Abrahamson, D. (2018, June). Design research as iterated cycles of cognitive-task ideation, implementation, and analysis. 

Paper presented at the annual meeting of the Jean Piaget Society, Amsterdam, May 31 – June 2.

Design research is a practice-oriented approach to building theory of cognition, teaching, and learning through reflecting on iterated cycles of envisioning, engineering, implementing, and analyzing data from educational activities. Espousing a complex dynamical-systems epistemology that subsumes both constructivist and sociocultural models of conceptual development, I characterize, essentialize, and idealize the cognitive task not so much as a solution procedure but more so as a guided negotiation between personal and cultural forms. Operating in the embodied-design framework (Abrahamson, 2007, 2009a, 2014, 2015), I strive to build student experiences that elicit targeted personal resources, such as unarticulated sensorimotor capacity, and complementarily I create opportunities for students to expand, accommodate, complexify, and empower these resources through the appropriation of cultural forms.

The presentation will survey and juxtapose two projects, respectively exemplifying the perception-based and action-based genres of embodied design.

The perception-based design for probability sought to elicit students’ innate capacity to infer relative likelihoods of random samples by gauging the samples’ representativeness of a source population (drawing out four marbles from a tub of mixed green and blue marbles); students were then guided to negotiate these tacit, qualitative constructions of the phenomenon with a complementary disciplinary view, namely combinatorial analysis from classicist theory. They accepted the classicist construction once they appreciated its inferential parity with their naïve view (Abrahamson, 2009b, 2012a, 2012b).

The action-based design for proportionality sought to elicit students’ natural bimanual movement forms, which preserve the spatial interval between the hands, and challenge the students to adapt these forms to a new way of moving, in which the interval changes correlative to the hands’ height above a baseline. Students were then guided to adopt symbolic artifacts (a grid and numerals) as frames of reference to enhance their performance, and in so doing they adopted multiplicative forms of reasoning. They accepted the quantitative construction once they appreciated its functional parity with their naïve orientation to enacting the movement (Abrahamson & Bakker, 2016; Abrahamson & Sánchez-García, 2016; Abrahamson, Shayan, Bakker, & Van der Schaaf, 2016; Duijzer, Shayan, Bakker, Van der Schaaf, & Abrahamson, 2017).

Both projects used task-based semi-structured clinical interviews followed by micro-analysis of conceptual ontogeny. Both projects iteratively honed the researchers’ understanding of barriers and opportunities in reconciling naïve and disciplinary constructions of phenomena.

(Download all PDFs at  https://edrl.berkeley.edu/publications/ )

Abrahamson, D. (2007). Both rhyme and reason: Toward design that goes beyond what meets the eye. In T. Lamberg & L. Wiest (Eds.), Proceedings of the Twenty Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 287 – 295). Stateline (Lake Tahoe), NV: University of Nevada, Reno.

Abrahamson, D. (2009a). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27-47.

Abrahamson, D. (2009b). Orchestrating semiotic leaps from tacit to cultural quantitative reasoning—the case of anticipating experimental outcomes of a quasi-binomial random generator. Cognition and Instruction, 27(3), 175-224.

Abrahamson, D. (2012a). Rethinking intensive quantities via guided mediated abduction. Journal of the Learning Sciences, 21(4), 626-649. doi:10.1080/10508406.2011.633838

Abrahamson, D. (2012b). Seeing chance: Perceptual reasoning as an epistemic resource for grounding compound event spaces. In R. Biehler & D. Pratt (Eds.), Probability in reasoning about data and risk [Special issue]. ZDM–The international Journal on Mathematics Education, 44(7), 869–881. doi:10.1007/s11858-012-0454-6

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.

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. (2015). Reinventing learning: A design-research odyssey. In S. Prediger, K. Gravemeijer, & J. Confrey (Eds.), Design research with a focus on learning processes [Special issue]. ZDM Mathematics Education, 47(6), 1013-1026.

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. doi:10.1186/s41235-016-0034-3

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. doi:10.1080/10508406.2016.1143370

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.

Duijzer, A. C. G., Shayan, S., Bakker, A., Van der Schaaf, M. F., & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. In J. Tarasuik, G. Strouse, & J. Kaufman (Eds.), Touchscreen tablets touching children’s lives [Special issue]. Frontiers in Psychology, 8(144). doi:10.3389/fpsyg.2017.00144