Students’ agency, creative reasoning, and collaboration in mathematical problem solving

Abstract

This paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

Lesson study with sharing and jumping tasks in online mathematics classrooms for rural area students

“…Mathematical thinking is crucial in learning and teaching mathematics (Stacey, 2006). When students think mathematically, they actively engage in their mathematics learning, attempting to make sense of ideas and constructing connections among various facts, procedures, and concepts (Hwang & Ham, 2021;Hansen, 2022). Moreover, effective mathematics learning officially starts with thinking activities in the learning process.…”

Research on Mathematics Problem Solving in Elementary Education Conducted from 1969 to 2021: A Bibliometric Review

“…However, researchers (i.e., Hansen, 2021;Öztürk et al 2020;Passolunghi et al, 2019) found that students' mathematics problem solving is influenced by affective factors. In fact, several emotional changes were captured in the study conducted by O'Dell (2018).…”

“…Despite the strong consensus among the mathematics education community on recognizing the development of students' mathematics problem solving ability as the main goal in the classroom, Lester and Cai (2016) noted that the consensus on effective instruction for developing students' problem solving ability is yet to be reached. Following this, Hansen (2021) urged the researchers to conduct more research on mathematics problem solving. Nonetheless, it is argued that the lack of accumulation of problem solving research is the main issue to be addressed for avoiding the recycling of flawed conjectured problem solving instructions in future research (English & Sriraman, 2010) Thus, it is warranted to conduct a review of the pastrelated studies for identifying the research gaps (Cason et al, 2019).…”

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“…It is also used by students and teachers to actively develop and comprehend mathematical ideas (Lam, 2012). Moreover, reasoning has the ability to improve students' understanding of mathematics and enhance the development of their creativity (Hansen, 2021). It is very important to develop students to participate in creative thinking activities (Nogerbek et al, 2022).…”