A NEW LOOK IN REPRESENTATIONS FOR MATHEMATICS AND SCIENCE LEARNING

Representations such as formal notations and diagrams routinely figure in students' learning of mathematics and science. However, in light o f the extensive research on students' misunderstanding in these subjec t matters, it is reasonable to ask whether other kinds of representati ons might help students to reach better understandings. Indeed, a numb er of educators have developed innovative representations, typically o n computers, that supposedly foster understanding through suggestive v isual analogies and 'microworld' to manipulate. Evaluative research on these 'new look' representations as well call them suggests that they indeed can help students to understand. In this review, we focus on e xactly how these representations aid understanding. We propose that th ey do so by facilitating the learner's construction of explanations, j ustifications, predictions, and the like. These constructions require search in problem spaces, in the sense of Newell and Simon (1972). The representations in question reduce the cognitive load of such searche s, clarify the structure of the problem spaces that need to be searche d, and make certain moves in the problem spaces more immediate. We inv oke Gentner's (1983) theory of 'structure mapping' to explain how thes e advantages are attained. We also examine several characteristics pit falls of representations in this style.