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Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations

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Abstract

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally accepted that making these visualizations interactive can improve their utility, it is still not clear what role interaction plays in such activities. Interacting with MVs can be viewed as performing low-level epistemic actions on them. In this paper, an epistemic action signifies an external action that modifies a given MV in a way that renders learners’ mental processing of the visualization easier, faster, and more reliable. Several, combined epistemic actions then, when performed together, support broader, higher-level epistemic activities. The purpose of this paper is to examine the role that interaction plays in supporting learners to perform epistemic activities, specifically spatial reasoning involving 3D MVs. In particular, this research investigates how the provision of multiple interactions affects the utility of 3D MVs and what the usage patterns of these interactions are. To this end, an empirical study requiring learners to perform spatial reasoning tasks with 3D lattice structures was conducted. The study compared one experimental group with two control groups. The experimental group worked with a visualization tool which provided participants with multiple ways of interacting with the 3D lattices. One control group worked with a second version of the visualization tool which only provided one interaction. Another control group worked with 3D physical models of the visualized lattices. The results of the study indicate that providing learners with multiple interactions can significantly affect and improve performance of spatial reasoning with 3D MVs. Among other findings and conclusions, this research suggests that one of the central roles of interaction is allowing learners to perform low-level epistemic actions on MVs in order to carry out higher-level cognitive and epistemic activities. The results of this study have implications for how other 3D mathematical visualization tools should be designed.

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Notes

  1. Here, ‘information-based’ is meant to suggest that epistemic activities of the learners revolve around the use of, working with, and thinking with the mathematical visualization.

  2. Cognitive activities refer to mental activities, and epistemic activities refer to mental as well as knowledge-oriented activities. Even though this subtle difference exists between the two terms, for the sake of simplicity, they are used interchangeably in this paper. The same thing is true of activities and tasks. Activities are more open-ended in nature, but tasks may be given to us and be more goal-oriented and purposeful. Additionally, activities are broader than tasks and may encompass several levels of tasks and subtasks. Once again, the two terms, activities and tasks, are used interchangeably here.

  3. Originally, 13 participants had signed up for each group. However, one participant in the MI Group had to leave in the middle of the study and was therefore dropped out of the study. Also, three participants in the SI Group did not show up for the study.

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Acknowledgments

We would like to thank the reviewers of this article for their valuable comments. This research has been funded by the Natural Sciences and Engineering Research Council of Canada.

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  1. The University of Western Ontario, London, ON, Canada

    Hai-Ning Liang & Kamran Sedig

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  1. Hai-Ning Liang
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  2. Kamran Sedig
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Correspondence to Kamran Sedig.

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Liang, HN., Sedig, K. Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations. Int J Comput Math Learning 15, 191–224 (2010). https://doi.org/10.1007/s10758-010-9165-7

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