A Study of the Knowledge Structure of Expert, Intermediate, and Novice Subjects in the Domain of Physics

ion than the novices. According to Giere, the primary difference between experts and novices is essentially the place at which they are operating on the graded structure. In Giere’s (1994) scheme, part of becoming an expert in physics is learning to categorize problems a t a higher level of abstraction. There are a few w eaknesses to Giere’s (1994) representation of knowledge th a t will be examined a t this time. The first w eakness is th a t Giere’s structure of models is an analogy to the structu re of concepts and this analogy m ay not be adequate. According to Giere, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 physics knowledge can be thought of as consisting of models structu red in a hierarchy in m uch the same way tha t concepts are s tructu red in Klausmeier’s (1990) view. However, this analogy may be only superficially true. Recall th a t in the case of conceptual knowledge, Klausmeier described in detail the criteria for establishing an example of a concept’s place in the hierarchy. In th is theory, each example of a concept is described by its attributes and these a ttribu tes define the position of the example in the conceptual structure . Similarly, Chi, Slotta, and de Leeuw (1994) offer a sim ilar graded s tructu re which is defined by the concept’s ontological category. In order for the hierarchical structure of models proposed by Giere to be representative of knowledge in physics, something analogous to the attribute is needed to define its structure. In particular, Giere (1988; 1994) alludes to the notion th a t more peripheral models are more difficult conceptually. However, it is not clear w hat attribu tes define a more conceptually difficult model. In his first interpretation of physics textbooks (1988), Giere suggests th a t more peripheral models in classical m echanics are defined by more complex force functions. However, in the structure in Figure 1, these force functions (F=k, F=-kx, F=k/r2) are listed a t a higher level. It is not clear how these and other functions are used to define models a t lower levels of abstraction. In the research on problem classification, novices used the surface features in the problems to create their categories (Chi et al, 1981; 1982; de Jong & Ferguson-Hessler, 1986; Veldhuis, 1990). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 These surface features are attributes of the models used to solve the problems. For example, the pendulum is an attribute of a model explaining its motion. Experts in these studies categorized the problems by the principles used to solve the problems (Chi et al, 1981; 1982; de Jong & Ferguson-Hessler, 1986; Veldhuis, 1990). Moreover, principles such as "Conservation of Energy" or "Newton’s 2nd Law" are not attributes of the models used to solve the problems in th a t they do not appear explicitly in the models themselves. An attribute of a model is som ething that is a part of the model such as the objects in the model, the graphs of the time evolution of variables, or the resulting equations of motion (Hestenes, 1992; 1987). In the example of the incline plane shown in Figure 2, Newton s Laws were used to create the conceptualized model shown. This is not explicit in the finished model in th a t Newton’s Laws are not explicitly represented in the model. However, the attributes "incline plane" or "frictionless" are always a part of the incline plane model itself. The hierarchy tha t Giere (1994) suggests describes the knowledge th a t novices have of the models in physics in term s of their surface features, b u t it does not explain experts’ knowledge. The experts’ knowledge is described by Giere to be a t a higher level, such as the "conservative or nonconservative models" level, bu t th is is not borne out in Chi et al’s results. The limitation in explaining the experts’ use of principles to categorize the problems may also be a w eakness of the probabilistic view of knowledge. Research on conceptual structure has found th a t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 the probabilistic view of concepts is inadequate to explain the role th a t theories play in the construction of coherent categories (Medin & W attenm aker, 1984; Murphy & Medin, 1985; Spalding & Murphy, 1996). For example, dogs and cats go together in a category, but dogs and chairs do not. The argum ent is th a t the attributes dogs and cats have in common fit an encom passing category such as "pets" or "animals" th a t dogs and chairs do not. However, one could name m any a ttribu tes tha t dogs and chairs have in common (found in houses, weigh less than 500 pounds, have four legs, etc.), b u t these a ttribu tes do not define a coherent category. Objects in a category m ay seem sim ilar because they are in the sam e category and not because of the attributes th a t they have in common (Medin & W attenm aker, 1984), i.e., a se t of cups are sim ilar because they are a category, b u t the attributes th a t they share do not necessarily define them . In order to account for the coherence of concepts, the coherent view of category construction requires th a t these concepts be linked by underlying principles th a t are common to the objects in the category (Murphy & Medin, 1985). Since experts classified problems by the principles used to solve the problems in Chi et al’s (1981) study, it is suggested here th a t their categorization conforms to the coherent view of categorization ra ther th an the probabilistic view in which the models are connected; th a t is, the models are connected not by their attributes, bu t by the principles used to solve the problems. A nother source from the literature th a t should be mentioned is the work by Reif and his colleagues (Eylon & Reif, 1984; Heller & Reif, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 1984; Reif & Heller, 1982) who have done research on knowledge s tru c tu re in physics and have developed a hierarchical model of knowledge to facilitate problem solving in physics. This structure is a prescriptive model (Heller & Reif, 1984; Reif & Heller, 1982), meaning th a t the model is not based on expert performance, b u t is based on how problem s should be solved and how novice learners should learn to solve problems. However, the knowledge structu re th a t Reif and colleagues presen t is a hierarchy of principles used to solve problems (Heller & Reif 1984; Reif & Heller, 1982). Studies using this hierarchical model of physics principles have been successful in facilitating problem solving in physics (Eylon & Reif, 1984). Although th is is not a description of the knowledge structu re th a t individuals have, it is supportive of the coherent view in which models are connected by the principles used to solve them. The last w eakness which both the structu re th a t Giere (1994) proposes and the coherent view of categorization (Medin & W attenm aker, 1984; M urphy & Medin, 1985; Spalding & Murphy, 1996) share is th a t neither are supported entirely by the research findings. In particular, Chi et al’s categorization study (1981) does not provide any support to the notion of a hierarchy. The subjects in Chi et al’s study categorized the problems only once into only one set of piles. A hierarchical structu re implies th a t the problems belong to more th a n one category where problems in larger categories have more general a ttribu tes in common and problems in smaller categories have more specific attributes in common. In order to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 support the idea of a hierarchy, the subjects m ust be allowed to categorize problems more th an once into bigger or sm aller piles in order to determine which attributes are more general and which more specific. The results of the previous research that novices use surface features to categorize problems (Chi et al, 1981) supports Giere’s (1994) hierarchy of models and suggests tha t novices’ knowledge is centered on attributes of models. However, the resu lts th a t experts use theories to categorize problems (Chi et al, 1981) supports the coherent view of category construction (Medin & W attenm aker, 1984; M urphy & Medin, 1985; Spalding & Murphy, 1996) ra th e r th an the s tructu re proposed by Giere. More specifically, the resu lts with experts suggest th a t models are classified by the principles th a t are used to create them. Neither view, the coherent view nor Giere’s view of the structure of knowledge can explain both the novices’ and experts’ categorizations. There are two ways to rectify this situation. The first is to claim th a t the knowledge of experts and novices in physics are completely different with no relationship to each other; That is, novices’ knowledge is entirely based on the objects in models and their attributes, as in Giere’s (1994) representation and th a t experts’ knowledge is entirely based on theories used to solve problem s as in the coherent view of category construction (Medin & W attenm aker, 1984; Murphy & Medin, 1985; Spalding & Murphy, 1996). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 The second way to resolve th is issue is to propose tha t knowledge structu re in physics is a combination of these two views. T hat is, models may be structured in a hierarchy with more specific m odels a t the bottom and more general models a t the top as Giere (1994) suggests; This is supported by the results of novices’ categorizations. These hierarchies are then clustered according to the theories used to create them as suggested by the coherent view of categorization (Medin & W attenmaker, 1984; Murphy & Medin, 1985; Spalding & Murphy, 1996) and supp