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 pro-nunciation 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 evidencefrom developmentof additional skills. The basic phenomena involved in single-digit addition performance are robust, widely repli-cated and well known, yet there has been much controversy as to the psychological processe