Basic and Exceptional Calculation Abilities in a Calculating Prodigy: A Case Study

References

• Ashcraft , M. H. 1992 . Cognitive arithmetic: A review of data and theory . Cognition , 44 : 75 – 106 .
   PubMed Web of Science ®Google Scholar
• Ashcraft , M. H. and Battaglia , J. 1978 . Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition . Journal of Experimental Psychology: Human Learning and Memory , 4 : 527 – 538 .
   Google Scholar
• Ashcraft , M. H. and Christy , K. S. 1995 . The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1–6 . Journal of Research in Mathematics Education , 26 : 396 – 421 .
   Web of Science ®Google Scholar
• Babcock , R. L. and Salthouse , T. A. 1990 . Effects of increased processing demands on age differences in working memory . Psychology & Aging , 5 : 421 – 428 .
   PubMed Web of Science ®Google Scholar
• Barlow , F. 1952 . Mental prodigies , New York : Greenwood Press .
   Google Scholar
• Bruyer , R. and Scailquin , J-C. 1999 . Assessment of visuo-spatial short-term memory and effect of aging . European Review of Applied Psychology , 49 : 175 – 180 .
   Web of Science ®Google Scholar
• Campbell , J. I. D. 1987 . Network interference and mental multiplication . Journal of Experimental Psychology: Learning, Memory and Cognition , 13 : 109 – 123 .
   Web of Science ®Google Scholar
• Campbell , J. I. D. 1995 . Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation . Mathematical Cognition , 1 : 121 – 164 .
   Google Scholar
• Campbell , J. I. D. and Clark , J. M. 1992 . “ Cognitive number processing: An encoding-complex perspective ” . In The nature and origin of mathematical skills , Edited by: Campbell , J. I. D. 457 – 492 . North Holland: Elsevier .
   Google Scholar
• Campbell , J. I. D. and Graham , J. D. 1985 . Mental multiplication skills: Structure, process, acquisition . Canadian Journal of Psychology , 39 : 338 – 366 .
   Web of Science ®Google Scholar
• Charness , N. and Campbell , J. I. D. 1988 . Acquiring skill at mental computation in adulthood: A task decomposition . Journal of Experimental Psychology: General , 117 : 115 – 129 .
   Web of Science ®Google Scholar
• Chase , W. G. and Ericsson , K. A. 1982 . “ Skill and working memory ” . In The psychology of learning and motivation , Edited by: Bower , G. H. Vol. 16 , 1 – 58 . New York : Academic Press .
   Google Scholar
• Dehaene , S. 1989 . The psychophysics of numerical comparison: A reexamination of apparently incompatible data . Perception & Psychophysics , 45 : 557 – 566 .
   PubMed Web of Science ®Google Scholar
• Dehaene , S. 1992 . Varieties of numerical abilities . Cognition , 44 : 1 – 42 .
   PubMed Web of Science ®Google Scholar
• Dehaene , S. , Dupoux , E. and Mehler , J. 1990 . Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison . Journal of Experimental Psychology: Human Perception and Performance , 16 : 626 – 641 .
   PubMed Web of Science ®Google Scholar
• Dorman , C. 1991 . Exceptional calendar calculation ability after early left hemispherectomy . Brain & Cognition , 15 : 26 – 36 .
   PubMed Web of Science ®Google Scholar
• Ericsson , K. A. 1985 . Memory skill . Canadian Journal of Psychology , 39 : 188 – 231 .
   Web of Science ®Google Scholar
• Ericsson , K. A. and Kintsch , W. 1995 . Long-term working memory . Psychological Review , 102 : 211 – 245 .
   PubMed Web of Science ®Google Scholar
• Ericsson , K. A. , Krampe , R. T. and Tesch-Romer , C. 1993 . The role of deliberate practice in the acquisition of expert performance . Psychological Review , 100 : 363 – 406 .
   Web of Science ®Google Scholar
• Ericsson , K. A. and Lehmann , A. C. 1996 . Expert and exceptional performance: Evidence of maximal adaptation to task constraints . Annual Review of Psychology , 47 : 273 – 305 .
   PubMed Web of Science ®Google Scholar
• Ericsson , K. A. and Staszewski , J. J. 1989 . “ Skilled memory and expertise: Mechanisms of exceptional performance ” . In Complex information processing. The impact of Herbert A. Simon , Edited by: Klahr , D. and Kotovski , K. 235 – 267 . Mahwah , NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Faust , M. W. , Ashcraft , M. H. and Fleck , D. E. 1996 . Mathematics anxiety effects in simple and complex addition . Mathematical Cognition , 2 : 25 – 62 .
   Google Scholar
• Fayol , M. , Barrouillet , P. and Renaud , A. 1997 . Mais pourquoi l'écriture des grands nombres estelle aussi difficile? . Revue de Psychologie de l'Education , 3 : 87 – 107 .
   Google Scholar
• Frensch , P. A. and Geary , D. C. 1993 . Effects of practice on component processes in complex mental addition . Journal of Experimental Psychology: Learning, Memory and Cognition , 19 : 433 – 456 .
   PubMed Web of Science ®Google Scholar
• Gallistel , C. R. and Gelman , R. 1992 . Preverbal and verbal counting and computation . Cognition , 44 : 43 – 74 .
   PubMed Web of Science ®Google Scholar
• Giaquinto , M. 1995 . Concepts and calculation . Mathematical Cognition , 1 : 61 – 81 .
   Google Scholar
• Ginsburg , H. P. , Kossan , N. E. , Schwartz , R. and Swanson , D. 1983 . “ Protocol methods in research on mathematical thinking ” . In The development of mathematical thinking , Edited by: Ginsburg , H. P. 8 – 47 . New York : Academic Press .
   Google Scholar
• Groen , G. J. and Parkman , J. M. 1972 . A chronometric analysis of simple addition . Psychological Review , 79 : 329 – 343 .
   Web of Science ®Google Scholar
• Graham , D. J. and Campbell , J. I. D. 1992 . Network interference and number-fact retrieval: Evidence from children alpha-plication . Canadian Journal of Psychology , 46 : 65 – 91 .
   PubMed Web of Science ®Google Scholar
• Hamann , M. S. and Ashcraft , M. H. 1986 . Textbook presentations of basic addition facts . Cognition and Instruction , 3 : 173 – 192 .
   Google Scholar
• Hatano , G. and Osawa , K. 1983 . Digit memory of grand experts in abacus-derived mental calculation . Cognition , 15 : 95 – 111 .
   PubMed Web of Science ®Google Scholar
• Hermelin , B. and O'Connor , N. 1986 . Idiot savant calendrical calculators: Rules and regularities . Psychological Medicine , 16 : 885 – 893 .
   PubMed Web of Science ®Google Scholar
• Hermelin , B. and O'Connor , N. 1990 . Factors and primes: A specific numerical ability . Psychological Medicine , 16 : 885 – 893 .
   Google Scholar
• Hinrichs , J. V. , Yurko , D. S. and Hu , J. M. 1981 . Two-digit number comparison: Use of place information . Journal of Experimental Psychology: Human Perception & Performance , 7 : 890 – 901 .
   Web of Science ®Google Scholar
• Hitch , G. J. 1978 . The role of short-term working memory in mental arithmetic . Cognitive Psychology , 10 : 302 – 323 .
   Web of Science ®Google Scholar
• Hittmair-Delazer , M. , Sailer , U. and Benke , T. 1995 . Impaired arithmetic facts but intact conceptual knowledge. A single case study of dyscalculia . Cortex , 31 : 139 – 147 .
   PubMed Web of Science ®Google Scholar
• Hittmair-Delazer , M. , Semenza , C. and Denes , G. 1994 . Concepts and facts in calculation . Brain , 117 : 715 – 728 .
   PubMed Web of Science ®Google Scholar
• Ho , E. D. R. , Tsang , A. K. T. and Ho , D. Y. F. 1991 . An investigation of calendar calculation ability of a Chinese calendar savant . Journal of Autism and Developmental Disorders , 21 : 315 – 327 .
   PubMed Web of Science ®Google Scholar
• Howe , M. J. and Smith , J. 1988 . Calendar calculating in “idiots savants”: How do they do it? . British Journal of Psychology , 79 : 371 – 386 .
   PubMed Web of Science ®Google Scholar
• Hunter , I. M. L. 1962 . An exceptional talent for calculative thinking . British Journal of Psychology , 53 : 243 – 258 .
   PubMed Web of Science ®Google Scholar
• Hunter , I. M. L. 1977 . “ Mental calculation ” . In Thinking. Readings in cognitive science , Edited by: Johnson-Laird , P. N. and Watson , P. C. 35 – 45 . Cambridge : Cambridge University Press .
   Google Scholar
• Hurst , L. C. and Mulhall , D. J. 1988 . Another calendar savant . British Journal of Psychiatry , 152 : 274 – 277 .
   PubMed Web of Science ®Google Scholar
• Jensen , A. R. 1990 . Speed of information processing in a calculating prodigy . Intelligence , 14 : 259 – 274 .
   Web of Science ®Google Scholar
• Kelly , S. J. , Macaruso , P. and Sokol , S. M. 1997 . Mental calculation in an autistic savant: A case study . Journal of Clinical and Experimental Neuropsychology , 19 : 172 – 184 .
   PubMed Web of Science ®Google Scholar
• LeFevre , J. , Bisanz , J. , Daley , K. E. , Buffone , L. , Greenham , S. L. and Sadesky , G. S. 1996 . Multiple route to solution of single-digit multiplication problems . Journal of Experimental Psychology: General , 125 : 384-306
   Web of Science ®Google Scholar
• LeFevre , J. , Sadesky , G. S. and Bisanz , J. 1996 . Selection of procedure in mental addition: Reassessing the problem size effect in adults . Journal of Experimental Psychology: Learning, Memory and Cognition , 22 : 216 – 230 .
   Web of Science ®Google Scholar
• Lemaire , P. and Siegler , R. S. 1995 . Four aspects of strategic change: Contribution to children's learning of multiplication . Journal of Experimental Psychology: General , 124 : 384-306
   Google Scholar
• McCloskey , M. 1992 . Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia . Cognition , 44 : 107 – 157 .
   PubMed Web of Science ®Google Scholar
• McCloskey , M. , Aliminosa , D. and Sokol , S. M. 1991a . Facts, rules, and procedures in normal calculation: Evidence from multiple single-patient studies of impaired arithmetic fact retrieval . Brain and Cognition , 17 : 154 – 203 .
   PubMed Web of Science ®Google Scholar
• McCloskey , M. , Harley , W. and Sokol , S. M. 1991b . Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged subjects . Journal of Experimental Psychology: Learning, Memory and Cognition , 10 : 46 – 60 .
   Google Scholar
• McCloskey , M. and Macaruso , P. 1995 . Representing and using numerical information . American Psychologist , 50 : 351 – 363 .
   PubMed Web of Science ®Google Scholar
• Miller , K. , Perlmutter , M. and Keating , D. 1984 . Cognitive arithmetic: Comparison of operations . Journal of Experimental Psychology: Learning, Memory and Cognition , 10 : 46 – 60 .
   PubMed Web of Science ®Google Scholar
• Milner , B. 1971 . Interhemispheric differences in the localization of psychological processes in man . British Medical Bulletin , 27 : 272 – 277 .
   PubMed Web of Science ®Google Scholar
• Mitchell , F. D. 1907 . Mathematical prodigies . American Journal of Psychology , 18 : 61 – 143 .
   Google Scholar
• O'Connor , N. and Hermelin , B. 1984 . Idiot savant calendrical calculators: Maths or memory? . Psychological Medecine , 14 : 801 – 806 .
   PubMed Web of Science ®Google Scholar
• Power , R. J. D. and Longuet-Higgins , J. C. 1978 . Learning to count: A computational model of language acquisition . Proceedings of the Royal Society of London , 200 : 391 – 417 .
   Google Scholar
• Remond-Besuchet , C. , Noël , M-P. , Seron , X. , Thioux , M. , Brun , M. and Aspe , A. 1999 . Selective preservation of exceptional arithmetical knowledge in a demented patient . Mathematical Cognition , 5 : 41 – 63 .
   Google Scholar
• Russo , J. E. , Johnson , E. J. and Stephens , D. 1989 . The validity of verbal protocols . Memory and Cognition , 17 : 759 – 769 .
   PubMed Web of Science ®Google Scholar
• Sekuler , R. , Rubin , E. and Armstrong , R. 1971 . Processing numerical information: A choice time analysis . Journal Experimental Psychology , 35 : 75 – 80 .
   Google Scholar
• Seron , X. and Noël , M. P. 1995 . Transcoding numbers from arabic code to the verbal one or vice versa: How many routes? . Mathematical Cognition , 1 : 215 – 243 .
   Google Scholar
• Seron , X. , Pesenti , M. , Noël , M. P. , Deloche , G. and Cornet , J-A. 1992 . Images of numbers, or “When 98 is upper left and 6 sky blue” . Cognition , 44 : 159 – 196 .
   PubMed Web of Science ®Google Scholar
• Siegler , R. S. 1987 . The peril of averaging data over strategies: An example from children's addition . Journal of Experimental Psychology: General , 106 : 250 – 264 .
   Web of Science ®Google Scholar
• Siegler , R. S. 1988 . Strategy choice procedures and the development of multiplication skill . Journal of Experimental Psychology: General , 117 : 82 – 138 .
   Web of Science ®Google Scholar
• Siegler , R. S. and Jenkins , E. A. 1989 . How children discover new strategies , Mahwah , NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Siegler , R. S. and Shrager , J. 1984 . “ A model of strategy choice ” . In Origins of cognitive skills , Edited by: Sophian , C. Mahwah , NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Smith , S. B. 1983 . The great mental calculators. The Psychology, methods, and lives of calculating prodigies, Past and Present , New York : Columbia University Press .
   Google Scholar
• Smith , S. B. 1988 . “ Calculating Prodigies ” . In The exceptional brain , Edited by: Obler , L. K. and Fein , D. 19 – 47 . New York : Guilford Press .
   Google Scholar
• Staszewski , J. J. 1988 . “ Skilled memory and expert mental calculation ” . In The nature of expertise , Edited by: Chi , M. T. H. , Glaser , R. and Farr , M. J. Mahwah , NJ : Lawrence Erlbaum Associates, Inc .
   Google Scholar
• Treffert , D. A. 1988 . The idiot savant: A review of the syndrome . American Journal of Psychiatry , 145 : 563 – 572 .
   PubMed Web of Science ®Google Scholar
• Zbrodoff , N. J. and Logan , G. D. 1990 . On the relation between production and verification tasks in the psychology of simple arithmetic . Journal of Experimental Psychology: Learning, Memory and Cognition , 16 : 83 – 97 .
   Web of Science ®Google Scholar