Embodied Mathematical Imagination and Cognition (EMIC) Research Colloquium Coloquio de Investigación: Cognición e Imaginación Matematica Incorporada Colloque de Recherche: Imagination et Cognition Mathématiques Intégrées

Virtual and augmented reality (VR/AR) serve an increasingly central role in mathematics education and teacher training (Bock & Dimmel, 2021). As with any such advancement, the research community must contribute to this process of technology transfer and translation based on rigorous methodology and sound theoretically-principled designs for curriculum, instruction, and assessment. However, few studies in AR/VR are informed by a clear theoretical framework (Mikropoulos & Natsis, 2011). VR/AR offers learners unprecedented access to mathematical objects and tools through sensorimotor and collaborative processes that may generate new forms of mathematical inscriptions, even entirely new branches of mathematics (Nathan, 2024). EMIC contributes a compelling framework for the empirical study of embodied interactions (collaborative gesture; multimodal analytics) using VR/AR, the design of future platforms and activities (affordances and constraints), and formative and summative assessments of nonverbal ways of knowing (Abrahamson, 2014; Alibali & Nathan, 2012; Arzarello et al., 2009; De Freitas & Sinclair, 2014; Edwards et al., 2014; Radford, 2009; Walkington et al., 2021) that address the whole learner , facilitate the development of diverse learners, and foster inclusive and effective educational experiences (McKinney de Royston, et al., 2020).

The EMIC working group officially started in East Lansing, MI during PME-NA 2015. We have convened annually at PME-NA ever since, organizing events that investigate the embodied

nature of mathematics through physical and digital games, arts and crafts, individual and collaborative dance and movement, language, perception, immersive experiences, and more. EMIC members continue to explore new technologies (e.g., Harrison et al., 2018; Walkington et al., 2021) and research methods (e.g., Abrahamson et al., 2021; Closser et al., 2021) that acknowledge and leverage the inherently embodied nature of mathematical cognition. They go beyond scholarly publications and presentations to offer:

• novel embodied technologies, including some that have gone to scale for classroom use, special education, and emerging bilinguals;
• teacher learning for instructional uses of gestures;
• and webinars for teachers and parents. In addition to the authors, the organizers/institutions will include Dr. Teruni Lamberg (UNR), David Kirkland (Clark County School District), and Dr. Candace Walkington (SMU).

VR/AR technology is rapidly altering the landscape of mathematics education and STEM professional work through immersion and direct, body-based interactions with (holographic) mathematical objects. In 2024, we will organize hands-on activities and group discussions around the proliferation of VR/AR technologies in classroom instruction and research. On

1 , we will do introductions and then give an overview of grounded and embodied mathematical thinking and teaching. We will then talk about published findings on the educational value of VR/AR technology for supporting math learning and teaching and its connection with embodied learning (e.g., Garzón et al., 2020). We will invite participants to engage and observe the use of an example VR system for teaching about powers of ten. We will explain why students often struggle to understand orders of magnitude and reason about very small and very large numbers in domains such as nanotechnology, and demonstrate how VR provides perceptual experiences that can improve their mathematical reasoning. Day 1 will conclude with an open-ended Q&A on the nature of embodiment theory and embodied design principles for VR/AR. On Day 2 , organizers will facilitate exploring EMIC accounts of VR/AR in collaborative, embodied math activities. We address research methods for analyzing collaborative embodiment in immersive learning environments and some of the benefits and challenges for implementing these interventions in authentic learning contexts. We will then break into small design groups where participants consider ways VR/AR could be used to explore other topics in mathematics education, and ways of supporting diverse learners with varying physical abilities and linguistic and cultural experiences. We will report these ideas to the whole group, theorizing about the nature of learning in ways that inform research and the design of valid knowledge assessments for a broad range of learners and math topics, which will be chronicled in a shared document.

Day 3 will start with reflections on the design ideas and learning principles generated during

Days 1 & 2. We explore ways that VR/AR enables novel forms of mathematical activity by directly interacting with and transforming geometric objects using body movements and perceptual processes. We then consider how VR/AR can support expanded notions of

mathematical representations, such as inscribing operations through person- and group-centered actions and perceptions, in contrast with disembodied, formalism-centered, symbolic notations and diagrams. We plan to have a facilitated discussion on why embodiment offers a unique set of theoretical and methodological resources for designing meaningful learning experiences.

Embodied learning theory and design principles provide key insights into how perceptually concrete, bodily experiences and collaboration in VR/AR can engage learners across a wide range of topics and grade levels. Movement- and perception-based mathematical activities can reach students who may otherwise feel left out of highly discursive and symbol-based activities. Through EMIC, we aim to foster an engaged community committed to transformative education.