Figure 1414

A schematic diagram of the sortings of physics problems by a novice and expert, adapted from Chi, Glaser, and Rees (1983). The squares indicate higher-order categories which organise lower-order groupings (circles). The conceptual groups represented by circles can be further subdivided into smaller groupings (triangles). The numbers indicate the number of problems in the category. Note how the expert's categorisation reveals a hierarchical organisation that is missing from the novice's categorisation, which is completely flat.

The model's long-term memory is a distributed memory that encodes previous problem situations (see Chapters 1 and 9). This memory has input units that are divided into three types: data units, final goal units, and subgoal units. The data units can encode different sorts of symbols in problem statements (e.g., the explicitly mentioned objects and variables), while the final goal units encode the required quantity to be found in the problem. Problems are encoded in memory using these two sets of units. From experience of solving previous problems, the memory learns an association between a particular set of problem statements (including their goals) and a set of useful subgoals (see Figure 14.15).

The model goes through four main processing stages when solving a problem. First, the problem to be solved is encoded by both the distributed memory system and the production system. In the distributed memory, the problem statement is encoded as activations to the appropriate data and final goal units (it should be noted that no encoding of subgoals occurs). The production system encodes the problem as a structured representation in its working memory. Second, the encoded problem is processed by the distributed memory until it settles into a stable state, at which point one or more of the units in the subgoal set achieve a high activation. Third, the production system then comes into play and uses its sets of inference rules on the problem representation and the sub-goals generated by the distributed memory. These inference rules are used to reach the goals of the problem using forward inference. If forward inference fails, then the system starts backward inference. Fourth, if a solution is learned in the third stage then the subgoals that were found to be useful are used along with the problem statement and goal to put the network through a learning cycle that encodes the association between these three entities. So, in the future, if the same or a similar problem is met, the network will produce a certain set of suitable subgoals to be adopted. Lamberts

Production system Distributed memory

Production system Distributed memory

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