Modeling the process of problem-solving by associative networks capable of improving the performance

In this paper a model of neural network underlying arithmetic problem-solving is described. Memory models of procedural memory, semantic memory, and working memory, which are necessary to represent the process of the problem-solving, are constructed within a framework of a model of associative processor, HASP, proposed by one of the authors (Hirai 1983). Performance of the model has been simulated on a digital computer. By memorizing primitive knowledge of addition of two digits such as 6 + 8 = 14 in the semantic memory and procedural knowledge for the control of the process of adding in the procedural memory, the model can perform addition of multiple numbers with multiple digits. By making explicit serial associations between consecutive procedural steps, the performance of the model can be improved, because a current procedural step primes the next one. In addition, if a preceding procedural step is a subset of the next one, merging between the two steps occurs. The performance can be improved about 20% by these priming and merging. By memorizing incorrect procedures, the model can generate four kinds of bugs of addition which were observed in children's performance.