauss (1967). The primary difference is that grounded theory emphasizes the importance of grounding constructs empirically when analyzing data. The design research approach that I and my colleagues take also emphasizes the importance of developing constructs in response to problems encountered while intervening to support and understand students’ mathematical learning.
- 7.
This project was conducted by Paul Cobb, Kay McClain, Chrystal Dean, Jana Visnovska, Qing Zhao, Teruni Lamberg, Melissa Gresalfi, and Lori Tyler. In their dissertation studies, Dean (2005) documented the gradual transition of one of these groups into a professional learning community during the first 2 years of our collaboration with the teachers, and Visnovska (2009) documented the collective learning of this community during the final 3 years of our collaboration.
- 8.
- 9.
Kay McClain did subsequently analyze aspects of her role as teacher in the later classroom design experiments that focused on statistics (e.g., McClain, 2002).
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Cobb, P., Stephan, M., Bowers, J. (2010). Introduction. In: Sfard, A., Gravemeijer, K., Yackel, E. (eds) A Journey in Mathematics Education Research. Mathematics Education Library, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9729-3_8
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