Thursday, 12 September 2013

The conceptual change approach to mathematics learning and teaching

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 metacognitive skills to correctly identify different kinds of learning and apply the most effective strategies in dealing with them (Vosniadou, 2003).


The conceptual change approach was brought to the field of learning and instruction from the philosophy and history of science (Kuhn, 1970; Lakatos, 1970) by science educators who saw certain analogies between theory changes in the history of science and students’ learning of science (e.g., Posner, Strike, Hewson,& Gertzog, 1982). Since the 1970s researchers such as Viennot (1979), Novak (1977) and Driver and Easley (1978) realized that students bring to the science learning task alternative frameworks or misconceptions that are robust and difficult to extinguish. Posner et al. (1982) and also McCloskey (1983) saw these alternative frameworks as theories that need to be replaced by the currently accepted, correct scientific views through a process of conceptual change. Drawing on Kuhn (1970), Posner et al. (1982) argued that in order for students to be able to replace their alternative conceptual frameworks with the currently accepted scientific views: (a) there must be dissatisfaction with existing conceptions, (b) the new conception must be intelligible, (c) the new conception must appear initially plausible, and (d) the new concept should suggest the possibility of a fruitful program.


The Posner et al. (1982) theoretical framework became the leading paradigm that guided research and instructional practices in science education, until it became subject to several criticisms (i.e., Caravita & Halden, 1994; Smith, diSessa, & Roschelle, 1993). These critics pointed out that the conceptual change approach focuses on the mistaken qualities of students’ prior knowledge and ignores their productive ideas, that alternative conceptions may be not as robust as they seem to be, that cognitive conflict is not an effective instructional strategy, and that instruction that ‘‘confronts misconceptions with a view to replacing them is misguided and unlikely to succeed’’ (Smith et al., p. 153). Caravita and Halden (1994) also pointed out that conceptual change happens in a larger situational, educational, and socio/cultural context, that it is affected by motivational and affective variables, and that we need to recognize that science is socially constructed and validated (see also Driver, Asoko, Leach & Mortiner, 1994; Pintrich, 1999). We agree with all of the above-mentioned criticisms of the original conceptual change approach. Most important, we find a great deal of truth in the recommendation to study the knowledge acquisition process in greater detail, and in particular,
the need to focus on ‘‘detailed descriptions of the evolution of knowledge systems’’ (Smith et al., 1993: p. 154) over long periods of time. Indeed, research in cognitive development provides an important source of information about the processes of conceptual change (e.g., Carey, 1985; Gallistel & Gelman, 1992; Hatano
& Inagaki, 1998). More specifically, Vosniadou and her colleagues have attempted to provide a cognitive developmental approach to conceptual change through detailed descriptions of the development of knowledge in several areas of the natural sciences, such as observational astronomy (Vosniadou, 1994, 2003; Vosniadou & Brewer, 1992, 1994) mechanics (Ioannides & Vosniadou, 2001; Megalakaki, Ioannides, Vosniadou, & Tiberghien, 1997), geophysics (Ioannidou & Vosniadou, 2001), chemistry (Kouka, Vosniadou, & Tsaparlis, 2001), and biology (Kyrkos & Vosniadou, 1997).


The results of these studies have shown that young children answer questions about force, matter, the earth in space, or about the composition of earth, mostly in an internally consistent way, revealing the existence of narrow but coherent initial explanatory frameworks. These explanatory frameworks are different in their structure, in the phenomena they explain, and in their individual concepts, from the scientific theories to which children are exposed through systematic instruction. The process of learning science is a slow and gradual one, during which children usually add the new, scientific, information to their initial explanatory frameworks,
destroying their coherence and creating synthetic models. Examples of such synthetic models are the model of the dual sphere, the hollow sphere, or the flattened sphere, the model of the sun and the moon revolving around a spherical earth in a geocentric solar system, etc. (see Vosniadou & Brewer, 1992, 1994). One could argue that the cognitive developmental approach to conceptual change is not very different from the classical conceptual change approach put forward by Posner et al. (1982). But this is not the case. The cognitive developmental approach to conceptual change meets all the criticisms of Smith et al. (1993). First,
misconceptions are not considered as unitary, faulty conceptions that represent a different physical theory. Rather, we describe a knowledge system consisting of many different elements organized in complex ways. Second, we make a distinction between the learner’s initial explanatory framework, prior to systematic instruction, and misconceptions that are produced after instruction. We believe that most of these misconceptions can be characterized as synthetic models—i.e., attempts by learners to synthesize the new information with the initial explanatory framework. Third, our theoretical position is a constructivist one. Not only it assumes that new information is built on existing knowledge structures; it also uses constructivism to explain students’ misconceptions and to provide a comprehensive framework for making meaningful and detailed predictions about the knowledge acquisition process. Finally, while our cognitive approach investigates only one facet of conceptual change, it is complementary and not contradictory to other approaches that deal with motivational/affective and socio/cultural factors (Anderson, Greeno, Reder, & Simon, 2000).



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