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problem can be solved. The hypothesis guiding their research is that the representation is
constructed in the context of the knowledge available for a particular type of problem.
Experts categorize problems differently than novices because of a more highly developed
knowledge structure.
Joan I. Heller and Frederick J. Reif (1984) further showed the importance of
knowledge organization and problem representation with their work on the "physics
description" of a problem. It is important to “describe” a problem with care before
attempting to search for its solution, explicit knowledge about what types of information
should be included in an effective description, and explicit systematic procedures
specifying how to generate such a description. The physics description contains the
"physics" of the solution.
The work of Alan Schoenfeld in mathematics problem solving must also be
mentioned. The problem-solving strategy students followed in this dissertation research
is heavily based on Schoenfeld's work. Running as a thread through Schoenfeld's work,
one can find the following many-sided argument for the merits of heuristic instruction
(Schoenfeld, 1985; Schoenfeld, 1989; Nickerson, Perkins, and Smith, 1985):
- Heuristicsheuristics. help students to solve problems when the students know and apply the
- Students lack a good set of heuristics.
- Students do not reliably pick up heuristics have to be taught explicitly. spontaneously from examples; heuristics
- Students do not reliably apply heuristics theyprompting is necessary. know about; some sort of guidance or
- A "managerial strategy" for approaching prcan help students to apply heuristics and lead to substantially improved problem oblems, taken together with heuristics,
solving performance in mathematics.
The Managerial Strategy of Schoenfeld has the following five phases: