Search

This study introduces a framework for analyzing opportunities for mathematical reasoning (MR) in school mathematics, using MR-relevant claims and their derivation as the unit of analysis. We contend that this approach can effectively capture a broad range of opportunities for MR across various teaching situations. The framework, rooted in commognition, entails identifying necessary object-level narratives (NOLs) and the processes involved in their construction and substantiation. After theoretical development, the framework was refined through analyses of mathematics lessons in Norwegian primary school classrooms. Examples from the data illustrate how to utilize the framework in analysis and what such analyses can reveal in four typical teaching situations: the introduction of new mathematical objects, the introduction of procedures, work on exercise tasks, and work on problem-solving tasks. Drawing from the analysis of these examples, we discuss the value of the framework for analyzing MR in school mathematics and how such analysis can benefit teachers and researchers. [ABSTRACT FROM AUTHOR]

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a mathematics teacher attempting to share authority as well as applying several moves recognized as supporting meaningful student learning. Data has been collected in a fourth-grade Norwegian classroom and is analyzed by means of open coding, inspired by literature. We identify the moves used by the teacher, and we rank these moves along two dimensions: (1) their potential to support mathematical reasoning and (2) their potential for sharing authority. From this, we uncover how a teacher's work of orchestrating mathematical discussions involves moves in all four quadrants, and we discuss how the interplay of moves affects the authority structures and the collaborative reasoning in the classroom. [ABSTRACT FROM AUTHOR]