the psychology of learning and motivation - Percepts and Concepts ...

272 Jose P. Mestre et al.selects a likely principle/concept, justi¢es that it can be applied, and for theexpert the principle is chunked with procedures/equations for applying it(Larkin, 1979). It is the justification process for applying the major principle/conceptbased on the question asked and the problem’s story linethat often remains tacit in traditional instruction (Larkin, 1981a).For example, conservation of mechanical energy is a major idea inmechanics, and is relatively easy to apply in problem solving—one simplysets the mechanical energy (made up of the sum of potential and kineticenergies) in some initial state equal to the mechanical energy is some finalstate, and solves for whatever unknown is asked for in the particularproblem under consideration. The hard part, and what often remainstacit, is how to decide if conservation of mechanical energy is a usefulprinciple to select (Larkin, 1981a). To apply conservation of mechanicalenergy requires that no external nonconservative forces do work on thesystem under consideration. If some external force does work on thesystem, then the work-energy theorem (another major idea in mechanicsrelated to conservation of mechanical energy) should be applied, notconservation of mechanical energy. Thus, an expert reading a problemthat initially appears amenable to the application of conservation of energychecks the problem context to make sure that there are no externalnonconservative forces doing work; if there aren’t, then conservation ofmechanical energy is a good bet; if there are external nonconservativeforces doing work, then the expert can switch seamlessly to consideringthe work-energy theorem as a viable alternative. To determine whetherthere are external nonconservative forces doing work, the expert looks foradditional contextual cues such as whether there is friction, tension forcesdue to strings or ropes, or external agents pushing or pulling (Anzai &Yokoyama, 1984; de Jong & Ferguson-Hessler, 1991; Savelsbergh, deJong, & Ferguson-Hessler, 2002). Looking for these clues in the problemthat lead to this decision is not trivial and can be very difficult for novices.Finding such justi¢cations for applying certain major ideas is somethingthat experts do all the time, and something that most novices do not knowhow to do well, if at all. Examining justifications for applying a particularconcept/principle in a problem context is a very useful expert skill andpermeates mechanics, and indeed all of physics problem solving. In addition,successful problem solvers can generate an organized solution plan forhow to apply principles (Finegold & Mass, 1985; Priest & Lindsay, 1992).1.3. Novice problem solving in introductory physicsNovices can become rather proficient at physics problem solving, andeventually after much practice show the kind of top-down CPS approachdescribed in the previous section (Eylon & Reif, 1984). But, this transitionis difficult, especially since equation-based approaches such as means-endsanalysis (Larkin, 1983; Larkin et al., 1980; Newell & Simon, 1972; Simon