Testing Different Learning Strategies on a Simple Connectionist Model of Numerical Fact Retrieval

The use of fingers for counting plays an acknowledged role in the development of early arithmetic skills. In this paper, the main question on which we will focus our attention is the following: how does finger use in counting routines affects learning of arithmetical skills? We first analyze finger-using counting strategies from an algorithmic stance. Through this analysis it could be possible to inspect the relevant operations and the implicit knowledge necessary to perform that specific counting routine. Second, the algorithmic features of the finger-using counting routine will be simulated on a feed-forward back-propagation neural network designed to study the learning and retrieval of a set of basic number facts namely, the results of single digit additions. We tested the network on different learning strategies to check whether the strategy modeled on the finger counting routine gains any advantages. Moreover, we tested the net on the problem size effect for each of the learning strategies simulated. The results of the simulations show that the learning strategy based on the finger counting algorithmic features leads the net to a faster reduction of the number of errors during the training phase and, interestingly, to reproduce the problem size effect.