User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

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

Primary tabs

Pesenti, Mauro [UCL] Seron, Xavier [UCL] Samson, Dana [UCL] Duroux, Bruno

We describe the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. The study shows how the highly efficient long-term memory storage and retrieval processes of this calculating prodigy, his knowledge of calculation algorithms, and his good short-term memory capacity all contribute to his calculation expertise. Moreover, his pattern of performance in tasks based on memory retrieval strategies sheds new light on the problem-size/difficulty effect exhibited by normal subjects in basic arithmetical operations. When direct memory retrieval is the only strategy used by this calculating prodigy to answer a problem, the size of the item and the size of the answer do not affect the response latency. This result supports interpretations of the problem-size/difficulty effect in terms of learning and practice, and challenges interpretations in terms of magnitude itself.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 1999
Language Anglais
Journal information "Mathematical Cognition" - Vol. 5, no.2, p. 97-148 (1999)
Peer reviewed yes
issn 1354-6791
e-issn 1464-0724
Publication status Publié
Affiliation UCL - SSH/IPSY - Psychological Sciences Research Institute
Links
  1. Ashcraft Mark H., Cognitive arithmetic: A review of data and theory, 10.1016/0010-0277(92)90051-i
  2. Ashcraft M. H., Journal of Experimental Psychology: Human Learning and Memory, 4, 527 (1978)
  3. Ashcraft Mark H., Christy Kelly S., The Frequency of Arithmetic Facts in Elementary Texts: Addition and Multiplication in Grades 1-6, 10.2307/749430
  4. Babcock Renée L., Salthouse Timothy A., Effects of increased processing demands on age differences in working memory., 10.1037/0882-7974.5.3.421
  5. Barlow F., Mental prodigies (1952)
  6. Bruyer R., European Review of Applied Psychology, 49, 175 (1999)
  7. Campbell J. I. D., Journal of Experimental Psychology: Learning, Memory and Cognition, 13, 109 (1987)
  8. Campbell J. I. D., Mathematical Cognition, 1, 121 (1995)
  9. Campbell Jamie I.D., Clark James M., Chapter 12 Cognitive Number Processing: An Encoding-Complex Perspective, The Nature and Origins of Mathematical Skills (1992) ISBN:9780444890146 p.457-491, 10.1016/s0166-4115(08)60894-8
  10. Campbell Jamie I. D., Graham David J., Mental multiplication skill: Structure, process, and acquisition., 10.1037/h0080065
  11. Charness Neil, Campbell Jamie I. D., Acquiring skill at mental calculation in adulthood: A task decomposition., 10.1037/0096-3445.117.2.115
  12. Chase W. G., The psychology of learning and motivation, 16, 1 (1982)
  13. Dehaene Stanislas, The psychophysics of numerical comparison: A reexamination of apparently incompatible data, 10.3758/bf03208063
  14. Dehaene Stanislas, Varieties of numerical abilities, 10.1016/0010-0277(92)90049-n
  15. Dehaene S., Journal of Experimental Psychology: Human Perception and Performance, 16, 626 (1990)
  16. Dorman Casey, Exceptional calendar calculation ability after early left hemispherectomy, 10.1016/0278-2626(91)90013-x
  17. Ericsson K. Anders, Memory skill., 10.1037/h0080059
  18. Ericsson K. Anders, Kintsch Walter, Long-term working memory., 10.1037/0033-295x.102.2.211
  19. Ericsson K. Anders, Krampe Ralf T., Tesch-Römer Clemens, The role of deliberate practice in the acquisition of expert performance., 10.1037/0033-295x.100.3.363
  20. Ericsson K. A., Lehmann A. C., EXPERT AND EXCEPTIONAL PERFORMANCE: Evidence of Maximal Adaptation to Task Constraints, 10.1146/annurev.psych.47.1.273
  21. Ericsson K. A., Complex information processing. The impact of Herbert A. Simon, 235 (1989)
  22. Faust Michael W., Mathematics Anxiety Effects in Simple and Complex Addition, 10.1080/135467996387534
  23. Fayol M., Revue de Psychologie de l'Education, 3, 87 (1997)
  24. Frensch P. A., Journal of Experimental Psychology: Learning, Memory and Cognition, 19, 433 (1993)
  25. Gallistel C.R., Gelman Rochel, Preverbal and verbal counting and computation, 10.1016/0010-0277(92)90050-r
  26. Giaquinto M., Mathematical Cognition, 1, 61 (1995)
  27. Ginsburg H. P., The development of mathematical thinking, 8 (1983)
  28. Groen Guy J., Parkman John M., A chronometric analysis of simple addition., 10.1037/h0032950
  29. Graham D. Jeffrey, Campbell Jamie I. D., Network interference and number-fact retrieval: Evidence from children's alphaplication., 10.1037/h0084310
  30. Hamann Mary Sue, Ashcraft Mark H., Textbook Presentations of the Basic Addition Facts, 10.1207/s1532690xci0303_2
  31. Hatano Giyoo, Osawa Keiko, Digit memory of grand experts in abacus-derived mental calculation, 10.1016/0010-0277(83)90035-5
  32. Hermelin B., Psychological Medicine, 16, 885 (1986)
  33. Hermelin B., O'Connor N., Idiot savant calendrical calculators: rules and regularities, 10.1017/s0033291700011892
  34. Hinrichs J. V., Journal of Experimental Psychology: Human Perception & Performance, 7, 890 (1981)
  35. Hitch Graham J, The role of short-term working memory in mental arithmetic, 10.1016/0010-0285(78)90002-6
  36. Hittmair-Delazer M., Sailer U., Benke Th., Impaired Arithmetic Facts But Intact Conceptual Knowledge a Single—Case Study of Dyscalculia, 10.1016/s0010-9452(13)80112-8
  37. Hittmair-Delazer M., Semenza C., Denes G., Concepts and facts in calculation, 10.1093/brain/117.4.715
  38. Ho Eric D. F., Tsang Adolf K. T., Ho David Y. F., An investigation of the calendar calculation ability of a Chinese calendar savant, 10.1007/bf02207328
  39. Howe Michael J. A., Smith Julia, Calendar calculating in ‘idiots savants’: How do they do it?, 10.1111/j.2044-8295.1988.tb02296.x
  40. HUNTER IAN M. L., AN EXCEPTIONAL TALENT FOR CALCULATIVE THINKING, 10.1111/j.2044-8295.1962.tb00831.x
  41. Hunter I. M. L., Thinking. Readings in cognitive science, 35 (1977)
  42. Hurst L. C., Mulhall D. J., Another calendar savant, 10.1192/bjp.152.2.274
  43. Jensen Arthur R., Speed of information processing in a calculating prodigy, 10.1016/0160-2896(90)90019-p
  44. Kelly Stephen J., Macaruso Paul, Sokol Scott M., Mental calculation in an autistic savant: A case study, 10.1080/01688639708403848
  45. LeFevre J., Journal of Experimental Psychology: General, 125, 384-306 (1996)
  46. LeFevre J., Journal of Experimental Psychology: Learning, Memory and Cognition, 22, 216 (1996)
  47. Lemaire P., Journal of Experimental Psychology: General, 124, 384-306 (1995)
  48. McCloskey Michael, Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia, 10.1016/0010-0277(92)90052-j
  49. McCloskey Michael, Aliminosa Donna, Sokol Scott M., Facts, rules and procedures in normal calculation: Evidence from multiple single-patient studies of impaired arithmetic fact retrieval, 10.1016/0278-2626(91)90074-i
  50. McCloskey M., Journal of Experimental Psychology: Learning, Memory and Cognition, 10, 46 (1991)
  51. McCloskey Michael, Macaruso Paul, Representing and using numerical information., 10.1037/0003-066x.50.5.351
  52. Miller K., Journal of Experimental Psychology: Learning, Memory and Cognition, 10, 46 (1984)
  53. Milner B., British Medical Bulletin, 27, 272 (1971)
  54. Mitchell Frank D., Mathematical Prodigies, 10.2307/1412172
  55. O'Connor N., Hermelin B., Idiot savant calendrical calculators: maths or memory?, 10.1017/s0033291700019772
  56. Power R. J. D., Longuet-Higgins H. C., Learning to Count: A Computational Model of Language Acquisition, 10.1098/rspb.1978.0024
  57. Remond-Besuchet C., Noel M.-P., Seron X., Thioux M., Brun M., Aspe X., Selective Preservation of Exceptional Arithmetical Knowledge in a Demented Patient, 10.1080/135467999387315
  58. Russo J. Edward, Johnson Eric J., Stephens Debra L., The validity of verbal protocols, 10.3758/bf03202637
  59. Sekuler Robert, Rubin Elliot, Armstrong Robert, Processing numerical information: A choice time analysis., 10.1037/h0031366
  60. Seron X., Mathematical Cognition, 1, 215 (1995)
  61. Seron Xavier, Pesenti Mauro, Noël Marie-Pascale, Deloche Gérard, Cornet Jacques-André, Images of numbers, or “when 98 is upper left and 6 sky blue”, 10.1016/0010-0277(92)90053-k
  62. Siegler Robert S., The perils of averaging data over strategies: An example from children's addition., 10.1037/0096-3445.116.3.250
  63. Siegler R. S., Journal of Experimental Psychology: General, 117, 82 (1988)
  64. Siegler R. S., How children discover new strategies (1989)
  65. Siegler R. S., Origins of cognitive skills (1984)
  66. Smith S. B., The great mental calculators. The Psychology, methods, and lives of calculating prodigies, Past and Present (1983)
  67. Smith S. B., The exceptional brain, 19 (1988)
  68. Staszewski J. J., The nature of expertise (1988)
  69. The idiot savant: a review of the syndrome, 10.1176/ajp.145.5.563
  70. Zbrodoff N. J., Journal of Experimental Psychology: Learning, Memory and Cognition, 16, 83 (1990)
Bibliographic reference Pesenti, Mauro ; Seron, Xavier ; Samson, Dana ; Duroux, Bruno. Basic and Exceptional Calculation Abilities in a Calculating Prodigy: A Case Study. In: Mathematical Cognition, Vol. 5, no.2, p. 97-148 (1999)
Permanent URL http://hdl.handle.net/2078.1/145886