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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 locations, they logged into a single virtual classroom with their respective groups and were able to see and manipulate the same geometric shapes as well as see their collaborators' avatars and actions on the shapes in real time in the shared virtual space. This paper introduces a novel multimodal data analysis method for analyzing participants' interactive patterns in collaborative forms of actions, gestures, movements, and speech. Results show that collaborative speech has a strong simultaneous relationship with actions on virtual objects and virtual hand gestures. They also showed that body movements and positions, which often focus on virtual objects and shifts in these movements away from or around the object, often signal key interactional collaborative events. In addition, this paper presents five emergent multimodality interaction themes showing participants' collaborative patterns in different problem-solving stages and their different strategies in collaborative problem-solving. The results show that virtual objects can be effective media for collaborative knowledge building in shared VR environments, and that structured activity design and moderate realism may benefit shared VR learning environments in terms of equity, adaptability, and cost-effectiveness. We show how multimodal data analysis can be multi-dimensional, visualized, and conducted at both micro and macro levels.

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 Einstein's conceptual reliance on trains for his Theory of Relativity and the Wright brothers' use of wind tunnels in aeronautics illustrate how materialist design drives progress on complex design problems. A key aspect is the application of scale-down methodology, where complex systems are reconceptualized as interactions among nearly decomposable subsystems that can be redesigned and integrated back into the entire system. The application of materialist design is illustrated with the redesign of an embodied video game that uses real-time motion capture technology to promote high school geometry reasoning and proof, following its use in an ethnically and linguistically diverse classroom. Our embodied perspective offers particular insights for understanding and implementing designs of complex learning environments, and assessing their influences on educational practices and student outcomes. [This article was published in "Educational Technology Research and Development" (EJ1310136).]

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition transduction to investigate the cognitive relevance of directed actions to students' mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a direct effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement-based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students' intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed.

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students' mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions. GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

This classroom-based investigation sought to document how, in real time, STEM teachers and students attempt to locate the invariant mathematical relations that are threaded through the range of activities and representations in these classes, and how highlighting this common thread influences student participation and learning. The authors conducted multimodal discourse analyses of teacher-student interactions during multiday observations in 3 urban high school STEM classes. The focal lessons were in electrical engineering and mechanical engineering (within Project Lead the Way), and precollege geometry. Across 3 cases, teachers and students actively built and maintained cohesion of invariant mathematical relations across activities and representations. Pre- and post-lesson interviews revealed that teachers intentionally managed cohesion to provide the continuity across the curricular activities that teachers believed would promote student understanding. The findings contribute to ways of fostering STEM integration and ways of grounding abstractions to promote meaning making and transfer. [This paper was published in "Journal of Education Research" (EJ1134489).]

This study investigated middle school students' conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations' structures, including number of operations and position of the unknown, influenced students' performance on both tasks. On the story-writing task, students' performance on two-operator equations was poorer than would be expected on the basis of their performance on one-operator equations. Students made a wide variety of errors on the story-writing task, including (1) generating story contexts that reflect operations different from the operations in the given equations, (2) failing to provide a story context for some element of the given equations, (3) failing to include mathematical content from the given equations in their stories, and (4) including mathematical content in their stories that was not present in the given equations. The nature of students' story-writing errors suggests two main gaps in students' conceptual understanding. First, students lacked a robust understanding of the connection between the operation of multiplication and its symbolic representation. Second, students demonstrated difficulty combining multiple mathematical operations into coherent stories. The findings highlight the importance of fostering connections between symbols and their referents.

Maintaining shared understanding in classroom interaction is challenging for both teachers and students. In this paper, we consider the role of teachers' gestures in promoting shared understanding. Our specific aim was to document ways in which teachers use their own gestures to support students' contributions to the classroom discourse. We present three illustrative cases that represent the range of variation in teachers' use of speech (i.e., repeating the students' speech vs. not speaking at all) and variation in the spatial positioning of the teacher, the student, and the referents of the student's speech. We argue that teachers use gestures, both to ensure that they share common ground with the individual student who is speaking and to foster common ground among the class as a whole.

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 linguistically diverse students. Advancements in multimodal learning analytics, leveraging sensor technologies, offer innovative solutions for capturing and analysing body movements. This study employs these novel approaches to demonstrate how learners' machine‐detected body movements during the learning process relate to their verbal and nonverbal contributions to the co‐construction of embodied math knowledge. These findings substantiate the feasibility of utilizing learners' machine‐detected body movements as a valid indicator for inferring their engagement with the collaborative knowledge construction process. In addition, we empirically validate that these inferred different levels of learner engagement indeed impact the desired learning outcomes of the intervention. This study contributes to our scientific understanding of multimodal approaches to knowledge expression and assessment in learning, teaching, and collaboration.Practitioner notesWhat is already known about this topicPrevious research emphasizes the importance of gestures as essential tools for constructing common ground and reflecting shared meaning‐making in learning and teaching contexts.The prior studies in multimodal learning analytics (MMLA) suggest that certain forms of body movements and postures can be differentiated based on the automatic detection of upper body joint locations.Empirical observations indicate that co‐thought gestures typically involve smaller hand or arms movement that are closer to the gesturer's body than co‐speech gestures used in interpersonal communication.What this paper addsThis paper fills the research gap by examining the use of gestures in collaborative learning, offering insights into how individuals contribute verbally and nonverbally to collaborative knowledge construction.This paper introduces the concept of using machine‐detected body movements as a viable proxy for inferring learners' engagement in collaborative knowledge‐building activities.Leverages sensor technologies for automatic detection of body movements, the innovative approach in this work seeks to overcome the time‐intensive and laborious process of manually coding gestures.Implications for practice and/or policyBy recognizing the potential significance of learners' body movements in indicating engagement levels with collaborative knowledge‐building activities, instructors can set up computer‐supported collaborative learning (CSCL) environments to enable capturing these movements.Given the crucial role of gestures in learning, teaching, and collaboration, educators can create more equitable formative assessment practices for linguistically diverse students by developing strategies that align with multimodal forms of knowledge expression.Research can expand beyond mathematics to explore the transferability of these findings to other subjects, helping educators create comprehensive pedagogical approaches that leverage multimodal interactions across disciplines. [ABSTRACT FROM AUTHOR]

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 central challenges: (1) many of the ways spatial ability is defined and subdivided are often not based in well-evidenced theoretical and analytical frameworks, and (2) the sheer variety of spatial assessments. These challenges impede progress in designing spatial skills interventions for improving mathematics thinking based on causal principles, selecting appropriate metrics for documenting change, and analyzing and interpreting student outcome data. We offer solutions by providing a practical guide for navigating and selecting among the various major spatial taxonomies and instruments used in mathematics education research. We also identify current limitations of spatial ability research and suggest future research directions. [ABSTRACT FROM AUTHOR]

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally conceived, it is a three-step progression that begins with enacting a physical instantiation of a concept, moves to an iconic depiction and then fades to the more abstract representation of the same concept. The goals of this paper are: (1) to improve the theoretical framework of concreteness fading by defining and bringing greater clarity to the terms abstract, concrete and fading; and (2) to describe several testable hypotheses that stem from concreteness fading as a theory of instruction. Making this theory of instruction more "concrete" should lead to an optimised concreteness fading technique with greater promise for facilitating both learning and transfer.

Among Walter Kintsch's insights about human cognition was that reading comprehension, inference making, and learning from text emerge from an interactive process between the reader and the text, leading to a reader's situation model (SM) that depicts what the text is about relative to the reader's prior experiences. SMs mediate readers' inference making and learning from text using holistic, dynamic depictions, including nonverbal content that complements verbal propositional information encoded by the reader's textbase. I propose to extend Kintsch's legacy by revealing ways that the SM emerges as an interaction between an evocative text and an embodied reader. Gestures, in particular, are implicated as a source of readers' SM formation that supports increased comprehension, inference making, and learning from text. Exploring the role embodied processes play in reading offers novel lines of empirical inquiry and theory development aimed at advancing understanding of discourse comprehension and reading to learn. [ABSTRACT FROM AUTHOR]

In this Brief Report, we share the main findings from our line of research into embodied cognition and proof activities. First, attending to students' gestures during proving activities can reveal aspects of mathematics thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our understanding of students' proving practices, particularly when attending to dynamic gestures depicting relationships that are difficult to communicate verbally. Second, directing students to produce physical actions before asking them to construct a mathematical proof has the potential to influence their subsequent reasoning in useful ways, as long as the directed actions have a relationship with the proof content that is clearly meaningful to the students. We discuss implications for assessment practices and teacher education and we suggest directions for future research into embodied mathematical proof practices.

To learn from a text, students must make meaningful connections among related ideas in that text. This study examined the effectiveness of two methods of improving connections--elaborative interrogation and diagrams--in written lessons about posterior probability. Undergraduate students (N = 198) read a lesson in one of three questioning conditions (read twice, embedded questioning, and elaborative interrogation) and one of three diagram conditions (text only, diagram without redundant text, and diagram with redundant text). Elaborative interrogation negatively affected learning from the lesson, relative to reading the lesson twice. One possible explanation for this finding is that the quality of answers to the elaborative interrogations was poor. When the lesson was read twice, diagrams helped learning from the lesson relative to text only. Implications of these findings for instruction in probabilistic reasoning are discussed.

The question of the relationship between gesture production and mental models was explored in three experiments focusing on inference making when learning from reading a scientific text. Participants engaged in one-on-one interviews after reading an illustrated tutorial on the human circulatory system. Participants gestured more frequently when responding to mental model-based inference test questions (Experiment 1; N = 22) than textbase or general knowledge questions. Learning from a text lacking illustrations resulted in comparable inference making (Experiment 2; N = 48) but elevated gesture production. Restricting gesture production with hand tapping led to inferior inference making (Experiment 3; N = 79). Results support an embodied cognition view of mental model formation where inference making stimulates gesture production, and restricting gestures selectively impairs inference making. The results are interpreted within the Gesture as Model Enactment (GAME) framework. Activation of motor control systems via gesture support simulated actions that contribute to mental model formation. Implications for learning and assessing knowledge are explored.

This research investigated how teachers express links between ideas in speech, gestures, and other modalities in middle school mathematics instruction. We videotaped 18 lessons (3 from each of 6 teachers), and within each, we identified "linking episodes"--segments of discourse in which the teacher connected mathematical ideas. For each link, we identified the modalities teachers used to express linked ideas and coded whether the content was new or review. Teachers communicated most links multimodally, typically using speech and gestures. Teachers' gestures included depictive gestures that simulated actions and perceptual states, and pointing gestures that grounded utterances in the physical environment. Compared to links about new material, teachers were less likely to express links about review material multimodally, especially when that material had been mentioned previously. Moreover, teachers gestured at a higher rate in links about new material. Gestures are an integral part of teachers' communication during mathematics instruction.

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for each of these claims drawn from the gestures that teachers and learners produce when they explain mathematical concepts and ideas. We argue that (a) "pointing" gestures reflect the grounding of cognition in the physical environment, (b) "representational" gestures manifest mental simulations of action and perception, and (c) some "metaphoric" gestures reflect body-based conceptual metaphors. Thus, gestures reveal that some aspects of mathematical thinking are embodied. (Contains 1 table, 3 footnotes and 12 figures.)

I explore a belief about learning and teaching that is commonly held in education and society at large that nonetheless is deeply flawed. The belief asserts that mastery of "formalisms"--specialized representations such as symbolic equations and diagrams with no inherent meaning except that which is established by convention--is prerequisite to applied knowledge. A "formalisms first" (FF) view of learning, rooted in Western dualist philosophy, incorrectly advocates the introduction of formalisms too early in the development of learners' conceptual understanding and can encourage a formalisms-only mind-set toward learning and instruction. I identify the prevalence of FF in curriculum and instruction and outline some of the serious problems engendered by FF approaches. I then turn to promising alternatives that support "progressive formalization", problem-based learning, and inquiry learning, which capitalize on the strengths of formalisms but avoid some of the most costly problems found in FF approaches. (Contains 3 footnotes and 1 table.)