Extended Reality (XR) Poses Challenges and Opportunities for Cultivating Geometry Reasoning

• In Event: Measuring the Impact of Extended Reality in Education: Challenges and Opportunities

Abstract

Extended Reality (XR) systems that use VR and AR to expand the range of visual and proprioceptive experiences, offer novel ways of engaging students’ spatial reasoning about virtual and holographic objects (Dimmel et al., 2021). The development of a new class of XR dynamic geometry software (DGS) engages students with the affordances and constraints of actual mathematical objects that conform to the programmed properties of their abstract relatives (e.g., Chan & Leung, 2014). Examples of these include parallel lines that extend beyond one’s sight and never touch, spatial rotations performed by moving one’s body as well as the object, and investigating objects from the inside as well as the outside.
As the technology advances, issues remain regarding the ways we cultivate and assess mathematical thinking and learning in classrooms. Our team has been working to design and implement GeoGebra-AR, a 3D holographic version of the widely used DGS (Tomaschko & Hohenwarter, 2019). We focus on two central issues that have emerged from our time working in schools and with teachers: Assessing nonverbal ways of knowing; and designing curriculum activities for the affordances and constraints of XR-DGS experiences.
In findings with high school students (n=120; Author et al., 2023a; see Figure 2.1) we did not observe statistically reliable benefits in geometry justification performance for GeoGebra-AR compared to closely matched use of traditional GeoGebra on a tablet. This may partly be due to the limits of traditional paper-and-pencil assessments to evaluate students’ multimodal reasoning, including students’ gestures that both describe and simulate the mathematical transformations used to inform their thinking. Teachers also do not spontaneously attend to students’ gestures and use them to evaluate their mathematical reasoning (Sung et al., 2021), though they can be trained to do so.
A second issue addresses the appropriate designs for learning experiences for XR. Mathematics instruction is often didactic but can foster deeper learning through collaborative problem solving (e.g., Fennema et al., 1996). Yet these constructivist approaches seldom offer guidelines for the immersive experiences that characterize XR learning environments. When asked to identify the unique benefits and potentials for XR for geometry education, high school teachers (n=4; Author et al., 2023b) were keen on the opportunities that can further develop students’ visualization skills, explore object cross-sections, and directly experience 3D properties such as surface area and volume through immersion and unfolding. After using GeoGebra-AR (Figure 2.2), teachers described the need for activities that are at once structured and open-ended, akin to guided discovery learning (Brown & Campione, 1994), employing teaching methods that are not typical of many secondary math classes. They suggested that “diagrams” and “proofs” could one day be replaced by holographic images and animations (cf. Dimmel et al., 2021).
Our paper highlights examples of the kinds of classroom instruction and assessment practices that operate more harmoniously with XR experiences for secondary mathematics. In doing so, we also offer insights into the emerging ways that these advancements in learning environments are changing the nature of teaching, testing, and the content of mathematics itself.

Authors

• Mitchell J. Nathan, University of Wisconsin - Madison

• Candace A. Walkington, Southern Methodist University

• Michael I. Swart, University of Wisconsin - Madison