Dor Abrahamson
Dor Abrahamson researches mathematics learning and teaching. He develops and evaluates theoretical models of these processes by analyzing empirical data collected during implementations of his innovative pedagogical design. Drawing on embodiment and sociocultural paradigms, Abrahamson is particularly interested in modeling how learners coordinate between informal and formal views on situated phenomena and what roles teachers play in ushering these coordinations. Abrahamson’s analyses of pedagogical interactions focus on student and teacher use of inference, various modalities, media, discursive genres, semiotic systems, and metaphor.
At the core of Abrahamson’s practice are cognitive domain re-analyses with an eye on creating learning materials and activities. Using both traditional media, such as concrete manipulatives, and recent technologies, such as motion sensors, touch screens, and agent-based simulations, Abrahamson has worked mostly on the concepts of proportion, probability, algebra, and geometry. This line of research also informs the creation of design frameworks.
Abrahamson’s pedagogical inventions have been incorporated into high-profile instructional units that are widely disseminated both through school-based curricular materials and via computer-based interactive software.
Supervisors: Karen Fuson, Uri Wilensky
At the core of Abrahamson’s practice are cognitive domain re-analyses with an eye on creating learning materials and activities. Using both traditional media, such as concrete manipulatives, and recent technologies, such as motion sensors, touch screens, and agent-based simulations, Abrahamson has worked mostly on the concepts of proportion, probability, algebra, and geometry. This line of research also informs the creation of design frameworks.
Abrahamson’s pedagogical inventions have been incorporated into high-profile instructional units that are widely disseminated both through school-based curricular materials and via computer-based interactive software.
Supervisors: Karen Fuson, Uri Wilensky
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To investigate these questions, we survey the history of digital resources for mathematics education through the prism of philosophical and psychological theories—enactivist cognition and ecological dynamics—that look to capture the role of embodied interaction in cognitive development and conceptual learning. Then, through three case studies of contemporary digital educational resources, a proposal is put forth for how these embodied theories of learning could inform the design of educational technologies compatible with how people naturally learn. First, students should learn to enact new physical movement forms that have been designed to instantiate the targeted concepts. Students learn to move in these new ways by developing perceptual orientations that enable them to solve situated motor-control problems. Only then are these new cognitive skills formalized in disciplinary semiotic forms. Perhaps future technology can be as powerful a learning tool as the historical yarn ball.
To investigate these questions, we survey the history of digital resources for mathematics education through the prism of philosophical and psychological theories—enactivist cognition and ecological dynamics—that look to capture the role of embodied interaction in cognitive development and conceptual learning. Then, through three case studies of contemporary digital educational resources, a proposal is put forth for how these embodied theories of learning could inform the design of educational technologies compatible with how people naturally learn. First, students should learn to enact new physical movement forms that have been designed to instantiate the targeted concepts. Students learn to move in these new ways by developing perceptual orientations that enable them to solve situated motor-control problems. Only then are these new cognitive skills formalized in disciplinary semiotic forms. Perhaps future technology can be as powerful a learning tool as the historical yarn ball.
Embodied design (ED, Abrahamson, 2009; Abrahamson & Lindgren, 2014; Abrahamson et al., 2020) is a design-based research program investigating the phenomenology of designing, teaching, enacting, and learning a culture’s cognitive practices. ED’s design rationale is to identify, source, embrace, and leverage humans’ naturalistic perceptuomotor, social, and affective capacities for engaging in organized activity as cognitive means of adopting new practices that empower interactions with the environment. ED’s theoretical perspectives braid constructivism, enactivism, sociocultural theory, ecological psychology, and dynamic systems theory as these synergistically account for evidence of knowing, teaching, and learning. ED’s conceptual reach is pan-curricular, albeit its current ambit encompasses STEM domains. In form, ED’s innovative educational resources are either material, digital, or hybrid. ED products are accessible to students of diverse sensory, motor, and neural constitution, while nurturing from investigations into diverse cultural epistemologies. ED methods include: quasi-experimental methodologies for gathering multimodal data from task-based semi-structured clinical interviews; collaborative micro-ethnographic qualitative analysis of teaching–learning interaction; ethnomethodology and conversation analysis, as combined with co-operative action; and multimodal learning analytics, such as cross-Recurrence Quantification Analysis. ED’s outreach is to collaborate with teachers in developing applicable principles of instructional practice with embodied design resources, prepare teachers to create their own design solutions to emerging pedagogical situations, and rethink the contents and nature of classroom discourse.
In all this, ED perceives the role of interactive digital resources as constituting instrumented fields of promoted action (Abrahamson & Trninic, 2015). These technological learning environments occasion opportunities for students to engage with challenging motor-control problems whose perceptuomotor solution fosters new pre-semiotic dynamical images at the core of reasoning about mathematical notions (Pirie & Kieren, 1989), such as vestibular feeling of balance to mobilize algebraic thinking, or kinesthetic sense of covariation to mobilize proportional thinking.
ED’s claim is that conceptual reasoning is inherently situated and enactive, organized through tacit spatial–temporal forms that include perceptual structures and rhythmic iteration. These perceptual–rhythmic patterns emerge as students collaboratively negotiate solutions to problems of jointly enacting movements under environmental and task constraints. Then, furnished with supplementary semiotic resources provided by attentive facilitators, students appropriate invariant figural features of these new resources into their operational–discursive habits of being and acting. In so doing, students reconfigure perceptions of their own movement forms within these new frames of reference, thus grounding normative disciplinary expression in multimodal enactment.
The chapter elaborates on all the above through discussing examples of embodied designs for mathematics education.