Expert problems solvers are characterized by continuous evaluation of their progress towards a solution. Part of this evaluation includes reflection upon the problem’s solution, both from an ideal knowledge perspective as well as that of the solver’s knowledge per se. In order to facilitate this process, a deliberate and explicit prompt may be useful as part of cognitive apprenticeship in order to foster diagnostic behavior in novice problem solvers. Two experiments involving introductory students will be discussed. The first is based on an individual diagnostic behavior ("self-diagnosis") in which the student is prompted to diagnose errors on a quiz during recitation, and the second is based on a group diagnostic behavior ("peer reflection") in which groups in a recitation discuss their homework solutions together. In both cases, consideration will be given not just to physical content but also to elements of a preferred method of problem-solving strategy. I will also present a study on a section of upper-level undergraduates with regard to attempting the same problem twice in an exam situation. This is done in order to investigate the premise that as more advanced problem solvers, they will more readily take part in the reflection exercise without the explicit prompting that may be more necessary for introductory students.
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