Neuropsychologia 42 (2004) 482–496 Deficient arithmetic fact retrieval—storage or access problem? A case study Liane Kaufmann a,∗ , Aliette Lochy b,c , Arthur Drexler b , Carlo Semenza d a University Children’s Hospital of Innsbruck, Anichstrasse 35, Innsbruck A-6020, Austria b University of Innsbruck, Innsbruck, Austria c University of Louvain-la-Neuve, Louvain-la-Neuve, Belgium d University of Trieste, Trieste, Italy Received 29 November 2002; received in revised form 9 September 2003; accepted 16 September 2003 Abstract 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 ex- plicit/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. © 2003 Elsevier Ltd. All rights reserved. Keywords: Addition/multiplication facts; Explicit/implicit access; Production/verification/priming tasks; Developmental dyscalculia 1. Introduction Arithmetic fact knowledge (simple single digit problems, like 6 + 2 = 8, 6–2 = 4, 6 × 2 = 12, 6/2 = 3) is stored in long-term memory (LTM)—possibly in form of net- work associations (for a review, see Ashcraft, 1992)—and can be retrieved from there in a similar way to semantic knowledge (McCloskey, Caramazza, & Basili, 1985). When learning arithmetic, children solve arithmetic facts mainly by the use of overt counting (Fuson, 1988) which involves finger counting as well. The shift from counting strategies to memory retrieval is determined by the strength of fact representations in memory (Geary & Burlingham-Dubree, 1989; Lemaire & Siegler, 1995). This strength would de- ∗ Corresponding author. Tel.: +43-512-504x3502. E-mail address: liane.kaufmann@uklibk.ac.at (L. Kaufmann). pend on the frequency of encountering and solving the same problems, leading to storage of the terms and their answer. However, it has been shown that fact retrieval processes are not always entirely automatic and that other processes than automatic retrieval from LTM are used, not only in children (Baroody, 1994; Siegler, 1988; Siegler & Shrager, 1984) but also in adults (Barrouillet & Fayol, 1998; Geary & Wiley, 1991; LeFevre & Kulak, 1994; LeFevre, Sadesky, & Bisanz, 1996). These other processes include for instance, the use of computational strategies such as (automatic) procedural backup strategies like counting, as well as conceptually based backup strategies like problem decomposition. Not only the strength of fact representation in LTM may influence a successful direct retrieval, but also it has been suggested that this process depends on inhibi- tion (Barrouillet, Fayol, & Lathulière, 1997) and working memory (WM) systems (Lemaire, Abdi, & Fayol, 1996). 0028-3932/$ – see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.neuropsychologia.2003.09.004