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

Area of Science:

• Cognitive Science
• Educational Psychology
• Neuroscience

Background:

• Physical models like tangrams are used in early math education.
• Computational media extend manipulation-based learning to virtual mathematical entities.
• Mechanisms of how manipulation builds internal structures for problem-solving are unclear.

Purpose of the Study:

• To model how manipulations create internal traces and how these traces support problem-solving.
• To investigate the cognitive and neural underpinnings of manipulation-based learning in mathematics.

Main Methods:

• Two groups of sixth-grade students solved area problems.
• One group manipulated tangrams; the other completed a descriptive test.
• Eye-movement trajectories were recorded during problem-solving.

Main Results:

• Distinct eye-movement patterns were observed between the tangram and descriptive test groups.
• A second study confirmed that the tangram's geometric structure, not mere manipulation, drove these differences.
• A theoretical model was developed to explain these findings.

Conclusions:

• Geometric structure is crucial for manipulation-based learning, influencing cognitive processes.
• The developed model accounts for how action-traces generated by geometric manipulation support problem-solving.
• Findings have implications for designing effective educational tools and strategies.