Constraints on Embodiment: Iconicity May Damage Sensorimotor Grounding

• In Event: 69.045 - On the Interaction Between Embodied and Symbolic Mathematics Knowledge: Implications for Instruction

Abstract

Researchers have long debated best pedagogical practices for introducing new mathematical concepts. The formalisms-first approach (e.g., Kaminski, Sloutsky, & Heckler, 2008) posits that students should first learn symbolical representations of a new concept and only then apply their formal strategies to situated contexts. In contrast, the progressive-formalization approach (e.g., Goldstone, Landy, & Son, 2008) posits that students should begin from concrete situations and then progressively formalize their understandings of the situations towards adopting and using normative abstract representations.

Our embodiment approach (a) borrows the progressive-formalization epistemological position that abstract notions are grounded in concrete situations; yet also (b) partially subscribes to the formalism-first ontological position that mathematical concepts should be grounded in generic images. Our design-based research evaluated an embodiment heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives and formal mathematical rules.

We compared student performance under conditions of working with stark (acontextual) vs. iconic (situated) manipulatives in the empirical context of the Mathematics Imagery Trainer for Proportion. Students working with the MITp are asked to move two cursors so as to make the screen green and keep it green. Unknown to the students, the screen will become green only if the cursors’ respective heights along the screen relate by a particular ratio (otherwise, the screen is red).
We summarize findings from analyzing 25 individually administered task-based semi-structured clinical interviews with Grade 4 – 6 participant students, 14 in the “stark-then-iconic” condition and 11 in the “iconic-then-stark” condition. We exclusively interviewed students around the numerical item of a 1:2 ratio. As our primary methodological approach, we engaged in a micro-genetic analysis of selected episodes from the data corpus, focusing on the study participants’ range of physical actions and multimodal utterance around the available media.

We found tradeoffs of situatedness: Whereas iconic objects elicit richer narratives than stark objects, these narratives may detrimentally constrain the scope of potential sensorimotor schemes students develop in attempt to solve manipulation problems (cf., Day, Motz, & Goldstone 2015). The finding is relevant to mathematics pedagogy, because sensorimotor schemes mediate conceptual learning. It follows that the situatedness of certain instructional materials is liable to impede mathematical learning by precluding the emergence of sensorimotor schemes pertinent to a cognitive sequence toward the generalization of rules.

References

Day, S. B., Motz, B. A., & Goldstone, R. L. (2015). The cognitive costs of context: The effects of concreteness and immersiveness in instructional examples. Frontiers in Psychology, 6.

Goldstone, R. L., Landy, D., & Son, J. Y. (2008). A well-grounded education. In M. DeVega, A. M. Glenberg & A. C. Graesser (Eds.), Symbols and embodiment (pp. 327–355). Oxford: Oxford University Press.

Kaminski, J. A., Sloutsky V. M., & Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320, 454–455.

Sloutsky, V. M., Kaminski, J. A., & Heckler, A. F. (2005). The advantage of simple symbols for learning and transfer. Psychonomic Bulletin & Review, 12(3), 508-513.

Authors

• Dana Melinda Rosen, University of California - Berkeley

• Alik Palatnik, Technion Israel Institute of Technology

• Dor Abrahamson, University of California - Berkeley