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In this study, we modified a classic problem solving task, number series completion, in order to explore the contribution of implicit memory to inductive reasoning. Participants were required to complete number series sharing the same underlying algorithm (e.g., +2),differing in both constituent elements (e.g., 2 4 6 8 versus 5 7 9 11) and correct answers (e.g., 10 versus 13). In Experiment 1, reliable priming effects emerged, whether primes and targets were separated by four or ten fillers. Experiment 2 provided direct evidence that the observed facilitation arises at central stages of problem solving, namely the identification of the algorithm and its subsequent extrapolation. The observation of analogous priming effects in a severely amnesic patient strongly supports the hypothesis that the facilitation in number series completionwas largely determined by implicit memory processes. These findings demonstrate that the influence of implicit processes extends to higher level cognitive domain such as induction reasoning.

The purpose of the present paper is to provide a critical review of the neuropsychological evidence elucidating the incidence and nature of numerical difficulties in dementia. Though long neglected, the occurrence of dyscalculia in the early stage of Alzheimer's disease (AD) has caught the attention of many, and both group studies and single-case investigations converge in identifying number processing and numerical difficulties among the early signs of dementia. Yet analysis of the available data suggests that the pattern of decline may vary greatly across individuals: numerical difficulties may be highly selective and limited to single processing mechanisms but also extended to all aspects of numerical abilities. Overall, data from AD, in agreement with acquired disorders in focal lesioned patients, confirm the dissociations between multiple functional components of the number processing and calculation system.

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Aim of the present functional magnet resonance imaging (fMRI) study was to detect modifications of cerebral activation patterns related to learning arithmetic. Thirteen right-handed subjects were extensively trained on a set of 18 complex multiplication problems. In the following fMRI session, trained and untrained problems (closely matched for difficulty) were presented in blocked order alternating with a number matching task and a fact retrieval task. Importantly, left hemispheric activations were dominant in the two contrasts between untrained and trained condition, suggesting that teaming processes in arithmetic are predominantly supported by the left hemisphere. Contrasting untrained versus trained condition, the left intraparietal sulcus showed significant activations, as well as the inferior parietal lobule. A further significant activation was found in the left inferior frontal gyrus. This activation may be accounted for by higher working memory demands in the untrained as compared to the trained condition. Contrasting trained versus untrained condition a significant focus of activation was found in the left angular gyrus. Following the triple-code model [Science 284 (1999) 9701, the shift of activation within the parietal lobe from the intraparietal sulcus to the left angular gyrus suggests a modification from quantity-based processing to more automatic retrieval. The present study shows that the left angular gyrus is not only involved in arithmetic tasks requiring simple fact retrieval, but may show significant activations as a result of relatively short training of complex calculation. (C) 2003 Elsevier B.V. All rights reserved.

Aim of the present functional magnet resonance imaging (fMRI) study was to detect modifications of cerebral activation patterns related to learning arithmetic. Thirteen right-handed subjects were extensively trained on a set of 18 complex multiplication problems. In the following fMRI session, trained and untrained problems (closely matched for difficulty) were presented in blocked order alternating with a number matching task and a fact retrieval task. Importantly, left hemispheric activations were dominant in the two contrasts between untrained and trained condition, suggesting that learning processes in arithmetic are predominantly supported by the left hemisphere. Contrasting untrained versus trained condition, the left intraparietal sulcus showed significant activations, as well as the inferior parietal lobule. A further significant activation was found in the left inferior frontal gyrus. This activation may be accounted for by higher working memory demands in the untrained as compared to the trained condition. Contrasting trained versus untrained condition a significant focus of activation was found in the left angular gyrus. Following the triple-code model [Science 284 (1999) 970], the shift of activation within the parietal lobe from the intraparietal sulcus to the left angular gyrus suggests a modification from quantity-based processing to more automatic retrieval. The present study shows that the left angular gyrus is not only involved in arithmetic tasks requiring simple fact retrieval, but may show significant activations as a result of relatively short training of complex calculation.

Despite the high incidence of numerical deficits in neurological patients, little attention has been paid to the development of diagnostic tools. In fact, most of the published reports on acquired numerical disorders, whether single case or group studies, do not refer to standardised measures of performance providing little, if any, control data specifically collected for the examination. In this study we present data of 282 healthy controls of different age groups and educational levels in a new battery of Number Processing and Calculation (NPC). The NPC battery includes a total of 35 tasks, assessing different counting abilities, various aspects of number comprehension (such as parity and magnitude judgements), numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. Special attention is paid to the assessment of different calculation abilities, including simple fact retrieval, rule based processing, mental calculation and written calculation in all four operations. Moreover, text problem solving is assessed as well as the understanding of arithmetic principles. Thus, the NPC battery differs from the EC 301 battery proposed by Deloche et al., 1994 (Dellatolas, Deloche, Basso, & Claros-Salinas, 2001) and allows a more fine grained diagnosis which is relevant for planning targeted interventions. The battery is easy to administer and does not require special materials or equipment.

Though a few case studies reported a dissociation between intact writing of Arabic and impaired writing of alphabetical script, a detailed experimental analysis of such a dissociation is still lacking. We report a follow-up study of a patient with a parieto-occipital lesion who is affected by severe peripheral agraphia for letters, but not for Arabic digits. While letters in writing to dictation are frequently illegible, distorted, or consist in meaningless strokes, Arabic digits are well-formed and fluently produced. In a series of tasks, including copying of letters with tachistoscopic presentation and handwriting on a digitizing tablet, several processing levels are assessed in order to localize JS' functional writing impairment and to determine different processing routes for letters and for numbers. Overall, the results of the experimental investigation suggest a notation specific deficit in the activation of graphomotor patterns for letters, but not for digits. The study thus adds evidence to the so far reported dissociations between Arabic and alphabetical scripts. (C) 2002 Elsevier Science Ltd. All rights reserved.

Though a few case studies reported a dissociation between intact writing of Arabic and impaired writing of alphabetical script, a detailed experimental analysis of such a dissociation is still lacking. We report a follow-up study of a patient with a parieto-occipital lesion who is affected by severe peripheral agraphia for letters, but not for Arabic digits. While letters in writing to dictation are frequently illegible, distorted, or consist in meaningless strokes, Arabic digits are well-formed and fluently produced. In a series of tasks, including copying of letters with tachistoscopic presentation and handwriting on a digitizing tablet, several processing levels are assessed in order to localize JS' functional writing impairment and to determine different processing routes for letters and for numbers. Overall, the results of the experimental investigation suggest a notation specific deficit in the activation of graphomotor patterns for letters, but not for digits. The study thus adds evidence to the so far reported dissociations between Arabic and alphabetical scripts.

The aim of the present study was to evaluate the efficacy of a reorganisation approach in the rehabilitation of simple arithmetic deficits as an instance of disturbed semantic knowledge. We report the case of FS, who underwent targeted training to overcome specific difficulties with multiplication facts. The programme was based on the strategic use of his residual knowledge and explicit reference to the principles underlying simple arithmetic. The purpose of this approach was to facilitate the reacquisition process by reducing the number of facts to be memorised and inducing a meaningful organisation of this knowledge in memory. The positive outcome of the intervention speaks in favour of a reorganisation rationale in the rehabilitation of arithmetic skills, where the integration of declarative, procedural, and conceptual knowledge critically mediate the re-acquisition process

This study questions the evidence that a parity rule is used during the verification of multiplication. Previous studies reported that products are rejected faster when they violate the expected parity, which was attributed to the use of a rule (Krueger, 1986; Lemaire & Fayol, 1995). This experiment tested an alternative explanation of this effect: the familiarity hypothesis. Fifty subjects participated in a verification task with contrasting types of problems (even x even, odd x odd, mixed). Some aspects of our results constitute evidence against the use of the parity rule: False even answers were rejected slowly, even when the two operands were odd. We suggest that the odd-even effect in verification of multiplication could not be due to the use of the parity rule, but rather to a familiarity with even numbers (three quarters of products are indeed even).