Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics
Article first published online: 21 JUN 2007
2007 International Mind, Brain, and Education Society and Blackwell Publishing, Inc.
Mind, Brain, and Education
Volume 1, Issue 2, pages 84–97, June 2007
How to Cite
Singer, F. M. (2007), Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics. Mind, Brain, and Education, 1: 84–97. doi: 10.1111/j.1751-228X.2007.00009.x
- Issue published online: 21 JUN 2007
- Article first published online: 21 JUN 2007
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.