More Evidence for the Role of the Central Executive in Retrieving Arithmetic Facts – A Case Study of Severe Developmental Dyscalculia

It has been shown repeatedly that simple mental calculation depends not only on long-term memory (LTM) representations but also on working memory (WM) resources. The study describes the performance of an adolescent, M.O., exhibiting severe developmental dyscalculia, but literacy problems as well. Despite having relatively preserved procedural skills, M.O. exhibited outstanding difficulties in retrieving arithmetic facts which are most pronounced on multiplication and division problems. Interestingly, his performance on non-numerical memory tests was within average (independent of modality), while his attention span was just below average. Testing the different components of WM, the results emphasize the major role of the central executive in solving simple mental calculations.

[1]  Arthur J. Baroody,et al.  An evaluation of evidence supporting fact-retrieval models , 1994 .

[2]  Jamie I. D. Campbell.  Network interference and mental multiplication. , 1987 .

[3]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[4]  A. Miyake,et al.  Models of Working Memory: Mechanisms of Active Maintenance and Executive Control , 1999 .

[5]  Pierre Noël Barrouillet,et al.  Selecting between Competitors in Multiplication Tasks: An Explanation of the Errors Produced by Adolescents with Learning Difficulties , 1997 .

[6]  Mark H. Ashcraft,et al.  Cognitive Psychology and Simple Arithmetic: A Review and Summary of New Directions. , 1995 .

[7]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[8]  S. Dehaene,et al.  Dissociable mechanisms of subitizing and counting: neuropsychological evidence from simultanagnosic patients. , 1994, Journal of experimental psychology. Human perception and performance.

[9]  Alfonso Caramazza,et al.  Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia , 1985, Brain and Cognition.

[10]  K. Fuson.  Children's Counting and Concepts of Number , 1987 .

[11]  Marie-Pascale Noël,et al.  The isolation of numerals at the semantic level , 1998 .

[12]  Max Coltheart,et al.  Psycholinguistic assessments of language processing in aphasia (PALPA) , 1996 .

[13]  R. Siegler,et al.  Four aspects of strategic change: contributions to children's learning of multiplication. , 1995, Journal of experimental psychology. General.

[14]  L. R. Peterson,et al.  Short-term retention of individual verbal items. , 1959, Journal of experimental psychology.

[15]  M. Ashcraft.  Cognitive arithmetic: A review of data and theory , 1992, Cognition.

[16]  G Denes,et al.  Concepts and facts in calculation. , 1994, Brain : a journal of neurology.

[17]  R. Siegler,et al.  Strategy choice procedures and the development of multiplication skill. , 1988, Journal of experimental psychology. General.

[18]  M McCloskey,et al.  Models of arithmetic fact retrieval: an evaluation in light of findings from normal and brain-damaged subjects. , 1991, Journal of experimental psychology. Learning, memory, and cognition.

[19]  K. A. Ericsson,et al.  Long-term working memory. , 1995, Psychological review.

[20]  S. Dehaene,et al.  Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. , 1990, Journal of experimental psychology. Human perception and performance.

[21]  Lauren B. Resnick,et al.  A Developmental Theory of Number Understanding. , 1984 .

[22]  G. Mandler,et al.  Subitizing: an analysis of its component processes. , 1982, Journal of experimental psychology. General.

[23]  M. Delazer,et al.  Arithmetic Facts without Meaning , 1997, Cortex.

[24]  David C. Geary,et al.  Children's Mathematical Development: Research and Practical Applications , 1996 .

[25]  E. Warrington,et al.  Short term Memory Impairment and Arithmetical Ability , 1996, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[26]  Stanislas Dehaene,et al.  Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowledge of Arithmetic , 1997, Cortex.

[27]  G. Denes,et al.  A specific deficit for numbers in a case of dense acalculia. , 1991, Brain : a journal of neurology.

[28]  Kristine L Koontz,et al.  Identifying Simple Numerical Stimuli: Processing Inefficiencies Exhibited by Arithmetic Learning Disabled Children , 1996 .

[29]  C. Reynolds,et al.  Factor structure, factor indexes, and other useful statistics for interpretation of the Test of Memory and Learning (TOMAL) , 1996 .

[30]  S. Dehaene,et al.  Language and calculation within the parietal lobe: a combined cognitive, anatomical and fMRI study , 2000, Neuropsychologia.

[31]  J. LeFevre,et al.  Individual differences and developmental change in the associative relations among numbers , 1991 .

[32]  David C. Geary,et al.  External validation of the strategy choice model for addition , 1989 .

[33]  Jeffrey Bisanz,et al.  Selection of Procedures in Mental Addition: Reassessing the Problem Size Effect in Adults , 1996 .

[34]  Jamie I. D. Campbell,et al.  Mental multiplication skill: Structure, process, and acquisition. , 1985 .