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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

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Tools for Thought: The Case of Mathematics.

Valeria Giardino¹

¹CNRS/AHP-PReST, Nancy, France.

|August 23, 2018

Summary

This study explores how mathematical notations and visualizations function as cognitive tools. It introduces concepts like material anchors and representational affordance to explain their role in mathematical thinking.

Keywords:

Cognitive tools Distributed cognition External and material representations Manipulative imagination Material anchors Philosophy of notation Representational affordances

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Area of Science:

Cognitive Science
Philosophy of Mathematics
Mathematics Education

Background:

Representational cognitive tools, such as notations and visualizations, are crucial for mathematical understanding.
Previous work introduced the concept of manipulative imagination to explain their cognitive function.

Purpose of the Study:

To analyze the functioning of representational cognitive tools in mathematics.
To explore the roles of notations and visualizations in mathematical reasoning.
To introduce and discuss key concepts for characterizing these tools.

Main Methods:

Case studies using algebraic and logical formulas.
Analysis of topological diagrams.
Discussion of manipulative imagination.
Introduction of material anchor and representational affordance concepts.

Main Results:

Formulas and diagrams serve as concrete examples of representational cognitive tools.
Manipulative imagination is a key factor in utilizing these tools effectively.
Material anchors and representational affordance provide a framework for understanding tool functionality.

Conclusions:

Notations and visualizations are integral to mathematical cognition.
The concepts of material anchor and representational affordance enhance the understanding of how these tools are used.
Further research can build upon these concepts to explore mathematical learning and problem-solving.