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

It is increasingly apparent that effective mathematics education systems need to address the needs of embodied learners by designing educational experiences that: 1) are grounded in people's natural propensities for movement, sensation, perception, and collaborative interactions with cultural and scientific tools; 2) support "multiple linguistic repertoires," (McKinney de Royston, et al., 2020, p. 10) including verbal, nonverbal, and multimodal ways of knowing, communicating, and assessment; and 3) facilitate learners' participation in systems that support the distributed nature of knowledge and reasoning (e.g., Abrahamson 2014; Alibali & Nathan, 2012; Arzarello et al., 2009; De Freitas & Sinclair, 2014; Edwards et al., 2014; Radford 2009; Walkington et al., 2021).

The EMIC working group officially started in East Lansing, MI during PME-NA 2015. However, it emerged from a variety of earlier initiatives, including a 2007 AERA symposium, "Mathematics Learning and Embodied Cognition," a 6-year NSF-REESE grant (Nemirovsky et al., 2008), special issues of Educational Studies in Mathematics (2009), The Journal of the Learning Sciences (2012), and an NCTM 2013 research pre-session keynote panel, "Embodied cognition: What it means to know and do mathematics." A group of PME-NA members recognized a "critical mass" of investigators involved in related projects, and contributed findings and conceptual frameworks to form a stable and growing mathematics education

research community to discuss, explore, and advance this scholarly program. We have convened annually at PME-NA ever since, organizing events that investigate the embodied nature of mathematics through physical and digital games, art and craft, 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). 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 programs for instructional uses of gestures;
• and webinars for teachers and parents.

The organizers (including the authors; and coordinator M. Nathan) have several years of experience co-designing and facilitating the PME-NA sessions. In 2023, we will organize hands-on activities and group discussions around the central questions that frame this year's conference theme, "Engaging all Learners." On Day 1 , we will first do introductions and a brief overview of grounded and embodied mathematical thinking and teaching. We will then form 3 groups for those most interested in (1) student thinking, (2) teaching and teachers, and (3) embodied design. Groups will describe what engagement means to them, ways of documenting engagement, and benefits for math education from high levels of engagement. Each group will identify one math idea (e.g., division by fractions, or teaching with multiple representations) and generate one high- and one low-engagement activity for the same math idea. Members of the other groups will participate in the high- and low-engagement activities in a jigsaw-type design. The whole group will convene to share these ideas and experiences so all participants will have delved into the topic of engagement from each group perspective. Day 1 will conclude with open-ended Q&A on the nature of embodiment theory, research methods, and design principles. On Day 2 , we will continue our 3 participant-groups focused on embodied learning, teaching, and technology (membership can be fluid). Each group will co-design a math activity for high engagement. Organizers will facilitate effective practices for group co-design, such as record keeping, and having all voices respected. Collaborative co-design will operate on two levels: (1 Math) What is the mathematics to be learned, taught, or assessed? (2 engagement) What makes this activity engaging? For which learners? How can we know if learners are engaged? Groups will present to the whole group their provisional designs and proposed principles for embodied engagement. Day 2 will conclude with a facilitated discussion identifying principles, practices , and assessment methods for engaging all learners.

Day 3 People will engage with the designed activities and use Jam Board (or another online group discourse tool) to share impressions of the experiences. Participants will then reconfigure around common themes that arose in topic-specific groups on Days 1 & 2. It will invite participants to identify cross-cutting themes. A facilitated discussion will follow on why embodiment is a powerful lens for designing for engagement.

Embodied approaches to design, instruction, and assessment offer natural inroads for engaging all learners. Movement-based and perception-based learning activities can reach students who may otherwise feel left out of highly discursive and symbol based activities. Teachers may explore a greater range of teaching practices by applying effective instructional methods such as using gestures for connection making, and for using nonverbal indicators of students' reasoning, trouble spots, insights, and learning. The emergence of embodied

technologies using movement sensors and AR/VR offer new ways of interacting with mathematical ideas. By working with these ideas with the PME-NA community, we hope to foster a more engaged community committed to transformative education.