scholarly journals Adult Students' Reasoning in Geometry: Teaching Mathematics through Collaborative Problem Solving in Teacher Education

2007 ◽  
Vol 4 (1) ◽  
pp. 1-30
Author(s):  
Raymond Bjuland
Author(s):  
Johanna Pöysä-Tarhonen ◽  
Päivi Häkkinen ◽  
Pasi Tarhonen ◽  
Piia Näykki ◽  
Sanna Järvelä

AbstractCollaborative problem solving (CPS) is widely recognized as a prominent 21st-century skill to be mastered. Until recently, research on CPS has often focused on problem solution by the individual; the interest in investigating how the theorized problem-solving constructs function as broader social units, such as pairs or small groups, is relatively recent. Capturing the complexity of CPS processes in group-level interaction is challenging. Therefore, a method of analysis capturing various layers of CPS was developed that aimed for a deeper understanding of CPS as a small-group enactment. In the study, small groups of teacher education students worked on two variations of open-ended CPS tasks—a technology-enhanced task and a task using physical objects. The method, relying on video data, encompassed triangulation of analysis methods and combined the following: (a) directed content analysis of the actualized CPS in groups, (b) process analysis and visualizations, and (c) qualitative cases. Content analysis did not show a large variation in how CPS was actualized in the groups or tasks for either case, whereas process analysis revealed both group- and task-related differences in accordance with the interchange of CPS elements. The qualitative cases exemplified the interaction diversity in the quality of coordination and students’ equal participation in groups. It was concluded that combining different methods gives access to various layers of CPS; moreover, it can contribute to a deeper articulation of the CPS as a group-level construct, providing divergent ways to understand CPS in this context.


Author(s):  
Juuso Henrik Nieminen ◽  
Man Ching Esther Chan ◽  
David Clarke

AbstractThe 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.


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