This article presents an analytical approach for documenting the identities for teaching that mathematics teachers negotiate as they participate in 2 or more communities that define high-quality teaching differently. Drawing on data from the first 2 years of a collaboration with a group of middle school mathematics teachers, the article focuses on…

Our primary purpose in this article is to propose an interpretive scheme for analyzing the identities that students develop in mathematics classrooms that can inform instructional design and teaching. We first introduce the key constructs of normative identity and personal identity, and then illustrate how they can be used to conduct empirical…

Explores the relationship between classroom discourse and mathematical development in a first-grade classroom. Addresses issues such as the teacher's role and the role of symbolization in supporting reflective shifts in the discourse. Contrasts the analysis of reflective discourse with Vygotskian accounts of learning that also stress the…

This article focuses on the relationship between research and development and the types of justifications given for reform activities. It cautions that research is not to persuade others that an innovation works but rather to examine an innovation critically. (AIM)

Presents a way of interpreting mathematics classrooms, by advancing the notion of sociomathematical norms, to account for how students develop mathematical beliefs and values and how they become intellectually autonomous in mathematics. Includes episodes from a second-grade classroom to clarify the processes by which sociomathematical norms are…

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

A methodology for exploring limits and subtleties of children's construction of mathematical concepts and operations is described. It is believed that the failure to observe children's constructive processes firsthand denies a researcher the experimental base so crucial in formulating explanations of processes. Researchers are encouraged to teach…

In an attempt to bridge the perceived distinction between internalized conceptions of mathematics and their external representations, this discussion treats mathematics both as an individual, constructive activity and as a communal, social practice. It is argued that this approach might transcend the tripartite scheme of teacher, student, and…

Presents a response to Orton's article (this issue), claiming that the previous author presents a highly idiosyncratic interpretation of the Cartesian dualism, creates a gulf between theory and practice, and implies that the social and cultural aspects of mathematical activity can be dismissed. (65 references) (Author/MKR)

Analysis of the role that (n=4) second graders' use of the hundred board played in supporting their conceptual development found that the board did not support the construction of increasingly sophisticated concepts of 10, but did support their ability to reflect on their mathematical activity. (54 references) (Author/MKR)

Described is a study of second grade classes that participated in a year-long project in which instruction was generally compatible with a socioconstructivist theory of knowledge and recent recommendations of the National Council of Teachers of Mathematics. Methods, results, and implications for mathematics instruction are discussed. (CW)