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Beyond Conceptual Change: Using Representations to Integrate Domain‐Specific Structural Models in Learning Mathematics

Beyond Conceptual Change: Using Representations to Integrate Domain‐Specific Structural Models in... ABSTRACT— Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mind, Brain, and Education Wiley

Beyond Conceptual Change: Using Representations to Integrate Domain‐Specific Structural Models in Learning Mathematics

Mind, Brain, and Education , Volume 1 (2) – Jun 1, 2007

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Publisher
Wiley
Copyright
2007 International Mind, Brain, and Education Society and Blackwell Publishing, Inc.
ISSN
1751-2271
eISSN
1751-228X
DOI
10.1111/j.1751-228X.2007.00009.x
Publisher site
See Article on Publisher Site

Abstract

ABSTRACT— Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer.

Journal

Mind, Brain, and EducationWiley

Published: Jun 1, 2007

References