Recombinant Enaction: Manipulatives Generate New Procedures in the Imagination, by Extending and Recombining Action Spaces

• Published in: Cognitive science 2018-03, Vol.42 (2), p.370-415
• Main Authors: Rahaman, Jeenath, Agrawal, Harshit, Srivastava, Nisheeth, Chandrasekharan, Sanjay
• Format: Article
• Language: English
• Subjects: Adolescent; Child; Cognitive ability; Comparative Analysis; Computer applications; Distributed cognition; Embedding; Enactive cognition; Epistemic action; Eye Movements; Eye Movements - physiology; Female; Forward models; Geometric Concepts; Humans; Imagination - physiology; Learning - physiology; Learning Processes; Male; Manipulative Materials; Manipulatives; Mathematical models; Mathematics - methods; Mathematics education; Mathematics Instruction; Object Manipulation; Problem Solving; Problem Solving - physiology; Students; Teaching Methods; Transfer
• ISSN: 0364-0213; 1551-6709
• DOI: 10.1111/cogs.12518

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation‐based learning—particularly how actions generate new internal structures that support problem‐solving—are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action‐traces recombine during problem‐solving. This model is based on a study of two groups of sixth‐grade students solving area problems. Before problem‐solving, one group manipulated a tangram, the other group answered a descriptive test. Eye‐movement trajectories during problem‐solving were different between the groups. A second study showed that this difference required the tangram's geometrical structure, just manipulation was not enough. We propose a theoretical model accounting for these results, and discuss its implications.