POSTPONED: Professor Dor Abrahamson and Professor David Tall

  • 25 March 2020 - 25 March 2020
  • 14:00-17:00
  • SCH.0.13 - Schofield Building

14:00 – 15:00 Prof Dor Abrahamson “Embodied Design: bringing forth mathematical perceptions" (University of California, Berkeley, USA).

Abstract: Embodied design (Abrahamson, 2009, 2014, 2015, 2017) is a theory-based pedagogical framework for building content-oriented learning environments, where students ground STEM concepts through first solving non-symbolical control-and-anticipation problems and then adopting normative disciplinary forms as means of enhancing their enactive, cognitive, and discursive interactions. In particular, the action-based genre of embodied design specifies how to create conditions for students to develop new goal-oriented sensorimotor perceptions of situations (i.e., affordances) as the prospective meanings of mathematical concepts. 

In this talk, I will motivate embodied design within the E-turn in the cognitive sciences and situate the framework among the current range of design rationales for interactive STEM educational products. 

Demonstrating empirical findings from multimodal evaluation studies of embodied designs for mathematics (proportions, geometry, trigonometry, parabolas, etc.), in which we analyzed and integrated audio–video, clinical, and eye- tracking data, I will argue that the framework implements key principles of Enactivism, namely that: “(1) perception consists in perceptually guided action and (2) cognitive structures emerge from the recurrent sensorimotor patterns that enable action to be perceptually guided” (Varela, Thompson, & Rosch, 1991, p. 173; see Hutto, Kirchhoff, & Abrahamson, 2015). 

Specifically, the embodied meanings of mathematical concepts—that is, the situated, invariant, and dynamical sensorimotor perceptual structures that students discern, generate, and maintain in response to challenging interaction tasks—emerge spontaneously as their tacit, adaptive, pragmatic means of facilitating and regulating the coordination of motor actions that enact control movements (Abrahamson, Shayan, Bakker, & van der Schaaf, 2016). 

I will end by reissuing a call for the learning sciences to adopt perspectives and methodologies of the movement sciences, in particular coordination dynamics, as tools for investigating, characterizing, and engineering embodied design for mathematics (Abrahamson, 2019; Abrahamson & Trninic, 2015; Abrahamson & Bakker, 2016; Abrahamson & Sánchez–García, 2016). 

In sum, at the Embodied Design Research Laboratory, we design for a particular inclination of prehensile cognitive architecture—human’s ecologically adaptive propensity to seek, grope for, grasp, and use multimodal perceptual structures that facilitate bimanual motor control, where these dynamically invariant perceptual structures may be imaginary. 

The ambitious hypothesis emerging from our work is that the phenomenology of inventing and imagining mathematical objects is a sociocultural exaptation of this evolutionary inclination (cf. Gould & Vrba, 1982). Future design-based research on the cultivation of math cognition will pursue this hypothesis.


Abrahamson, D. (2009). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27–47. [Electronic supplementary material at ].

Abrahamson, D. (2014). Building educational activities for understanding: An elaboration on the embodied- design framework and its epistemic grounds. International Journal of Child-Computer Interaction, 2(1), 1– 16. doi:10.1016/j.ijcci.2014.07.002

Abrahamson, D. (2015). The monster in the machine, or why educational technology needs embodied design. In V. R. Lee (Ed.), Learning technologies and the body: Integration and implementation (pp. 21–38). New York: Routledge.

Abrahamson, D. (2017). Embodiment and mathematical learning. In K. Peppler (Ed.), The SAGE encyclopedia of out-of-school learning (pp. 247–252). New York: SAGE.

Abrahamson, D. (2019, April). Moving perception forward in learning sciences discourse. Paper presented at the annual meeting of the Digital Turn in Epistemology group—“Mathematical ability,” Freudenthal Institute, Utrecht University, The Netherlands, April 15–17, 2019.

Abrahamson, D., & Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. In N. Newcombe and S. Weisberg (Eds.), Embodied cognition and STEM learning [Special issue]. Cognitive Research: Principles and Implications, 1(1), 1–13.

Abrahamson, D., & Sánchez-García, R. (2016). Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Sciences, 25(2), 203–239.

Abrahamson, D., Shayan, S., Bakker, A., & Van der Schaaf, M. F. (2016). Eye-tracking Piaget: Capturing the emergence of attentional anchors in the coordination of proportional motor action. Human Development, 58(4-5), 218–244.

Abrahamson, D., & Trninic, D. (2015). Bringing forth mathematical concepts: Signifying sensorimotor enactment in fields of promoted action. ZDM Mathematics Education, 47(2), 295–306.

Gould, S. J., & Vrba, E. S. (1982). Exaptation—a missing term in the science of form. Paleobiology, 8(1), 4– 15.

Hutto, D. D., Kirchhoff, M. D., & Abrahamson, D. (2015). The enactive roots of STEM: Rethinking educational design in mathematics. In P. Chandler & A. Tricot (Eds.), Human movement, physical and mental health, and learning [Special issue]. Educational Psychology Review, 27(3), 371–389.

15:00 – 15:15 Break

15:15 – 15:50 Reading Group Sessions

15:50 – 16:00 Break

16:00 – 17:00 Prof David Tall “The long-term success and failure of mathematics education” (University of Warwick & Visiting Professor, Loughborough University)

Abstract: Some new ideas on the long-term development of mathematical thinking (available in recent papers on my academic website) offering an overall framework for the longer term development of math ed research. This includes the supportive and problematic aspects as mathematics becomes more sophisticated in new contexts and cultural relationships between different communities. It seeks simple ideas that make sense to teachers, learners and experts with different forms of expertise. It will consist of a ten minute overall introduction, a 26 minute video presenting a particular long-term development illustrating some of the principles, and time for discussion.

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