In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during ritualized formats of communication and replaced by social conventions. Specific aspects of the problem of meaning development were investigated in two second-grade teaching cases. These were used to develop decisive requirements for maintenance of an…

Discusses how one teacher encouraged students to communicate mathematically when discussing the lyrics to the song "Billy Boy." Students' problem solving was assessed by means of classroom discussion. (MKR)

Reports on an 18-month investigation of a teacher's actions during class discussions in a second-grade classroom in which student disagreement was resolved by argumentation. Concludes that creating a classroom environment in which students struggle with their own learning requires that teachers understand the complex relationship between the…

Argues that "student talk" is an important developmental activity in mathematics. Gives suggestions that will facilitate student talk. (PK)

Although mathematics can be described as a formalized language, the signs and symbols of mathematical representation are subject to individual interpretation, which, if inaccurate, can lead to inhibitions about and interferences with the mathematical learning process. The purpose of this study was to explore communication in an intermediate-level…

Presents a case study of a middle school mathematics teacher using a discourse-oriented teaching method for a three-year period. Demonstrates how the teacher provided both analytic scaffolding (help in structuring mathematical ideas) and social scaffolding (help in establishing norms for social behavior). Finally, highlights parallels between…

Analyzes one third grader's participation in mathematics class discussions, his beliefs about class discussion, and his arithmetical development throughout a school year in a problem-centered learning classroom. Concludes that a fruitful classroom discussion both necessitates and, conversely, is facilitated by the negotiation of social norms and…

Investigates the characteristics of oral and written communication in a German third-grade mathematics class and theorizes how this knowledge might be applied to improve instruction. Develops several lessons incorporating communication skills into activities that illustrate fundamental mathematical concepts. Includes lesson transcripts, writing…