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Understanding the cognitive processes of mathematical problem posing: evidence from eye movements

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Abstract  

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students’ behavior in these three stages of problem posing, especially focusing on investigating the influence of task situation format and mathematical maturity on students’ thinking. The study was conducted using a 2 × 2 mixed design: task situation format (with or without specific numerical information) × subject category (master’s students or sixth graders). Regarding the task situation format, students’ performance on tasks with numbers was found to be significantly better than that on tasks without numbers, which was reflected in the metrics of how well they understood the task and the complexity and clarity of the posed problems. In particular, students spent more fixation duration on understanding and processing the information in tasks without numbers; they had a longer fixation duration on parts involving presenting uncertain numerical information; in addition, the task situation format with or without numbers had an effect on students’ selection and processing of information related to the numbers, elements, and relationships rather than information regarding the context presented in the task. Regarding the subject category, we found that mathematical maturity did not predict the quantity of problems posed on either type of task. There was no significant main group difference found in the eye-movement metrics.

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Data availability

The dataset generated during the current study is not publicly available as it contains private information of participants that the authors acquired through video recording. Information on how to obtain it and reproduce the analysis is available from the corresponding author on request.

Notes

  1. An example of the problems posed by a sixth grader and a master’s student on the House Purchase Task is shown in Appendix 3.

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Funding

Ling Zhang was supported by a grant from the China Collaborative Innovation Center of Assessment toward Basic Education Quality at Beijing Normal University (2021–06-028-BZPK01). During the revision of this manuscript, Jinfa Cai was supported by a grant from the USA National Science Foundation ((DRL- 2101552). Any opinions expressed herein are those of the authors and do not necessarily represent the views of funding agencies.

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Authors and Affiliations

  1. Southwest University, Chongqing, China

    Ling Zhang & Naiqing Song

  2. Chinese Institute for Brain Research, Beijing, China

    Guowei Wu

  3. University of Delaware, Newark, DE, USA

    Jinfa Cai

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Appendices

Appendix 1

Table 10

Table 10 PPT-number test
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Appendix 2

Table 11

Table 11 Questionnaire test
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Appendix 3

8

Fig. 8
figure 8

Difference map (left) and Heat maps (right) for two groups subjects on two kinds of task situation format (number on and number off) on the stage of understanding the Pool Maintenance task. Note: The colors represent Z scores of fixation duration, with warm colors denoting longer fixation duration and cold colors denoting shorter fixation duration. Dark contours in the difference map indicated regions of significant difference (at the alpha level of 0.05, two-tailed)

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9

Fig. 9
figure 9

Difference map (left) and Heat maps (right) for two groups subjects on two kinds of task situation format (number on and number off) on the stage of constructing and expressing problem on the Pool Maintenance task. Note: The colors represent Z scores of fixation duration, with warm colors denoting longer fixation duration and cold colors denoting shorter fixation duration. Dark contours in the difference map indicated regions of significant difference (at the alpha level of 0.05, two-tailed)

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Appendix 4

Table 12

Table 12 An Example of the Problems Posed by a Sixth Grader and a Master’s Student on the House Purchase task
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Zhang, L., Song, N., Wu, G. et al. Understanding the cognitive processes of mathematical problem posing: evidence from eye movements. Educ Stud Math (2023). https://doi.org/10.1007/s10649-023-10262-9

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