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Structurally equivalent (or isomorphic) problems have been found to vary in difficulty because of problem solvers' different mental representations of the problems (Hayes and Simon 1977).
The major limitation with these methods are the deficiencies in analytical/numerical representations of the problems and the non-transferability of the knowledge acquired in solving a problem to help solve other problems.
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This result agrees with the verdict of causal decision theory given other accurate representations of the problem.
Science misconceptions were investigated by comparison of the answers given to the same problem using different representations of the problem.
We argue that self-explanation may function as verbal mediation that supports the transformation between different external representations of the problem.
Accordingly, different conceptual frameworks were proposed that describe the cognitive processes of problem solving such as understanding the problem, building adequate representations of the problem, developing hypotheses, conducting experiments, and evaluating the solution (Jonassen [2011]; OECD [2005]).
Items referring to PR required students to, first, shift between different levels of representation (e.g., transforming a structural formula into a sum formula) and, second, build representations of the problem structure (e.g., by using concept maps).
Although RGP computations are expensive on time and computational power, their results are simple representations of the problem without being exposed to a priori information about the problem beforehand.
Based on a learner-initiating instruction strategy, LIM-G first comprehends the problem and then gives the learner the telegraphic and diagrammatic representations of the problem, which are more intuitive to understand.
Second, they had to choose among given representations of the problem solution (e.g., a journal article) and decide whether they were appropriate for different audiences (for further information on this approach, see Bernholt et al. 2012).
The computer can process and manipulate information; it can therefore embody useful representations of the problem world, of its users, and even of itself, adding further levels of structural complexity.
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