What affordances do open-ended real-life tasks offer for sharing student agency in collaborative problem-solving?

Juuso Henrik Nieminen,Man Ching Esther Chan,David Clarke

doi:10.1007/s10649-021-10074-9

Abstract

The important role of student agency in collaborative problem-solving has been acknowledged in previous mathematics education research. However, what remains unknown are the processes of agency in open-ended tasks that draw on real-life contexts and demand argumentation beyond “mathematical”. In this study, we analyse a video recording of two student groups (each consisting of four students) taking part in collaborative problem-solving. We draw on the framework for collaborative construction of mathematical arguments and its interplay with student agency by Mueller et al. (2012). This original framework is supplemented by (i) testing and revising it in the context of open-ended real-life tasks, with (ii) student groups rather than pairs working on the tasks, and by (iii) offering a strengthened methodological pathway for analysing student agency in such a context. Based on our findings, we suggest that the framework suits this new context with some extensions. First, we note that differences in student agency were not only identified in terms of the discourse students drew on, but in how students were able to shift between various discourses, such as between “mathematical” and “non-mathematical” discourses. We identify a novel discourse reflecting student agency, invalidation discourse, which refers to denying other students’ agency by framing their contribution as invalid. Finally, we discuss the need to reframe “mathematical” arguments—and indeed student agency—while the task at hand is open-ended and concerns real-life contexts.

Highlights

Over 20 years ago, Forman et al (1998) were struggling with the same issue as we do nowadays: How can research guide teachers to facilitate mathematical learning through collaborative argumentation? Collaborative mathematical activities do not just see students as individuals working together, but as a collective (Leeet al., 2006)
According to Sullivanet al. (2015), open-ended tasks require the teacher to relinquish some level of control over student activity so that students have a chance to build their own mathematical arguments rather than just finding those established by the teacher
We have drawn on Mueller et al (2012) to conceptualise agency as a socially constructed phenomenon that lies in the heart of mathematical collaboration

Summary

Introduction

Over 20 years ago, Forman et al (1998) were struggling with the same issue as we do nowadays: How can research guide teachers to facilitate mathematical learning through collaborative argumentation? Collaborative mathematical activities do not just see students as individuals working together, but as a collective (Leeet al., 2006). Over 20 years ago, Forman et al (1998) were struggling with the same issue as we do nowadays: How can research guide teachers to facilitate mathematical learning through collaborative argumentation? What remains undertheorised is the multifaceted nature of mathematical collaborative problem-solving (CPS) in the context of open-ended tasks. Such tasks often require students to collaborate without direct guidance by the teacher (Chan & Clarke, 2017; Langer-Osunaet al., 2020; Langer-Osuna, 2018; Yeo, 2017). Open-ended tasks sometimes draw on real-life contexts that require students to use their personal experiences in the collaborative process of producing mathematical arguments (Jurdak, 2006; Yeo, 2017). How collaboration manifests as learners would need to shift between literate and colloquial mathematical arguments—and perhaps even non-mathematical arguments—has been rarely elaborated

Methods

Results

Conclusion