In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

In various technology-enhanced learning (TEL) environments, knowledge co-creation progresses through multimodal interactions that integrate verbal and nonverbal modalities, such as speech and gestures. This study investigated two distinct analytical approaches for analyzing multimodal interactions--triangulating and interleaving--by applying them…

Epistemology is the branch of philosophy that studies the nature of knowledge (Hetherington, 2012; Moreland & Craig, 2017; Pritchard, 2014). Epistemology is central to the practice of research and education (Spears, 2003). The epistemological position that holds science as the best or only way of acquiring knowledge is known as scientism…

Collaborative learning, driven by knowledge co-construction and meaning negotiation, is a pivotal aspect of educational contexts. While gesture's importance in conveying shared meaning is recognized, its role in collaborative group settings remains understudied. This gap hinders accurate and equitable assessment and instruction, particularly for…

Spatial skills can predict mathematics performance, with many researchers investigating how and why these skills are related. However, a literature review on spatial ability revealed a multiplicity of spatial taxonomies and analytical frameworks that lack convergence, presenting a confusing terrain for researchers to navigate. We expose two…

Using five years of publishing data from the Journal of Higher Education, we describe the publication pipeline at the journal, explore trends with respect to topic, the geographic distribution of authors, and each paper's methodological approach. Following the presentation of these trends, we discuss implications for the field of higher education…

Augmented reality (AR), where digital holograms are layered over the real world, is rapidly being applied to different educational domains, including mathematics education. However, little is known about how AR can be effectively designed for collaborative use. There are both practical and theory-based reasons to set up collaboration in AR in…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

Over the past 50 years, a large body of work has demonstrated that during childhood and adolescence peers are strong socialization agents influencing youth development across a wide array of behavioral domains. In this report, we highlight how this long-standing research focus on peer influence may benefit from undertaking new directions that have…

Materialist design is presented as an embodied perspective on educational design that can be applied to redesign of classroom-based learning environments. Materialist design is informed by a framework of materialist epistemology, which positions material innovation on equal placement with symbol-based formal theory. Historical examples of…

We present an embodied theory of transfer as applied to mathematical ideas. Project-based learning (PBL) offers important sites for investigating transfer because students and teachers must track mathematical invariant relations that are embedded in complex settings where knowledge and information is distributed and extended across various…

Materialist design is presented as an embodied perspective on educational design that can be applied to redesign of classroom-based learning environments. Materialist design is informed by a framework of materialist epistemology, which positions material innovation on equal placement with symbol-based formal theory. Historical examples of…

This full length, empirical research paper investigates undergraduate engineering students' emerging conceptualizations of torsion-related concepts for the relations between the functions and behaviors of materials to their structures, both observable and unobservable. While cognitive processes are unavailable for direct inspection, advances in…

Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…