Deficient arithmetic fact retrieval—storage or access problem? A case study

This paper aims at clarifying the nature of fact retrieval difficulties in an 18-year-old young man (MO) who exhibited a puzzling pattern of developmental dyscalculia. Contrasting performance on explicit (production and verification tasks) and implicit (priming) tasks we observed poor overt retrieval of addition and multiplication facts, classical interference effects in verification tasks and inconsistency of error patterns. Hence, MO's performance pattern is suggestive of the existence of a partly stored network of facts (reflecting imperfect storage), but is also compatible with an access deficit according to Warrington and Cipolotti's [Brain 119 (1996) 611] criteria for distinguishing access and storage deficits in dysphasic patients. Furthermore, while MO displayed interference effects in verification tasks, he did not show automatic access to arithmetic facts in implicit tasks. Finally, similar to the findings of Roussel, Fayol, and Barrouillet [European Journal of Cognitive Psychology 14(1) (2002) 61] on normal subjects, MO's performance pattern is suggestive of the existence of differential processing mechanisms for addition and multiplication facts. We propose a unifying mechanism, namely a deficit of the central executive of working memory (WM), that accounts both for the constitution of a fuzzy network of fact representations, and for an access deficit modulated by attentional demands as required in explicit/implicit task paradigms. Overall, our results clearly provide evidence that even in (a developmental) case of a non-perfect network of memory representations (e.g. [Journal of Experimental Psychology: General 117 (1988) 258]), interference effects might be observed. Future studies thus need to be cautious before concluding that interference effects prove the existence of a well-established associative memory network of arithmetic facts.