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What can eye-tracking, combined with discourse analysis, teach us about the ineffectiveness of a group of students solving a geometric problem?

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Abstract

We present the analysis of an episode of mathematical problem solving in a group, where data came from multiple advanced recorders, including multiple video cameras, Smartpen recorders, and mobile eye tracking glasses. Analysis focused on a particular group that was ineffective in their problem-solving process. Relying on the commognitive theory of learning on the one hand, and on quantitative descriptors of eye-tracking data on the other hand, we ask how do the interpretations of the discourse analysis and gaze data complement each other in understanding the obstacles to problem-solving in this episode. The setting included four Finnish 9th grade students solving a geometrical problem in the students’ authentic mathematics classroom. The commognitive analysis revealed intensive social communication (subjectifying) along with the mathematical one (mathematizing), which seemed to interfere with the problem-solving process. Specifically, it masked the differences in students’ interpretation of the tasks, and did not allow explication of meta-rules according to which students endorsed mathematical claims. Diagrams of quantified gaze data enabled a more macro-level picture of the full 15 min interaction, revealing differential loci of attention of the group members and thus triangulating the micro-analysis.

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Funding

This research is a part of MathTrack project that is funded by the Academy of Finland (Grant Number 297856).

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Authors and Affiliations

  1. Technion – Israel Institute of Technology, Haifa, Israel

    Einat Heyd-Metzuyanim

  2. University of Helsinki, Helsinki, Finland

    Eeva S. H. Haataja, Markku S. Hannula & Enrique Garcia Moreno-Esteva

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  1. Einat Heyd-Metzuyanim
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  2. Eeva S. H. Haataja
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  3. Markku S. Hannula
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  4. Enrique Garcia Moreno-Esteva
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Correspondence to Einat Heyd-Metzuyanim.

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Appendix

Appendix

Full analytical tables of all students’ solutions

See Tables 4, 5, 6, 7, and 8.

Table 4 Mary’s solutions
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Table 5 Luke’s solutions
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Table 6 Viola’s solutions
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Table 7 Nabila’s solutions
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Table 8 Other students’ solutions presented during whole-classroom discussion
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Heyd-Metzuyanim, E., Haataja, E.S.H., Hannula, M.S. et al. What can eye-tracking, combined with discourse analysis, teach us about the ineffectiveness of a group of students solving a geometric problem?. Instr Sci 51, 363–396 (2023). https://doi.org/10.1007/s11251-023-09617-9

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