A framework for analyzing the collaborative construction of arguments and its interplay with agency

Abstract

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program.

Students’ Mathematical Reasoning, Communication, and Language Representations: A Video-Narrative Analysis

“…Finally, the analyses offered by the VMCAnalytics may be applied to preparing teachers who should be capable of facilitating conditions that invite student collaboration, meaning seeking, justification, and the use of language-both oral written. Prior research has investigated the extent to which teachers are able to recognize forms of reasoning that children express and whether it is possible to improve their ability to recognize various forms of mathematical reasoning through an instructional intervention (Maher et al, 2014;Mueller et al, 2012;Palius & Maher, 2013). The dissemination of this research has the potential to ECNU Review of Education 1 (3) inform the members of principal disciplines about the potential for shifting teachers' beliefs about students' learning to focus on what they really know about mathematical understanding, so that they can communicate effectively those understandings with language and non-language representations.…”

“…Students learn mathematics as a result of their efforts to make sense of mathematical concepts and procedures during their problem solving. Evidence ECNU Review of Education 1 3shows that students create their own meanings for themselves and reason thoughtfully by providing convincing arguments for their solutions (Mueller & Maher, 2009;Mueller, Yankelewitz, & Maher, 2012;Lindow, Wilkinson, & Peterson 1985;Wilkinson, Martino, & Camilli, 1994).…”

“…Their research has established that children, both primary and middle-school aged, can verbally articulate arguments in the form of proof by cases; induction; upper/lower bound and contradiction (Maher & Martino, 1996;Maher & Davis, 1995). The justifications that students produce may result from their coordinated efforts to make sense of the problem, notice patterns, and pose hypotheses (Mueller et al, 2012;Maher & Martino, 2000). Research has established that students continue in their efforts to refine their solutions through discussions, as they negotiate meaning with other students and structure their own investigations (Weber, Maher, Powell, & Lee, 2008;Maher, 2005).…”

An inferentialist account of students’ collaboration in mathematics education

“…While engaged in exploratory talk, partners exercise agency as they challenge and defend arguments and create and evaluate hypotheses ( Mueller et al 2012 p. 385). Martin et al (2006) proposed a framework similar to that of Mueller et al (2012) based on the notion of interaction and coaction. Interaction is described as the Bprocess of acting on the ideas of another in a reciprocal or complementary way,^while coactions refer to the Bprocess of acting with the ideas and actions of others in a mutual, joint way^ (Martin et al 2006, p. 156).…”

“…To examine and evaluate collaboration as a process, there have been some studies that used at least one framework from the cognitivist perspective (individual) and one from the social perspective (e.g., Mueller et al 2012;Oner 2016;Watson and Chick 2001). Yet, the focus in these studies was predominantly on one facet of collaboration.…”