Cobb P., Perlwitz M. & Underwood D. (1994) Construction individuelle, acculturation mathématique et communauté scolaire. Revue des sciences de l’éducation 20(1): 41–61. https://cepa.info/5944

We first distinguish between the school mathematics tradition typically established in textbook-based classrooms and the inquiry mathematics tradition established in classrooms where instruction is compatible with constructivism. We then focus on the inquiry mathematics tradition and consider the theoretical and pragmatic tensions inherent in the view that mathematical learning is both a process of active individual construction and a process of acculturation. Particular attention is given to the ways in which both constructivist and sociocultural theorists address this issue. Finally, we discuss the development of instructional activities for inquiry mathematics classrooms.

Cobb P., Perlwitz M. & Underwood D. (1996) Constructivism and activity theory: A consideration of their similarities and differences as they relate to mathematics education. In: Mansfield H., Patemen N. & Bednarz N. (eds.) Mathematics for tomorrow’s young children: International perspectives on curriculum. Kluwer, Dordrecht: 10–56. https://cepa.info/6868

The primary purpose of this chapter is to clarify the basic tenets of activity theory and constructivism, and to compare and contras instructional approaches developed within these global theoretical perspectives. This issue is worthy of discussion in that research and development programs derived from these two perspectives are both vigorous. For example, the work of sociocultural theorists conducted within the activity theory tradition has become increasingly influential in the United States in recent years. One paradigmatic group of studies conducted by Lave (1988), Newman, Griffin, and Cole (1089). and Scribner (1984) has related arithmetical computation to more encompassing social activities such as shopping in a supermarket, packing crates in a dairy, and completing worksheets in school. Taken together, these analyses demonstrate powerfully the need to consider broader social and cultural processes when accounting for children’s development of mathematic cal competeuce.

Cobb P., Perlwitz M. & Underwood-Gregg D. (1998) Individual construction, mathematical acculturation, and the classroom community. In: Larochelle M., Bednarz N. & Garrison J. (eds.) Constructivism and education. Cambridge University Press, New York NY: 63–80. https://cepa.info/5933

Excerpt: For the past six years we, together with Erna Yackel and Terry Wood, have conducted a classroom-based research and development project in elementary school mathematics.’ In this paper, we draw on our experiences of collaborating with teachers and of analyzing what might be happening in their classrooms to consider three interrelated issues. First, we argue that the teacher and students together create a classroom mathematics tradition or microculture and that this profoundly influences students’ mathematical activity and learning. Sample episodes are used to clarify the distinction between the school mathematics tradition in which the teacher acts as the sole mathe-matical authority and the inquiry mathematics tradition in which the teacher and students together constitute a community of validators. Second, we consider the theoretical and pragmatic tensions inherent in the view that mathematical learning is both a process of individual cognitive construction and a process of acculturation into the mathematical practices of wider society. In the course of the discussion, we contrast constructivist attempts to cope with this tension with approaches proposed by sociocultural theorists. Finally, we use the preceding issues as a backdrop against which to consider the development of instructional activities that might be appropriate for inquiry mathematics classrooms.

Cobb P., Wood T. & Yackel E. (1991) A constructivist approach to second grade mathematics. In: Glasersfeld E. (ed.) Radical constructivism in mathematics education. Kluwer, Dordrecht: 157–176. https://cepa.info/5284

Our overall objective in this paper is to share a few observations made and insights gained while conducting a recently completed teaching experiment. The experiment had a strong pragmatic emphasis in that we were responsible for the mathematics instruction of a second grade class (7 year-olds) for the entire school year. Thus, we had to accommodate a variety of institutionalized constraints. As an example, we agreed to address all of the school corporation’s objectives for second grade mathematics instruction. In addition, we were well aware that the school corporation administrators evaluated the project primarily in terms of mean gains on standardized achievement tests. Further, we had to be sensitive to parents’ concerns, particularly as their children’s participation in the project was entirely voluntary. Not surprising, these constraints profoundly influenced the ways in which we attempted to translate constructivism as a theory of knowing into practice. We were fortunate in that the classroom teacher, who had taught second grade mathematics “straight by the book” for the previous sixteen years, was a member of the project staff. Her practical wisdom and insights proved to be invaluable.

Cobb P., Yackel E. & Wood T. (1992) A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education 23(1): 2–33. https://cepa.info/2967

The representational view of mind in mathematics education is evidenced by theories that characterize learning as a process in which students modify their internal mental representations to construct mathematical relationships or structures that mirror those embodied in external instructional representations. It is argued that, psychologically, this view falls prey to the learning paradox, that, anthropologically, it fails to consider the social and cultural nature of mathematical activity and that, pedagogically, it leads to recommendations that are at odds with the espoused goal of encouraging learning with understanding. These difficulties are seen to arise from the dualism created between mathematics in students’ heads and mathematics in their environment. An alternative view is then outlined and illustrated that attempts to transcend this dualism by treating mathematics as both an individual, constructive activity and as a communal, social practice. It is suggested that such an approach might make it possible to explain how students construct mathematical meanings and practices that, historically, took several thousand years to evolve without attributing to students the ability to peek around their internal representations and glimpse a mathematically prestructured environment. In addition, it is argued that this approach might offer a way to go beyond the traditional tripartite scheme of the teacher, the student, and mathematics that has traditionally guided reform efforts in mathematics education.

Glasersfeld E. von & Cobb P. (1983) Knowledge as environmental fit. Man-Environment Systems 13(5): 216–224.