Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations |
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Authors: | Hai-Ning Liang and Kamran Sedig |
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Institution: | (1) The University of Western Ontario, London, ON, Canada;; |
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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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