(No) small adults: Children's processing of carry addition problems

Developmental Neuropsychology

Volumn 36, Issue 6, 2011, Pages 702-720

  Moeller, Korbinian ^a,b   Klein, Elise ^a,c   Nuerk, Hans Christoph ^b,c  

^a KNOWLEDGE MEDIA RESEARCH CENTER   (Germany)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c UNIVERSITY HOSPITAL RWTH AACHEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARTICLE; CHILD; CHILD DEVELOPMENT; COMPARATIVE STUDY; ELECTROOCULOGRAPHY; EYE FIXATION; EYE MOVEMENT; FEMALE; HUMAN; MALE; MATHEMATICAL PHENOMENA; PHYSIOLOGY; PROBLEM SOLVING; PSYCHOLOGICAL ASPECT; REACTION TIME; READING; VISION;

ADULT; CHILD; CHILD DEVELOPMENT; ELECTROOCULOGRAPHY; EYE MOVEMENTS; FEMALE; FIXATION, OCULAR; HUMANS; MALE; MATHEMATICAL CONCEPTS; PROBLEM SOLVING; REACTION TIME; READING; VISUAL PERCEPTION; YOUNG ADULT;

EID: 79960508560     PISSN: 87565641     EISSN: None     Source Type: Journal    
DOI: 10.1080/87565641.2010.549880     Document Type: Article

References (47)

1. Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. Neuro Report, 16, 1769-1773. (Pubitemid 41547044)
2. Barrouillet, P., & Fayol, M. (1998). Fromalgorithmic computing to directretrieval: Evidencefrom number and alphabetic arithmetic in children and adults. Memory & Cognition, 26, 355-368. (Pubitemid 28191345)
3. Blythe, H. I., Liversedge, S. P., Joseph, H S., White, S. J., & Rayner, K. (2009). Visual information capture during fixations in reading for children and adults. Vision Research, 49, 1583-1591.
4. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K.A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4, e125.
5. Deschuyteneer, M., De Rammelaere, S., & Fias, W. (2005). The addition of two-digit numbers: Exploring carry versus no-carry problems. Psychology Science, 47, 74-83.
6. Domahs, F., Delazer, M., & Nuerk, H.-C. (2006). What makes multiplication facts difficult. Experimental Psychology, 53, 275-282.
7. Domahs, F., Domahs, U., Schlesewsky, M., Ratinckx, E., Verguts, T., Willmes, K., & Nuerk, H.-C. (2007). Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence. Behavioral and Brain Functions, 3, 66. doi:10.1186/1744-9081-3-66 (Pubitemid 351359633)
8. Feng, G., Miller, K., Shu, H., & Zhang, H. (2009). Ortography and the development of reading processes: An eye- movement study of Chinese and English. Child Development, 80, 720-735.
9. Fürst, A. J., & Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition, 28, 774-782. (Pubitemid 30664112)
10. Green, H. J., Lemaire, P., & Dufau, S. (2007). Eye movement correlates of younger and older adults' strategies for complex addition. Acta Psychologica, 125, 257-278.
11. Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96, 284-309.
12. Imbo, I., & Vandierendonck, A. (2008). Effects of problem size, operation, and working memory span on simple- arithmetic strategies: differences between children and adults? Psychological Research, 72, 331-346.
13. Imbo, I., Vandierendonck, A., & De Rammelaere, S. (2007). The role of working memory in the carry operation of mental arithmetic: Number and value of the carry. The Quarterly Journal of Experimental Psychology, 60, 708-731.
14. Joseph, H. S., Liversedge, S. P., Blythe, H. I., White, S.J.,& Rayner, K. (2009). Word length and landing position effect during reading in children and adults. Vision Research, 49, 2078-2086.
15. Kalaman, D., & LeFevre, J. A. (2007). Working memory demands of exact and approximate addition. European Journal of Cognitive Psychology, 19, 187-212.
16. Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L. B.,... Ischebeck, A. (2006). Neural correlates of the number-size interference task in children. Neuro Report, 17, 587-591.
17. Kawashima, R., Taira, M., Okita, K., Inoue, K., Tajima, N., Yoshida, H.,. .. Fukuda, H. (2004). Afunctional MRI study of simple arithmetic\-A comparison between children and adults. Cognitive Brain Research, 18, 227-233.
18. Kazui, H., Kitagaki, H., & Mori, E. (2000). Cortical activation during retrieval of arithmetic facts and actual calculation: A functional magnetic resonance imaging study. Psychiatry and Clinical Neurosciences, 54, 479-485.
19. Klein, E., Moeller, K., Dressel, K., Domahs, F., Wood, G., Willmes, K., & Nuerk, H.-C. (2010). To carry or not to carry\-Is this the question? Disentangling the carry effect in multi-digit addition. Acta Psychologica, 135, 67-76.
20. Klein, E., Nuerk, H.-C., Wood, G., Knops, A., & Willmes, K. (2009). The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition. Brain and Cognition, 2, 369-381.
21. Kong, J., Wang, C., Kwong, K., Vangel, M., Chuac, E., & Gollub, R. (2005). The neural substrate of arithmetic operations and procedure complexity. Cognitive Brain Research, 22, 397-405. (Pubitemid 40276806)
22. Kucian, K., & Kaufmann, L. (2009). A developmental model of number representation. Behavioral and Brain Sciences, 32, 340-341.
23. Kucian, K., von Aster, M., Loenneker, T., Dietrich, T., & Martin, E. (2008). Development of neural networks for exact and approximate calculation: AFMRI study. Developmental Neuropsychology, 33, 447-473. (Pubitemid 351883461)
24. Mann, A., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2011). Attentional strategies in place-value integra- tion: A longitudinal study on two-digit number comparison. Zeitschriftfür Psychologie/Journal ofPsychology, 219, 42-49.
25. McConkie, G. W., Zola, D., Grimes, J., Kerr, P. W., Bryant, N. R., & Wolff, P. M. (1991). Children's eye movements during reading. In J. F. Stein (Ed.), Vision and visual dyslexia (pp. 251-262). London, England: Macmillan.
26. Miller, E. K. (2000). The prefrontal cortex and cognitive control. Nature Reviews Neuroscience, 1, 58-65.
27. Moeller, K., Fischer, M. H., Nuerk, H.-C., & Willmes, K. (2009). Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking. The Quarterly Journal of Experimental Psychology, 62, 323-334.
28. Moeller, K., Klein, E., & Nuerk, H.-C. (in press). On the cognitive instantiation of the carry effect in addition\-Evidence from eye-tracking. British Journal of Psychology.
29. Moeller, K., & Nuerk, H.-C. (2009). On the cognitive instantiation of the carry operation in addition. Evidence from eyetracking. Poster presented at the 27th European Workshop of Cognitive Neuropsychology, Bressanone, Italy, January 25-30, 2008.
30. Nuerk, H.-C., Geppert, B. E., van Herten, M., & Willmes, K. (2002). On the impact of different number representations in the number bisection task. Cortex, 38, 691-715. (Pubitemid 36007897)
31. Nuerk, H.-C., Graf, M., & Willmes, K. (2006). Grundlagen der Zahlenverarbeitung und des Rechnens. Sprache, Stimme, Gehoer, 30, 1-7.
32. Nuerk, H.-C., Kaufmann, L., Zoppoth, S., & Willmes, K. (2004). On the development of the mental number line: More, less, or neverholistic withincreasing age?Developmental Psychology, 40, 1199-1211.
33. Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line\-A review of multi-digit number processing. Zeitschriftfür Psychologie/Journal of Psychology, 219, 3-22.
34. Nuerk, H. C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition, 82, B25-33. (Pubitemid 32979189)
35. Nuerk, H.-C., & Willmes, K. (2005). On the magnitude representations of two-digit numbers. Psychology Science, 47, 52-72.
36. Pixner, S., Moeller, K., Zuber, J., & Nuerk, H.-C. (2009). Decomposed but parallel processing of two-digit numbers in 1st graders. The Open Psychology Journal, 2, 40-48.
37. Ratinckx, E., Nuerk, H.-C., van Dijk J.-P., & Willmes, K. (2006). Effects of interhemispheric interaction on two-digit Arabic numberprocessing. Cortex, 42, 1128-1137. (Pubitemid 44941598)
38. Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research. Psychological Bulletin, 124, 372-422. (Pubitemid 128461792)
39. Rayner, K., & Pollatesk, A. (1989). Thepsychology ofreading. Englewood Cliffs, NJ: Prentice Hall.
40. 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. (Pubitemid 41447043)
41. Salman, M. S., Sharpe, J. A., Eizenman, M., Lillakas, L., Westall, C., To, T.,... Steinbach, M. J. (2006). Saccades in children. Vision Research, 46, 1432-1439. (Pubitemid 43075318)
42. Siegler, R. S., & Shipley, C. (1995). Variation, selection, and cognitive change. In T. Simon and G. Halford (Eds.), Developing cognitive competence: New approaches toprocess modelling (pp. 31-76). Hillsdale, NJ: Erlbaum.
43. Torbeyns, J., Verschavel, L., & Ghesquiere, P. (2002). Strategic competence: Applying Siegler's theoretical and methodological framework to the domain of simple addition. European Journal of Psychology of Education, 17, 275-292.
44. Verguts, T., & De Moor, W. (2005). Two-digit comparison decomposed, holistic or hybrid? Experimental Psychology, 52, 195-200.
45. von Aster, M., & Shalev, R. (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49, 868-873. (Pubitemid 350020450)
46. Wood, G., Ischebeck, A., Koppelstaetter, F., Gotwald, T., & Kaufmann, L. (2009). Developmental trajectories of magnitude processing and interference control: An fMRI study. Cerebral Cortex, 19, 2755-2765.
47. Zago, L., Pesenti, M., Mellet, E., Crivello, F., Mazoyer, B., & Tzourio-Mazoyer, N. (2001). Neural correlates of simple and complex mental calculation. Neuro Image, 13, 314-327. (Pubitemid 34185020)