Mathematical learning and instruction - conceptual change approach

The term ‘‘conceptual change’’ is used to characterize the kind of learning required when the new information to be learned comes in conflict with the learners’ prior knowledge usually acquired on the basis of everyday experiences. It is claimed that in these situations, a major reorganization of prior knowledge is required—a conceptual change. Some of the situations where conceptual change is required involve, for example, the acquisition of the scientific concept of force which comes in conflict with the everyday concept of force as a property of physical objects (Chi, Slotta, & de Leeuw, 1994), understanding the Copernican view of the solar system which comes in conflict with the geocentric view (Vosniadou & Brewer, 1994), and the acquisition of the concept of fraction as it requires radical changes in the pre-existing concept of natural number (Hartnett & Gelman, 1998; Stafylidou & Vosniadou, 2004).

Some researchers in learning and instruction (e.g., Caravita & Halden, 1994) ask: Why should we call this type of learning ‘‘conceptual change’’ and not just ‘‘learning’’? While conceptual change is undeniably a form of learning, it is important to differentiate conceptual change from other kinds of learning because it requires different mechanisms to be accomplished and different instructional interventions to be taught. Most learning is additive and involves an enrichment of existing knowledge. Conceptual change cannot, however, be achieved through additive mechanisms. In fact, as we will argue in greater detail later, the use of  additive mechanisms in situations requiring conceptual change is one of the major causes of misconceptions. A common type of misconception is caused when the new information is added to the incompatible knowledge base, producing synthetic models, like ‘‘the hollow sphere’’ (Vosniadou & Brewer, 1992), or the belief that fractions are always smaller than the unit (Stafylidou & Vosniadou, 2004). It is important in instruction to distinguish cases requiring conceptual change and alert students against the use of additive mechanisms in these cases. More generally, it is important to develop intentional learners that have acquired the meta cognitive skills to correctly identify different kinds of learning and apply the most effective strategies in dealing with them (Vosniadou, 2003).