Hanna Fredriksdotter: Young students’ mathematical argumentation in social interaction: Video-based observations of student-student interaction during everyday work in the mathematics classroom

Abstract

Previous research indicates that students benefit from engaging in mathematical problem-solving activities together with peers. The aim of this thesis was to increase the knowledge of how social interaction can contribute to shaping young students’ mathematical argumentation. 

The analysis was based on a dialogical perspective on communication. In particular, an ethnomethodological approach was applied to the analysis of students’ social interaction while engaging in discussions about solutions to mathematical tasks. Students’ contributions to interaction were analysed using Conversation Analysis and multimodal analysis. In addition, the contents of students’ explanations, justifications and generalisations were analysed according to procedures of qualitative content analysis. 

The empirical material consisted of video recordings of naturally occurring interaction during mathematics lessons in two grade-6 classrooms (i.e., among students who are 11–12 years old). Findings were presented in four studies. Study I indicated that the mathematical argumentation among students working in the same classroom can orient towards very different social and sociomathematical norms. Study II focused on students’ use of different types of justifications, showing that their general arguments consistently built on (and agreed with) results of preceding examinations of particular examples. In Study III, students’ strategies of handling differing proposals were analysed, which showed that students often solicited explanations of peers’ proposals by commenting on or asking questions about them without explicitly criticising them. Moreover, when students conceded to someone else’s proposal and rejected their own, concessions and rejections were marked by affect-laden and/or embodied acts, indicating an urgency to display a change of state. In addition, marking their concessions may be part of students’ ways of displaying independent epistemic access to the mathematical task as well as to the differing proposal. Focusing on students’ methods of co-constructing general arguments, Study IV confirmed the importance of having access to and building on others’ arguments. In addition, Study IV showed how the use of linguistic resources can indicate that students have identified regularities and/or transferred known mathematical facts into a new context.

The detailed analysis of students’ argumentation while engaging in mathematical problem solving with peers emphasised the reflexive relation between “social” and “mathematical” aspects of interaction in the mathematics classroom. The analysis also exemplified how young students’ use of justifications can be a first stage in developing an understanding of formal mathematical proof.