Storage and retrieval of addition facts: The role of number comparison

It is proposed that arithmetical facts are organized in memory in terms of a principle that is unique to numbers - the cardinal magnitudes of the addends. This implies that sums such as 4 + 2 and 2 + 4 are represented, and searched for, in terms of the maximum and minimum addends. This in turn implies that a critical stage in solving an addition problem is deciding which addend is the larger. The COMP model of addition fact retrieval incorporates a comparison stage, as well as a retrieval stage and a pronunciation stage. Three tasks, using the same subjects, were designed to assess the contribution of these three stages to retrieving the answers to single-digit addition problems. Task 3 was the addition task, which examined whether reaction times (RTs) were explained by the model; Task 1 was a number naming task to assess the contribution of the pronunciation stage; Task 2 was a magnitude comparison task to assess the contribution, if any, of the comparison stage. A regression equation that included just expressions of these three stages was found to account for 71% of the variance. It is argued that the COMP model fits not only the adult RT data better than do alternatives, but also the evidence from development of additional skills.