Arithmetic Facts without Meaning

The paper presents a single-case study of patient J.G. showing severe calculation problems (and also agraphia, finger agnosia, right-left disorientation and apraxia) after the surgery of a left parietal tumor. Although the patient completely lost conceptual knowledge of arithmetic, she preserved part of memorised fact knowledge (multiplications and some additions and subtractions). The study indicates that arithmetic facts can be represented at a superficial level without understanding of the operation performed. The study completes a valid double dissociation between two types of knowledge involved in calculation (memorised facts and conceptual knowledge).

[1]  Michael McCloskey,et al.  Facts, rules and procedures in normal calculation: Evidence from multiple single-patient studies of impaired arithmetic fact retrieval , 1991, Brain and Cognition.

[2]  Jamie I. D. Campbell,et al.  Chapter 12 Cognitive Number Processing: An Encoding-Complex Perspective , 1992 .

[3]  E. Renzi,et al.  Normative Data and Screening Power of a Shortened Version of the Token Test , 1978, Cortex.

[4]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[5]  D. Benson,et al.  Verbal Paraphasia as a , 1969 .

[6]  Y. Lampl,et al.  Selective acalculia with sparing of the subtraction process in a patient with left parietotemporal hemorrhage , 1994, Neurology.

[7]  E. Renzi,et al.  Imitating gestures. A quantitative approach to ideomotor apraxia. , 1980, Archives of neurology.

[8]  Elizabeth K. Warrington,et al.  Arithmetic Skills in Patients with Unilateral Cerebral Lesions , 1986, Cortex.

[9]  C. Semenza,et al.  The Representation Of Arithmetical Facts: Evidence from two Rehabilitation Studies , 1996, Cortex.

[10]  Jamie I. D. Campbell Architectures for numerical cognition , 1994, Cognition.

[11]  Elizabeth K. Warrington,et al.  A dissociation between addition and subtraction with written calculation , 1994, Neuropsychologia.

[12]  Marcus Giaquinto Concepts and Calculation , 1995 .

[13]  A. Damasio,et al.  Lesion analysis in neuropsychology , 1989 .

[14]  J. Piaget Success and Understanding , 1978 .

[15]  J. Gerstmann Fingeragnosie und isolierte Agraphie — ein neues Syndrom , 1927 .

[16]  J. Greene Contributions to Neuropsychological Assessment , 1995 .

[17]  Lisa Cipolotti,et al.  Selective Impairment For Simple Division , 1995, Cortex.

[18]  A. Benton THE FICTION OF THE “GERSTMANN SYNDROME” , 1961, Journal of neurology, neurosurgery, and psychiatry.

[19]  R. Siegler The perils of averaging data over strategies: An example from children's addition. , 1987 .

[20]  A. Kashiwagi,et al.  Improvement of deficits in mnemonic rhyme for multiplication in Japanese aphasics , 1987, Neuropsychologia.

[21]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

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

[23]  Jamie I. D. Campbell The Nature and origins of mathematical skills , 1992 .

[24]  N. O’connor,et al.  Factors and primes: a specific numerical ability , 1990, Psychological Medicine.

[25]  Richard Power,et al.  The dictation of Italian numerals , 1990 .

[26]  M. McCloskey Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia , 1992, Cognition.

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

[28]  R. Sternberg,et al.  Complex Problem Solving : Principles and Mechanisms , 1992 .

[29]  Michael 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.

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

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

[32]  Lauren B. Resnick Syntax and Semantics in Learning to Subtract. , 1982 .

[33]  Integrating Clinical Assessment with Cognitive Neuroscience: Construct Validation of the California Verbal Learning Test. , 1988 .

[34]  S. Dehaene Varieties of numerical abilities , 1992, Cognition.

[35]  J. Gerstmann SYNDROME OF FINGER AGNOSIA, DISORIENTATION FOR RIGHT AND LEFT, AGRAPHIA AND ACALCULIA: LOCAL DIAGNOSTIC VALUE , 1940 .

[36]  G. Dahl WIP, reduzierter Wechsler-Intelligenztest , 1972 .

[37]  J. Hiebert,et al.  Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis , 1986 .

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

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

[40]  Kevin M. McConkey,et al.  Cognition in individual and social contexts , 1989 .

[41]  A. Benton Contributions to Neuropsychological Assessment: A Clinical Manual , 1983 .

[42]  A. Damasio,et al.  Troubled letters but not numbers. Domain specific cognitive impairments following focal damage in frontal cortex. , 1990, Brain : a journal of neurology.

[43]  Xavier Seron,et al.  Selective Impairment as Evidence for Mental Organisation of Arithmetical Facts: BB, A Case of Preserved Subtraction? , 1994, Cortex.

[44]  L. E. Bourne,et al.  On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects. , 1994 .

[45]  Jeffrey Bisanz,et al.  Formal methods in developmental psychology : progress in cognitive development research , 1987 .

[46]  Marie-Pascale Noël,et al.  Arabic Number Reading Deficit - a Single-case Study Or When 236 Is Read (2306) and Judged Superior To 1258 , 1993 .

[47]  Michael McCloskey,et al.  The organization of arithmetic facts in memory: Evidence from a brain-damaged patient , 1992, Brain and Cognition.

[48]  T. Benke,et al.  Impaired Arithmetic Facts But Intact Conceptual Knowledge a Single—Case Study of Dyscalculia , 1995, Cortex.

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

[50]  E K Warrington,et al.  The Fractionation of Arithmetical Skills: A Single Case Study , 1982, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[51]  Xavier Seron,et al.  Dot counting by brain damaged subjects , 1991, Brain and Cognition.

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

[53]  X. Seron,et al.  Lexicalization Errors in Writing Arabic Numerals - A Single-Case Study , 1995, Brain and Cognition.