Abstract:A perpetual problem learners face is identifying which aspects of embodied experiences are relevant for appreciating the world in culturally specific ways. Vygotsky argued that social interactions with more competent cultural members provide arenas for linking everyday and scientific concepts. However, the precise interactional mechanisms of how these linkages are forged remain underexamined. I argue that understanding these mechanisms requires examining how intersubjectivity is built and maintained. I propose… Show more
“…For example, sign language may offer advantages for collaboratively discovering new mathematical relationships in its use of physical space and motion to capture and organize ideas as compared with the linear constraints of spoken American English. Flood (2018) has also demonstrated the beneficial effects that exchanging, recycling, and transforming multimodally expressed ideas through revoicing can have on advancing new mathematical understandings. In addition, the use of haptic and tactile ways of communicating (e.g., conveying an idea by tracing a pattern on another person's body-c.f.…”
“…Appreciating how mathematical understandings emerge in UDL-inspired fields of promoted action between sensorily heterogenous mathematics students will require careful attention to participants' practical, situated, embodied, multimodal methods and resources for building and maintaining intersubjectivity (Flood et al 2016;Flood 2018;Koschmann and Mori 2016;Wittmann et al 2013). As part of this process, participants reciprocally work to render their experiences publicly available to others, using novel resources and methods that are perceptually available to their collaborators.…”
“…Concepts implemented to date in the Trainer activity architecture include proportions (Abrahamson et al 2014; Fig. 1a), the Cartesian field (Duijzer et al 2017), speed (Flood 2018), geometrical area (Shvarts 2017), parabolas (Shvarts and Abrahamson 2018; Fig. 1c), and trigonometry 1 3 (Alberto 2018).…”
Section: Enactivism: Cognition Emerges From Recurring Patterns In Permentioning
Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants' multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device.
“…For example, sign language may offer advantages for collaboratively discovering new mathematical relationships in its use of physical space and motion to capture and organize ideas as compared with the linear constraints of spoken American English. Flood (2018) has also demonstrated the beneficial effects that exchanging, recycling, and transforming multimodally expressed ideas through revoicing can have on advancing new mathematical understandings. In addition, the use of haptic and tactile ways of communicating (e.g., conveying an idea by tracing a pattern on another person's body-c.f.…”
“…Appreciating how mathematical understandings emerge in UDL-inspired fields of promoted action between sensorily heterogenous mathematics students will require careful attention to participants' practical, situated, embodied, multimodal methods and resources for building and maintaining intersubjectivity (Flood et al 2016;Flood 2018;Koschmann and Mori 2016;Wittmann et al 2013). As part of this process, participants reciprocally work to render their experiences publicly available to others, using novel resources and methods that are perceptually available to their collaborators.…”
“…Concepts implemented to date in the Trainer activity architecture include proportions (Abrahamson et al 2014; Fig. 1a), the Cartesian field (Duijzer et al 2017), speed (Flood 2018), geometrical area (Shvarts 2017), parabolas (Shvarts and Abrahamson 2018; Fig. 1c), and trigonometry 1 3 (Alberto 2018).…”
Section: Enactivism: Cognition Emerges From Recurring Patterns In Permentioning
Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants' multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device.
“…Group members engaged in multimodal co-construction, such that the external nature of gestures allowed students to copy, extend, correct, and revise each other's conceptions through gesture. Flood (2018), through an analysis of a middle school student's interactions with tutors around concepts of speed and ratio, demonstrates how multimodal revoicing-using gesture in conjunction with speech to reproduce, elaborate, or selectively modify an idea presented by a learner-can be used by tutors to move students toward conventional or culturally appropriate forms of reasoning. Another line of work (Hall et al, 2015;Ma, 2017;Ma and Hall, 2018) has explored ensemble routines, in which high school students learn to position and orient their bodies and coordinate their perspectives to accomplish a collective goal (e.g., formulating marching band patterns or large-scale geometric constructions), sometimes with the assistance of GPS technologies.…”
Section: Research On Collaborative Gesturingmentioning
A rising epistemological paradigm in the cognitive sciences-embodied cognition-has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students' physical movements, eye-gaze paths, and verbal-gestural utterance so as to track and evaluate emerging conceptual capacity. We-a cohort of cognitive scientists and design-based researchers of embodied mathematics-survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.
“…From Goodwin's perspective, learners' technology-mediated embodied experiences and their first attempts at representing these experiences comprise a substrate (2018) that we believe can be cultivated into robust, disciplinary understandings of mathematics through guided reflection, negotiation, and signification with more-capable others (tutors, teachers, parents, museum educators, etc. ; (Abrahamson & Trninic, 2014;Flood, 2018;Shvarts & Abrahamson, 2019). When culturally-competent others and learners negotiate divergent interpretations of experiences (Wertsch, 1984), zones of proximal development (Vygotsky, 1986) emerge that make socialization-including mathematical socialization-possible.…”
As technologies that put the body at the center of mathematics learning enter formal and informal learning spaces, we still know little about the teaching methods educators can use to support students' learning with these specialized systems. Drawing on ethnomethodology and conversation analysis (EMCA) and the CoOperative Action framework, we present three multimodal ways that educators can be responsive to learners' embodied ideas and help them transform sensorimotor patterns into mathematically significant perceptions. These techniques include (1) encouraging learners to use gesture to express and reflect on their ideas, (2) presenting multimodal candidate understandings to check comprehension of learners' embodied ideas, and (3) co-constructing multimodally expressed embodied ideas with learners. We demonstrate how these techniques create opportunities for learning and discuss implications for a multimodal, embodied practice of responsive teaching.
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