Exploring Technologies for Supporting High Schoolers’ Embodied Geometric Reasoning and Spatial Skills

• In Event: Learning and the Growing Body: Embodied Learning Research Across Different Age Groups

Abstract

Though proof construction is a method for generating new mathematical knowledge and a focus of secondary geometry education (Rav, 1999), students often struggle to construct viable, generalizable mathematical arguments and justifications (e.g., Healy & Hoyles, 2000; Martin et al., 2005). Studies on embodied and grounded mathematics have shown that high school students performed better on verbal geometric reasoning tasks when their explanations were accompanied by direct actions and dynamic representational gestures, which depict transformations (Walkington et al., 2022).
Another important component of embodied geometric reasoning is spatial abilities (Schenck, 2024; Walkington et al., 2022). When reasoning about measurement and geometry, students often need to create, hold, and manipulate mental representations of objects. Studies have shown that priming spatio-motoric systems through spatial puzzles can improve the likelihood that students produce transformational proofs (Schenck, 2024). Embodied interaction-based interventions, particularly those that utilize motion-capture technologies such as virtual reality (VR), may be particularly powerful for invoking and enhancing spatial abilities (Lee-Cultura & Giannakos, 2020). However, little is known about how embodied spatial interventions impact students’ verbal proof productions.
This contribution presents results from a pilot study with high school students (n = 38). After completing a demographic survey and spatial ability assessment, students were randomly assigned to three groups: a control group, a computer Tangram task, or a VR Tangram task. After spending 25 minutes on the intervention task, students were shown six 2D geometric conjectures and asked to justify whether the conjecture was always true or ever false. Videos of students’ geometric reasoning were transcribed and segmented by conjecture, resulting in 228 video clips. Transcripts were coded for the presence (0/1) of mathematical transformational proof and dynamic representational gestures.
Preliminary quantitative results have found that students in both Tangram task conditions were more likely to produce transformational proofs than students in the control conditions. Moreover, students in the VR Tangram condition were more likely to produce transformational proofs and dynamic depictive gestures than students in the other two conditions. A qualitative analysis of the types of gestures used during the reasoning task revealed that students in the VR condition incorporated translation and rotation gestures in their reasoning, which mirrored the actions needed to solve the VR Tangram puzzles.
Digital Tangram puzzles, such as those in VR and web-based simulations, may provide situational feedback (Nathan, 1998) about whether pieces are in the correct location and orientation and create beneficial internal action traces (Rahaman et al., 2017). Replaying these action traces (i.e., gestural replays) has been shown to support geometric reasoning (Walkington et al., 2022; Xia et al., 2022). Furthermore, the higher gestural congruency (Lindgren & Johnson-Glenberg, 2013) may explain why a VR-based puzzle task may show greater outcomes than a computer-based task. Though exploratory, this study adds to the growing literature on how gestures, spatial ability, and technologies can be leveraged to improve high schooler’s geometric thinking.

Author

• Kelsey E. Schenck, Southern Methodist University