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

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...

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Bibliographic Details
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
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Summary: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.
ISSN:0364-0213
1551-6709
DOI:10.1111/cogs.12518