Development of neural networks for exact and approximate calculation: A fMRI study

Developmental Neuropsychology

Volumn 33, Issue 4, 2008, Pages 447-473

  Kucian, Karin ^a   Von Aster, Michael ^a,b,c   Loenneker, Thomas ^c   Dietrich, Thomas ^a   Martin, Ernst ^a  

^a UNIVERSITY CHILDREN S HOSPITAL   (Switzerland)

^b German Red Cross Hospitals Westend   (Germany)

^c UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARTICLE; ATTENTION; CINGULATE GYRUS; CONTROLLED STUDY; FEMALE; FRONTAL LOBE; FUNCTIONAL MAGNETIC RESONANCE IMAGING; HUMAN; HUMAN EXPERIMENT; MALE; NERVE CELL NETWORK; NEUROIMAGING; NORMAL HUMAN; OCCIPITAL LOBE; PRIORITY JOURNAL; SCHOOL CHILD; SUBICULUM; WORKING MEMORY;

ADOLESCENT; ADULT; AGE FACTORS; BRAIN; BRAIN MAPPING; CHILD; FEMALE; HUMAN DEVELOPMENT; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; MALE; MATHEMATICS; MENTAL PROCESSES; NEURAL PATHWAYS; OXYGEN; REACTION TIME; SEX FACTORS;

EID: 45849107583     PISSN: 87565641     EISSN: None     Source Type: Journal    
DOI: 10.1080/87565640802101474     Document Type: Article

References (78)

1. Adams, J., & Hitch, G. (1997). Working memory and children's mental addition. Journal of Experimental Child Psychology, 67, 21-38.
2. Adleman, N., Menon, V., Blasey, C., White, C., Warsofsky, I., Glover, G., et al. (2002). A developmental fMRI study of the Stroop color-word task. NeuroImage, 16, 61-75.
3. Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. Neuroreport, 16, 1769-1773.
4. Ansari, D., & Karmiloff-Smith, A. (2002). Atypical trajectories of number development: A neuroconstructivist perspective. TRENDS in Cognitive Sciences, 6, 511-516.
5. Antell, S., & Keating, D. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695-701.
6. Ashcraft, M. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213-236.
7. Ashcraft, M., & Stazyk, E. (1981). Mental addition: A test of three verification models. Memory & Cognition, 9, 185-196.
8. Barch, D. (1999). Images in neuroscience. Cognition: The anterior cingulate and response conflict. American Journal of Psychiatry, 156, 1849.
9. Barch, D., Braver, T., Akbudak, E., Conturo, T., Ollinger, J., & Snyder, A. (2001). Anterior cingulate cortex and response conflict: Effects of response modality and processing domain. Cerebral Cortex, 11, 837-848.
10. Barch, D., Braver, T., Sabb, F., & Noll, D. (2000). Anterior cingulate and the monitoring of response conflict: Evidence from an fMRI study of overt verb generation. Journal of Cognitive Neuroscience, 12, 298-309.
11. Baroody, A. (1987). Development of counting strategies for single-digit addition. Journal of Education in Mathematics Education, 18, 141-157.
12. Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the U S A, 102, 14116-14121.
13. Burbaud, P., Camus, O., Guehl, D., Bioulac, B., Caille, J., & Allard, M. (2000). Influence of cognitive strategies on the pattern of cortical activation during mental subtraction. A functional imaging study in human subjects. Neuroscience Letters, 287, 76-80.
14. Carter, C. S., Braver, T. S., Barch, D. M., Botvinick, M. M., Noll, D., & Cohen, J. D. (1998). Anterior cingulate cortex, error detection, and the online monitoring of performance. Science, 280, 747-749.
15. Casey, B. J. (2002). Windows into the human brain. Science, 296, 1408-1409.
16. Chochon, F., Cohen, L., van de Moortele, P. F., & Dehaene, S. (1999). Differential contributions of the left and right inferior parietal lobules to number processing. Journal of Cognitive Neuroscience, 11, 617-630.
17. Cohen, L., Dehaene, S., Chochon, F., Lehéricy, S., & Naccache, L. (2000). Language and calculation within the parietal lobe: A combined cognitive, anatomical and fMRI study. Neuropsychologia, 38, 1426-1440.
18. Cohen Kadosh, R., Henik, A., Rubinsten, O., Mohr, H., Dori, H., van de Ven, V., et al. (2005). Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia, 43, 1238-1248.
19. Cowell, S. F., Egan, G. F., Code, C., Harasty, J., & Watson, J. D. (2000). The functional neuroanatomy of simple calculation and number repetition: A parametric PET activation study. NeuroImage, 12, 565-573.
20. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.
21. Dehaene, S., & Cohen, J. D. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.
22. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219-250.
23. Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. TRENDS in Neuroscience, 21, 355-361.
24. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970-974.
25. Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., et al. (2003). Learning complex arithmetic - An fMRI study. Brain Research Cognitive Brain Research, 18, 76-88.
26. Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience, 15, 47-56.
27. Gaillard, W. D., Grandin, C. B., & Xu, B. (2001). Developmental aspects of pediatric fMRI: Considerations for image acquisition, analysis, and interpretation. NeuroImage, 13, 239-249.
28. Genovese, C. R., Lazar, N. A., & Nichols, T. (2002). Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage, 15, 870-878.
29. Gerton, B. K., Brown, T. T., Meyer-Lindenberg, A., Kohn, P., Holt, J. L., Olsen, R. K., et al. (2004). Shared and distinct neurophysiological components of the digits forward and backward tasks as revealed by functional neuroimaging. Neuropsychologia, 42, 1781-1787.
30. Gogtay, N., Giedd, J. N., Lusk, L., Hayashi, K. M., Greenstein, D., Vaituzis, A. C., et al. (2004). From the cover: Dynamic mapping of human cortical development during childhood through early adulthood. Proceedings of the National Academy of Sciences of the U S A, 101, 8174-8179.
31. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496-499.
32. Halder, P., Brem, S., Bucher, K., Boujraf, S., Summers, P., Dietrich, T., et al. (2006). Electrophysiological and hemodynamic evidence for late maturation of hand power grip and force control under visual feedback. Human Brain Mapping, 28, 69-84.
33. Hauser, M. D., & Carey, S. (2003). Spontaneous representations of small numbers of objects by rhesus macaques: Examinations of content and format. Cognitive Psychology, 47, 367-401.
34. Hauser, M. D., Carey, S., & Hauser, L. B. (2000). Spontaneous number representation in semi-free-ranging rhesus monkeys. Proceedings of the Royal Society of London Series B-Biological Sciences, 267, 829-833.
35. Hauser, M. D., Tsao, F., Garcia, P., & Spelke, E. S. (2003). Evolutionary foundations of number: Spontaneous representation of numerical magnitudes by cotton-top tamarins. Proceedings of the Royal Society of London Series B-Biological Sciences, 270, 1441-1446.
36. Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg, P., Golaszewski, S., et al. (2005). Neural correlates of distance and congruity effects in a numerical Stroop task: An event-related fMRI study. NeuroImage, 25, 888-898.
37. Kawashima, R., Taira, M., Okita, K., Inoue, K., Tajima, N., Yoshida, H., et al. (2004). A functional MRI study of simple arithmetic - a comparison between children and adults. Brain Research Cognitive Brain Research, 18, 227-233.
38. Kazui, H., Kitagaki, H., & Mori, E. (2000). Cortical activation during retrieval of arithmetical facts and actual calculation: A functional magnetic resonance imaging study. Psychiatry and Clinical Neurosciences, 54, 479-485.
39. Klassencockpit. (Ausgabe 2003/2004). MS_Deutsch_61, MS_Mathematik_61. Rorschach: Kantonaler Lehrmittelverlag St. Gallen.
40. Klingberg, T., Forssberg, H., & Westerberg, H. (2002). Increased brain activity in frontal and parietal cortex underlies the development of visuospatial working memory capacity during childhood. Journal of Cognitive Neuroscience, 14, 1-10.
41. Kwon, H., Reiss, A. L., & Menon, V. (2002). Neural basis of protracted developmental changes in visuo-spatial working memory. Proceedings of the National Academy of Sciences of the U S A, 99, 13336-13341.
42. Lancaster, J. L., Woldorff, M. G., Parsons, L. M., Liotti, M., Freitas, C. S., Rainey, L., et al. (2000). Automated Talairach atlas labels for functional brain mapping. Human Brain Mapping, 10, 120-131.
43. Landerl, K., Wimmer, H., & Moser, E. (1997). Salzburger Lese- und Rechtschreibtest. Verfahren zur Differentialdiagnose von Störungen des Lesens und Schreibens für die 1. bis 4. Schulstufe. Bern: Huber.
44. Lawrence, N. S., Ross, T. J., Hoffmann, R., Garavan, H., & Stein, E. A. (2003). Multiple neuronal networks mediate sustained attention. Journal of Cognitive Neuroscience, 15, 1028-1038.
45. Le Fevre, J. A., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory and Cognition, 32, 216-230.
46. Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41, 1942-1958.
47. Lucangeli, D., Tressoldi, P. E., Bendotti, M., Bonanomi, M., & Siegel, L. S. (2003). Effective strategies for mental and written arithmetic calculation from the third to the fifth grade. Educational Psychology, 23, 507-520.
48. Marx, H. (1998). Knuspels Leseaufgaben. Gruppenlesetest für Kinder Ende des ersten bis vierten Schuljahres. Göttingen: Hogrefe.
49. Menon, V., Rivera, S. M., White, C. D., Glover, G. H., & Reiss, A. L. (2000). Dissociating prefrontal and parietal cortex activation during arithmetic processing. NeuroImage, 12, 357-365.
50. Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40, 847-858.
51. Pardo, J. V., Pardo, P. J., Janer, K. W., & Raichle, M. E. (1990). The anterior cingulate cortex mediates processing selection in the Stroop attentional conflict paradigm. Proceedings of the National Academy of Sciences of the U S A, 87, 256-259.
52. Pesenti, M., Thioux, M., Seron, X., & De Volder, A. (2000). Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: A PET study. Journal of Cognitive Neuroscience, 12, 461-479.
53. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499-503.
54. Pinel, P., Dehaene, S., Riviere, D., & LeBihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. NeuroImage, 14, 1013-1026.
55. Pinel, P., Le Clec, H. G., van de Moortele, P. F., Naccache, L., Le Bihan, D., & Dehaene, S. (1999). Event-related fMRI analysis of the cerebral circuit for number comparison. Neuroreport, 10, 1473-1479.
56. Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron, 41, 983-993.
57. Qin, Y., Carter, C. S., Silk, E. M., Stenger, V. A., Fissell, K., Goode, A., et al. (2004). The change of the brain activation patterns as children learn algebra equation solving. Proceedings of the National Academy of Sciences of the U S A, 101, 5686-5691.
58. Raichle, M. E., MacLeod, A. M., Snyder, A. Z., Powers, W. J., Gusnard, D. A., & Shulman, G. L. (2001). A default mode of brain function. Proceedings of the National Academy of Sciences of the U S A, 98, 676-682.
59. Rickard, T. C., Romero, S. G., Basso, G., Wharton, C., Flitman, S., & Grafman, J. (2000). The calculating brain: An fMRI study. Neuropsychologia, 38, 325-335.
60. Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15, 1779-1790.
61. Schlaggar, B. L., Brown, T. T., Lugar, H. M., Visscher, K. M., Miezin, F. M., & Petersen, S. E. (2002). Functional neuroanatomical differences between adults and school-age children in the processing of single words. Science, 296, 1476-1479.
62. Schmithorst, V. J., & Brown, R. D. (2004). Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions. NeuroImage, 22, 1414-1420.
63. Siegler, R. S. (1988). Individual differnces in strategy choices: Good students, not-so-good students and perfectionists. Child Development, 59, 833-851.
64. Sowell, E. R., Peterson, B. S., Thompson, P. M., Welcome, S. E., Henkenius, A. L., & Toga, A. W. (2003). Mapping cortical change across the human life span. Nature Neuroscience, 6, 309-315.
65. Sowell, E. R., Thompson, P. M., Leonard, C. M., Welcome, S. E., Kan, E., & Toga, A. W. (2004). Longitudinal mapping of cortical thickness and brain growth in normal children. Journal of Neuroscience, 24, 8223-8231.
66. Starkey, P., & Cooper, R. G., Jr. (1980). Perception of numbers by human infants. Science, 210, 1033-1035.
67. Talairach, J., & Tournoux, P. (1988). Co-planar stereotaxic atlas of the human brain: 3-dimensional proportional system: An approach to cerebral imaging. Stuttgart: Thieme Medical Publisher.
68. Tamm, L., Menon, V., & Reiss, A. L. (2002). Maturation of brain function associated with response inhibition. Journal of the American Academy of Child and Adolescent Psychiatry, 41, 1231-1238.
69. Temple, E., & Posner, M. I. (1998). Brain mechanisms of quantity are similar in 5-year-old children and adults. Proceedings of the National Academy of Sciences of the U S A, 95, 7836-7841.
70. Unterrainer, J., Wranek, U., Staffen, W., Gruber, T., & Ladurner, G. (2000). Lateralized cognitive visuospatial processing: Is it primarily gender-related or due to quality of performance? Neuropsychobiology, 41, 95-101.
71. van Harskamp, N. J., Rudge, P., & Cipolotti, L. (2002). Are multiplication facts implemented by the left supramarginal and angular gyri? Neuropsychologia, 40, 1786-1793.
72. Venkatraman, V., Ansari, D., & Chee, M. W. (2005). Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia, 43, 744-753.
73. von Aster, M. (2001). ZAREKI (Neuropsychological Test Battery for Number Processing and Calculation in Children). Lisse, Frankfurt am Main: Swets & Zeitlinger.
74. WMA. (2002). The World Medical Association's Declaration of Helsinki: Ethical Principles for Medical Research Involving Human Subjects. Washington: WMA General Assembly.
75. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749-750.
76. Wynn, K., Bloom, P., & Chiang, W. C. (2002). Enumeration of collective entities by 5-month-old infants. Cognition, 83, B55-62.
77. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1-B11.
78. Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8, 88-101.