Modeling the acquisition of counting with an associative network

Abstract

In the acquision of counting by children, there are three interesting phenomena (Fuson et al. 1982): (1) the number word sequence produced by children can be divided into three distinct portions, called the conventional, stable nonconventional, and unstable portions; (2) irregular number words such as "fifteen" are omitted more often than regular ones such as "fourteen", "sixteen", and "seventeen"; and (3) initially the number word sequence is in a recitation form, rather than in the form of an associative chain of separable serial elements. Our paper at first analyzes these phenomena from the viewpoint of associative memory by assuming the number word sequences are made up of many associative relationships between the number words. This assumption is not contradictory to the third phenomenon described above, because the associative relationships are not confined only to those between the serial number words. On the basis of these anaylses, an associative network model, HAPS proposed by one of the authors (Hirai 1983), is extended so that it can mimic some aspects of the learning of sequence which involves the above three phenomena. The learning and production of sequence by the network are simulated on a digital computer, and the results show that the three phenomena can be observed in the performance of the network.