Embodied Mathematical Imagination and Cognition (EMIC) Research Colloquium Coloquio de Investigación: Cognición e Imaginación Matemática Corporizada Colloque de Recherche: Imagination et Cognition Mathématiques Incarnées

A basic aspect of mathematical reasoning is how people impart meaning to symbols and procedures. For example, children regard

NUMBER as more than a string of numerals. To be meaningful, numbers evoke: location along a line, magnitude, place value, cultural associations, and so on. Theories of embodied mathematical cognition seek to offer accounts of how these meanings form from our sensorimotor interactions in the world and how to design objects and experiences to cultivate these formations, foster inclusive and effective educational experiences, test hypotheses and assess educational outcomes of all students (e.g., Abrahamson et al., 2020; Alibali & Nathan, 2012; Arzarello et al., 2009; De Freitas & Sinclair, 2014; Edwards et al., 2014; McKinney de Royston et al., 2020; Radford, 2009; Walkington et al., 2021).

The EMIC working group started at 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 and research methods that acknowledge and leverage the inherently embodied nature of mathematical cognition. Recent work goes beyond scholarly publications to offer novel technologies scaled for classroom use, special education, and multilingual learners; teacher learning for instructional uses of gestures; and webinars for teachers and parents.

Instituting substantive and lasting change in mathematics education requires foundational reframing of the nature of mathematical thinking and instruction, and even of mathematics itself.

We are inspired by this year's theme to offer ways EMIC meets this set of challenges by striving to educate our colleagues at PME-NA about how theories, practices, and design principles from embodied and enactivist approaches can reshape math education. One such challenge is Inclusion and Epistemic Justice . Embodiment surfaces key dimensions of epistemological pluralism and opens new pathways for inclusive instruction (Greenstein & Zhang, 2022). Further, scholars and practitioners are invited to interrogate the applicability of embodiment theory as it applies to learners with a diverse range of physical, cultural, linguistic, and neural characteristics. For example, neurodivergent and neurotypical children can interpret concepts such as sinusoidal functions in terms of their sense of balance and forms of self-regulation such as rocking behaviors, which can serve as the basis for understanding graphs of transcendental functions and properties such as amplitude, frequency, and phase (Tancredi, 2024). These insights can then feed back into the design of new forms of mathematical activity. A second challenge is Mathematics as Transformative . Enactivist views have led to new approaches to foster conceptual development by centering human experience and forms of physical, social, and cultural interactions. Strategic uses of physical materials and digital holograms in immersive environments using AR/VR technology and motion capture video games offer novel ways of designing mathematical learning experiences by giving learners and teachers direct sensorimotor access to abstract mathematical ideas. These experiences enable students to collaboratively explore and co-construct understandings and representations of covariation (York et al., 2022) and universal properties of space and shape through gross and fine motor coordination and perceptual processes (Bock & Dimmel, 2021; Walkington et al., 2021). These experiences are re-expressed through gestures and speech that form the basis of generalized conceptual reasoning (Kokushkin, 2024; Walkington et al., 2024; Xia et al., 2025). A third challenge is the need for educators to prepare learners to Respond to the Changes in a Dynamic World . Advancements in sensor and display technologies, research methodologies, and learning theories provide an ability to closely track these rapid changes and guide these developments in furtherance of educational objectives. For example, progress in advanced analysis and modeling tools using large, multimodal data sets offer investigators new ways of describing mathematical thinking and learning, and push for new forms of formative and summative assessment (Nathan, 2024; Tancredi et al., 2021). These three challenges guide our plan for organizing hands-on activities and group discussions to promote engaging classroom instruction and innovative research and design. Day 1 will have introductions and an overview of embodied mathematical thinking, teaching, and design principles. Participants will engage with activities in stations that span K-16 content areas: Play-doh to teach integrals, Speks toys to teach qualitative and quantitative dimensions of "deep creativity" for radical change, visual aids to understand fraction arithmetic, SunRule for unit and scale, embodied programming for geometric transformations, and balance board math for understanding transcendental functions. Day 1 concludes with Q&A on the nature of embodiment theory and design principles for education. Day 2 will explore VR/AR in collaborative, embodied geometry activities using headmounted displays and casted displays of first-person experiences as users navigate an immersive holographic environment filled with mathematical objects. We will discuss the technological and pedagogical uses and challenges of this rapidly expanding technology. Day 3 will reflect on the design ideas and learning principles experienced on Days 1 & 2. We explore how embodied and enactivist approaches to education enable novel forms of mathematical activity by grounding conceptual understandings of math ideas and abstractions.