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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 materials, symbolic inscriptions, and social interactions. We argue that transfer occurs when learners and teachers establish cohesion of their experiences by mapping modes of perceiving and acting that they successfully used in previous contexts to new contexts. Learners express that cohesion across contexts in a variety of ways, principally through speech, actions, and gestures, including gestural catchments and simulated actions. Students and teachers may engage in several forms of mapping, including explicit analogical mapping, constructing mappings implicitly via relational priming, and mapping relations via conceptual blending. Thus, we theorize that both teachers and students are integral to the transfer process. This embodied theory of transfer can account for near and far transfer, negative transfer, and "false" transfer, in which actors enact modes of perceiving and acting activated by cues that match only at a surface level. Embodied accounts of transfer have implications for educational practice. Some pedagogical approaches, such as concreteness fading, aim to foster and maintain cohesion of mathematical invariant relations. An embodied perspective on transfer can also inform the design of assessments, including both formative and summative assessments. [This chapter was published in: Hohensee, C., Lobato, J. (Eds.), "Transfer of Learning Progressive Perspectives for Mathematics Education and Related Fields," Research in Mathematics Education, (pp. 27-58). Chaim, Switzerland: Springer.]

Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts (N = 44) were asked to judge the truth and to justify their judgments for four geometry conjectures. Videotaped interviews were transcribed and coded for occurrences of gestures and speech during the proof production process. Analyses provide empirical support for claims that geometry proof production is an embodied activity, even when controlling for math expertise, language use, and spatial ability. "Dynamic depictive gestures" portray generalizable properties of shape and space through enactment of transformational operations (e.g., dilation, skewing). Occurrence of dynamic depictive gestures and nondynamic depictive gestures are associated with proof performance, insight, and intuition, as hypothesized, over and above contributions of spoken language. Geometry knowledge for proof may be embodied and accessed and revealed through actions and the transformational speech utterances describing these actions. These findings have implications for instruction, assessment of embodied knowledge, and the design of educational technology to facilitate mathematical reasoning by promoting and tracking dynamic gesture production and transformational speech. [This is the online version of an article published in "Journal of Educational Psychology" (ISSN 0022-0663). For the final published version of this article, see EJ1303738.]

This full paper concerns the use of gesture analysis to guide instructional approaches in engineering education. Engineering is rife with abstract mathematics and processes for quantifying physical phenomena. In engineering instruction, "formalisms first" is a practice that privileges formalisms over grounded and applied ways of knowing that are common in engineering curricula. By way of contrast, "progressive formalization" is an alternative pedagogical practice that intentionally grounds the meaning of mathematical formalisms in one's sensorimotor experiences in order that the formalisms are meaningful to learners. In the courses of explaining engineering concepts, instructors often make iconic gestures (gestures that represent objects, actions, and relationships) that are based in perception and action as a means for grounding domain knowledge prior to introducing formalisms. In response, students' gestures can be either concordant (i.e., conceptually aligned) or discordant (i.e., conceptually misaligned). The latter, also known as gesture-speech mismatches, are indices for states of transitional knowledge in which learners exhibit a readiness to learn. Thus, the current research observes the spontaneous gestures students make while describing torsional loading and investigates the added benefits of incorporating gesture into formative assessments of engineering education. Results indicate that students do use gestures as integral parts of their explanations in an engineering lab setting and that gestures and co-articulated speech were often matched. Instances of gesture-speech mismatches provides instructors opportunities to assess student knowledge, knowledge-in-transition, and initial learning and correct understandings prior to summative assessments.

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is "embodied" -- inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building on each other's reasoning. Here we examine how gestural embodied actions become distributed over multiple learners confronting mathematical tasks. We define "collaborative gestures" as gestural exchanges that take place as learners discuss and explore mathematical ideas, using their bodies in concert to accomplish a shared goal. We identify several ways in which learners' gestures can be used collaboratively and explore patterns in how collaborative gestures arise while proving geometric conjectures. Learners use collaborative gestures to extend mathematical ideas over multiple bodies as they explore, refine, and extend each other's mathematical reasoning. With this work, we seek to add to notions of important "talk moves" in mathematical discussions to also include a consideration of important "gesture moves". [This is the in press version of an article published in "Journal of Mathematical Behavior."]

Gestures are associated with powerful forms of understanding; however, their causative role in mathematics reasoning is less clear. We inhibit college students' gestures by restraining their hands, and examine the impact on language, recall, intuition, and mathematical justifications of geometric conjectures. We test four mutually exclusive hypotheses: (1) gestures are facilitative, through cognitive off-loading, verbal support, or transduction, (2) gestures are not facilitative, but being inhibited from gesturing increases cognitive demands, (3) gestures are a byproduct of reasoning processes that would take place with or without the gestures' overt presence, and (4) gestures can cause learners to focus on concrete, salient representations, inhibiting abstraction. We find support for the third hypothesis, concluding that learners making or being inhibited from making gestures does not seem to impact their problem-solving, cognitive, or language processes. This suggests that being unable to overtly perform personally-generated gestures is not a hindrance to learners; however this would not necessarily hold for directed or structured gestures. [This paper was published in "Learning and Instruction" v64 2019.]

Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et al. 2004)--so that these ideas are regarded as objective and universal. This stems from a Cartesian view of knowledge that separates mental experiences from physical experiences and ways of knowing (Lakoff & Núñez, 2000; also called the "romance of mathematics," p. xv). This Cartesian "duality" carries forth to the various fields touched by mathematics that also strive for objectivity and universality--topics as vast and diverse as the physical and social sciences, business, civics, and the arts. There is a growing appreciation, however, that for effective education, mathematics must be meaningful to novices and that this can occur by grounding the ideas and notations to learners' physical experiences and ways of knowing (Nathan, 2012). Grounding can occur when an abstract idea is given a concrete perceptual referent so that it is more readily understood (Goldstone & Son, 2005). One way that ideas can become grounded is through gesture. Gestures are spontaneous or purposeful movements of the body that often accompany speech and serve as a way to convey ideas or add emphasis to language as well as mathematics (Goldin-Meadow,2005). Gestures can act as a grounding mechanism by indexing symbols and words to objects and events, and by manifesting mental simulations of abstract ideas using sensorimotor processes (Alibali & Nathan, 2012). The grounding of novel, abstract ideas and notational systems through gesture, action, and material referents is part of the emerging framework of grounded and embodied cognition. Grounded cognition is a general framework that posits that formal notational symbol systems and the intellectual behavior are "typically grounded in multiple ways, including simulations, situated action, and, on occasion, bodily states" (Barsalou, 2008, p. 619). [This is a chapter published in: Macrine, S. L., Fugate, J. M. B. (Eds.), "Movement Matters: How Embodied Cognition Informs Teaching and Learning" (pp. 131-145), 2022, Cambridge, MA: MIT Press.]

Findings synthesized across five empirical, laboratory-and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for embodied mathematical thinking and learning. "The Hidden Village" is presented as an instance of an embodied learning environment that uses the narrative context of a visual novel to instantiate these design principles and investigate their influences on mathematical thinking and learning, and to inform a broader theoretical framework of grounded and embodied learning. The interplay of theoretical, empirical, and design considerations of grounded and embodied learning reframes learning, transfer, and assessment, offering promising new pathways for an emerging class of learning environments. Grounded and embodied learning Grounded and embodied learning (GEL) offers a framework for understanding and designing for meaning making based on body-based processes. These GEL processes include actions, gestures, operative speech, and collaborative movements, as well as processes for supporting simulated action and imagination. Evidence is mounting that GEL is also activated during interventions, such as when learners are prompted to perform directed actions or are prompted to engage in simulated actions. This paper summarizes a set of interwoven empirical, theoretical, and design advancements for mathematical reasoning and their implications for teaching, learning, learning environment design, and assessment. The theoretical contributions offer hypothesis-driven inquiry into the nature of learning and meaning making through body-based experiences, and principled guidance for the design of learning technology and educational experiences. Empirical contributions span several laboratory-and classroom-based studies of high school and college students and high school teachers; in all, some 346 participants who engaged in 5 single and multi-session investigations. These investigations provide evidence of the role of embodied processes for meaning making in support of mathematical reasoning and theoretically guided design principles to promote learning. Design advancements to technologies for embodied thinking and learning serve as essential instantiations of theoretically derived hypotheses, as well as vital spaces in which embodied behaviors are elicited and data collected. Empirical findings and theoretical progress inform improvements in learning environment design that then make possible further theoretical and empirical advancements. In the final section, we explore how the interplay of evidence, theory, and design offer pathways for progress on complex issues facing GEL, such as generalizing research, bridging research and practice, and the emergence of designs and design principles. [This paper was published in: "ICLS Proceedings," International Society of the Learning Sciences, 2022, pp. 179-186.]

Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students' limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on students' cognitive load, cognitive processing, learning, and interest. Middle-school students (N = 62) read a lesson on early algebra with original or revised visuals while their eye movements were recorded. Students in the low prior knowledge group had less cognitive load and cognitive processing with the revised lesson than the original lesson. However, the reverse was true for students in the middle prior knowledge group. There were no effects of the revisions on learning. The findings are discussed in the context of the expertise reversal effect as well as the cognitive theory of multimedia learning and cognitive load theory.[A list of key terms and definitions is included. [This article was published in: C. Was, F. J. Sansosti, & B. J. Morris (Eds.) "Eye-tracking technology applications in educational research," 2017 (p195-218). Hershey, PA: IGI Global.]

Learning from visual representations is enhanced when learners appropriately integrate corresponding visual and verbal information. This study examined the effects of two methods of promoting integration, color coding and labeling, on learning about probabilistic reasoning from a table and text. Undergraduate students (N = 98) were randomly assigned to learn about probabilistic reasoning from one of 4 computer-based lessons generated from a 2 (color coding/no color coding) by 2 (labeling/no labeling) between-subjects design. Learners added the labels or color coding at their own pace by clicking buttons in a computer-based lesson. Participants' eye movements were recorded while viewing the lesson. Labeling was beneficial for learning, but color coding was not. In addition, labeling, but not color coding, increased attention to important information in the table and time with the lesson. Both labeling and color coding increased looks between the text and corresponding information in the table. The findings provide support for the multimedia principle (Mayer, 2009), and they suggest that providing labeling enhances learning about probabilistic reasoning from text and tables. A problem from the pretest is appended.[This content was published in "Applied Cognitive Psychology" v30 n3 p440-453 May-June 2016.]

Grant peer review is a foundational component of scientific research. In the context of grant review meetings, the review process is a collaborative, socially mediated, locally constructed decision-making task. The current study examines how collaborative discussion affects reviewers' scores of grant proposals, how different review panels score the same proposals, and how the discourse practices of video conference panels differ from in-person panels. Methodologically, we created and videotaped four "constructed study sections," recruiting biomedical scientists with U.S. National Institutes of Health (NIH) review experience and an NIH scientific review officer. These meetings provide a rich medium for investigating the process and outcomes of such authentic collaborative tasks. We discuss implications for research into the peer review process as well as for the broad enterprise of federally funded scientific research.

This study investigates the associations of spontaneous "dynamic gesture" and "transformational speech" with the production of "deductive proofs" in participants' reasoning about geometric conjectures (N=77). Although statistical analysis showed no significant association, the result suggests that purposefully including directed actions and pedagogical language in interventions could promote the production of deductive proofs. [This paper was published in: "ICLS Proceedings," 2021, pp.1109-1110.]