Unlocking conceptual learning in mathematics and science with effective representational systems

The representational analysis and design project is investigating the critical role that representations have on conceptual learning in complex scientific and mathematical domains. The fundamental ideas are that the representations used for learning can substantially determine what is learnt and how easily this occurs, and that to improve conceptual learning effective representations should be found or invented. Through the conceptual analysis and empirical evaluation of a class of representations that appear to be particularly beneficial for conceptual learning, Law Encoding Diagrams (LEDs), the project has identified certain general characteristics of effective representations. In this paper a descriptive model of the components and processes of conceptual learning is presented and used for several purposes: to explain why the nature of representation used for learning is critical; to demonstrate how representations possessing the identified characteristics of effective representations appear to support the major processes of conceptual learning; to consider how computers may further enhance the potential benefit of LEDs for conceptual learning. (C) 2000 Elsevier Science Ltd. All rights reserved.