Richard Donato

Learning what counts as a mathematical explanation

Abstract Instructional practices are being transformed in many mathematics classrooms as a result of reform efforts in the United States and Europe. For example, students are being asked to take a more active role in explaining their problem solution strategies. In order to achieve these changes in student activity, teachers are being encouraged to restructure the communication patterns in their classrooms. The goal of this article is to examine, in detail, the discourse of one teacher and three of her middle school students during a single lesson on area measurement. Some concepts from sociocultural theory (e.g., authoritative versus internally persuasive discourse) are used to organize and interpret our analysis. The teacher observed in this study, tried to share responsibility and authority for explaining and evaluating mathematical problems with her students. We found that two of the three students initially tried to present explanations that differed from that used by the teacher on a previous day. Each time these students offered an alternative solution strategy, the teacher overlapped her speech with theirs. Eventually both students employed the teachers explanation. The third student who used the teachers explanation from the beginning did not encounter her overlapping speech. As a result of our analyses, we concluded that the teacher did achieve one of her goals for this lesson, the sharing of responsibility for providing explanations, but not the goal of sharing authority. The theoretical and instructional implications of our analysis for research on educational reform are addressed.

Discourse Perspectives on Formal Instruction.

Abstract Formal instruction in the second‐language classroom is generally characterised by two approaches: inductive and deductive presentations. In this paper, it will be argued that formal instruction is not easily reduced to explicit statements about the language or implicit strategies whereby the learner is expected to hypothesise and formulate structures of the language on their own. Rather, formal instruction can involve discursive negotiation resulting in the co‐construction of understanding between teacher and student. This study will report on the discourse of formal instruction of two foreign language teachers. It will be shown that explanation can be a negotiated process in which the teacher plays a role in collaborative sense‐making with the class. This finding reveals that the dichotomy of induction and deduction fails to capture the complexity of formal instruction, since it does not take into account its often interactive nature. Through protocol analysis, formal instruction will be examine...

The genesis of classroom discursive practices as history-in-person processes

This article reports findings from an investigation into how novice teachers’ classroom discursive practices were influenced by history-in-person processes. Thought-based and practice-based data sources of two novice teachers were analysed to understand how history is brought to the present through the minds and bodies of individuals as they are addressed by external forces. Findings suggested that one’s history-in-person interacts in complex and unpredictable ways with external factors and can result in contentious local practice. Thus, attention to both personal history and to institutional constraints must figure into interpretations of how novice teachers perform and how changing practice is approached.