Frederick Reif’s Milikan Lecture is another article on the core reading list.
Understanding and teaching important scientific thought processes, Am. J. Phys. 63, 17 (1995).
Reif proposes that the abilities to interpret scientific concepts and describe and organize scientific knowledge are all prerequisites to effective problem solving.
The ability to interpret scientific concepts and principles
Reif’s concept of interpreting a scientific concept in a variety of different scenarios is similar to McDermott’s idea of an operational definition. Students often misinterpret a concept (such as misidentifying direction of acceleration for a pendulum at different points in its trajectory) because they “retrieve remembered or plausible knowledge fragments which are often incorrect and which are rarely checked against a definition of the concept.” Accurate interpretation requires a procedure for interpreting a concept’s definition. In the case of the definition of acceleration as “the rate of change of velocity” this procedure involves explicit instructions for of how to determine each part of a definition (ie. how to define delta_v and delta_t in terms of velocity at two neighboring moments in time). These procedures should be taught explicitly rather than hoping that the students will infer them with practice. The following an interpretation procedure can be very tedious. Efficient interpretation requires an accumulation of special cases so that a given scenario can be matched to a special case and hence processed immediately without going through the step by step procedural interpretation.
The ability to describe knowledge effectively
Diagrams, words and mathematica symbols are all different types of descriptions. Reif defines a procedure for describing system with a “system diagram”. First, identify the motion (velocity and acceleration) then identify all interacting objects. Look at all long range forces then look at all contact forces. Lastly, break forces into vector components. Only at this point is the scenario fully described and student ready to apply a principle such as Newton’s 2nd law. Identifying interacting objects before discussing specific forces helps avoid the introduction of non-existent forces like “centrifugal force” that are not associated with a specific pair of objects.
The ability to organize knowledge effectively
Reif talks about organizing physics arguments in hierrarchical fashion rather than in a linear fashion. This is again similar to the overarching principles that modeling instruction is built around. This organization factors into Reif’s description of problem solving in terms of iteratively breaking the problem into subproblems that can be solved to build a solution to the full problem. In this case each level of subproblem can be thought of as corresponding to a different level of the knowledge hierarchy. This kind of hierarchy of organization and problem solving procedure could also be useful on a smaller scale. In Hands-on-Science we could think about problems involving the small particle model as involving a hierarchy starting with macroscopic characteristics that can be measured, moving to microscopic characteristics that can be inferred and finally to a conceptual model of what causes pressure at the microscopic level. At the moment we approach these problems in a very linear manner but thinking in terms of a hierarchy might help students recognize the importance and organization of each step in the solution.
The first step in problem solving is to analyze the problem. Problem analysis involves identifying known and desired quantities and likely drawing a diagram. An important part of problem analysis is making the connection between real world language and physics terms. It is non-trivial for a student to determine that “the reading on the scale” corresponds to “the normal force exerted by the scale on the person”. The need to analyze the problem is often not obvious to students who want to jump to constructing a solution. Having students analyze a problem and state a solution strategy but not actual solve the problem can help convince them of the importance and usefulness of analyzing a problem before attempting a solution.
Students are also often reluctant to spot check their answers once they solve a problem. To help encourage simple checks (units, magnitude, direction etc.) instructors should distinguish between answers that are simply wrong and answers that are nonsensical, deducting more points for the latter.
Other articles to read:
Reif and Allen, Cognition for interpreting scientific concepts: A study of acceleration, Cogn. Instruct. 9, 1-44 (1992).
Eylon and Reif, Effects of knowledge organization on task performance, Cogn. Instruct. 1, 5-44 (1984).
Schoenfeld, Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance, Cogn. Sci. 7, 329-363 (1983).