ABSTRACT
As noted in the introductory chapter, the contributors agreed to pursue their research interests by analyzing a single set of classroom video recordings and transcripts. These recordings covered both the small-group and whole-class portions of all lessons involving arithmetical activities that were conducted in one second-grade classroom during a 10-week period. The recordings were made in the course of a year-long classroom teaching experiment conducted during the 1986–1987 school year by Cobb, Yackel, and Wood (henceforth known as the American researchers). As originally conceived, this experiment was viewed as a natural extension of the one-on-one constructivist teaching experiment developed by Steffe and his colleagues (Cobb & Steffe, 1983; Steffe, 1983). The decision to conduct the experiment in a second-grade classroom was based on two considerations. First, prior research indicated that the traditional American practice of teaching standard algorithms for adding and subtracting multidigit numbers was detrimental to students’ subsequent learning. A majority of the students appeared to construct relatively immature, syntactically based conceptions of place-value numeration and to develop instrumental beliefs about mathematics in school. Second, conceptual models of children’s arithmetical learning developed by Steffe and his colleagues (Cobb & Wheatley, 1988; Steffe, Cobb, & von Glaserfeld, 1988; Steffe, von Glaserfeld, Richards, & Cobb, 1983) could be used both to analyze individual children’s mathematical activity and to guide the development of instructional activities.
