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.     

A Computational and Empirical Investigation of Graphemes in Reading

It is often assumed that graphemes are a crucial level of orthographic representation above letters. Current connectionist models of reading, however, do not address how the mapping from letters to graphemes is learned. One major challenge for computational modeling is therefore developing a model that learns this mapping and can assign the graphemes to linguistically meaningful categories such as the onset, vowel, and coda of a syllable. Here, we present a model that learns to do this in English for strings of any letter length and any number of syllables. The model is evaluated on error rates and further validated on the results of a behavioral experiment designed to examine ambiguities in the processing of graphemes. The results show that the model (a) chooses graphemes from letter strings with a high level of accuracy, even when trained on only a small portion of the English lexicon; (b) chooses a similar set of graphemes as people do in situations where different graphemes can potentially be selected; (c) predicts orthographic effects on segmentation which are found in human data; and (d) can be readily integrated into a full‐blown model of multi‐syllabic reading aloud such as CDP++ (Perry, Ziegler, & Zorzi, 2010). Altogether, these results suggest that the model provides a plausible hypothesis for the kind of computations that underlie the use of graphemes in skilled reading.