A computational model of counting along a mental line

Are mental additions of single-digit numbers solved through direct retrieval from long-term memory or through persistent use of an automatized counting procedure along a mental line? In this paper, we present an experiment based on small additions along an artificial mental line, which tends to show that for very small addends (+2 to +4), counting may still be used at the end of a 3-week training. To investigate this issue, we developed the AutoCoP computational model, which describes how small additions could be solved, based on attention, working memory and experience. The simulations of AutoCoP based on this experiment showed that the effects detected at the behavioral level are reproduced and consistent with the theory, which assumes the use of a counting procedure in experts.