Representing exact number visually using mental abacus

Journal of Experimental Psychology: General

Volumn 141, Issue 1, 2012, Pages 134-149

  Frank, Michael C ^a   Barner, David ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Abacus; Mental arithmetic; Number; Visual cognition

Indexed keywords

ADOLESCENT; ARTICLE; CHILD; FEMALE; HUMAN; IMAGINATION; MALE; MATHEMATICS; PHYSIOLOGY; PRESCHOOL CHILD; PROBLEM SOLVING;

ADOLESCENT; CHILD; CHILD, PRESCHOOL; FEMALE; HUMANS; IMAGINATION; MALE; MATHEMATICS; PROBLEM SOLVING;

EID: 84861748691     PISSN: 00963445     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0024427     Document Type: Article

References (38)

1. Alvarez, G. A., & Cavanagh, P. (2004). The capacity of visual short term memory is set both by visual information load and by number of objects. Psychological Science, 15(2), 106-111. doi:10.1111/j.0963-7214.2004.01502006.x
2. Alvarez, G. A., & Cavanagh, P. (2005). Independent resources for attentional tracking in the left and right visual hemifields. Psychological Science, 16(8), 637-643. doi:10.1111/j.1467-9280.2005.01587.x
3. Atkinson, J., Francis, M. R., & Campbell, F. W. (1976). The dependence of the visual numerosity limit on orientation, colour, and grouping in the stimulus. Perception, 5(3), 335-342. doi:10.1068/p050335
4. Barner, D., Chow, K., & Yang, S.-J. (2009). Finding one's meaning: A test of the relation between quantifiers and integers in language development. Cognitive Psychology, 58(2), 195-219. doi:10.1016/j.cogpsych.2008.07.001
5. Brooks, N. B., Goldin-Meadow, S., Frank, M. C., & Barner, D. (2011). The relationship between gesture and mental imagery: A case study of mental abacus representations. Manuscript in preparation.
6. Chen, F., Hu, Z., Zhao, X., Wang, R., Yang, Z., Wang, X., & Tang, X. (2006). Neural correlates of serial abacus mental calculation in children: A functional MRI study. Neuroscience Letters, 403(1-2), 46-51.
7. Cowan, N. (2000). The magical number 4 in shortterm memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87-185. doi:10.1017/S0140525X01003922
8. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284(5416), 970-974. doi:10.1126/science.284.5416.970
9. Feigenson, L. (2008). Parallel non-verbal enumeration is constrained by a setbased limit. Cognition, 107(1), 1-18. doi:10.1016/j.cognition.2007.07.006
10. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314. doi:10.1016/j.tics.2004.05.002
11. Feigenson, L., & Halberda, J. (2008). Conceptual knowledge increases infants' memory capacity. Proceedings of the National Academy of Sciences of the United States of America, 105(29), 9926-9930. doi: 10.1073/pnas.0709884105
12. Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819-824. doi:10.1016/j.cognition.2008.04.007
13. Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge, England: Cambridge University Press.
14. Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394-406. doi:10.1016/j.cognition.2010.02.002
15. Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496-499. doi:10.1126/science.1094492
16. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665-668. doi:10.1038/nature07246
17. Halberda, J., Sires, S. F., & Feigenson, L. (2006). Multiple spatially overlapping sets can be enumerated in parallel. Psychological Science, 17(7), 572-576. doi:10.1111/j.1467-9280.2006.01746.x
18. Hatano, G., Amaiwa, S., & Shimizu, K. (1987). Formation of a mental abacus for computation and its use as a memory device for digits: A developmental study. Developmental Psychology, 23(6), 832-838. doi: 10.1037/0012-1649.23.6.832
19. Hatano, G., Myake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5(1), 47-55. doi:10.1016/0010-0277(77)90016-6
20. Hatano, G., & Osawa, K. (1983). Digit memory of grand experts in abacus-derived mental calculation. Cognition, 15(1-3), 95-110. doi: 10.1016/0010-0277(83)90035-5
21. Hishitani, S. (1990). Imagery experts: How do expert abacus operators process imagery? Applied Cognitive Psychology, 4(1), 33-46. doi: 10.1002/acp.2350040104
22. Hu, Y., Geng, F., Tao, L., Hu, N., Du, F., Fu, K., & Chen, F. (2011). Enhanced white matter tracts integrity in children with abacus training. Human Brain Mapping, 32(1), 10-21. doi:10.1002/hbm.20996
23. Kojima, T. (1954). The Japanese abacus: Its use and theory. Tokyo, Japan: Tuttle.
24. Lee, Y., Lu, M., & Ko, H. (2007). Effects of skill training on working memory capacity. Learning and Instruction, 17(3), 336-344. doi: 10.1016/j.learninstruc.2007.02.010
25. Levitt, H. (1971). Transformed up-down methods in psychoacoustics. Journal of the Acoustical Society of America, 49(2), 467-477. doi: 10.1121/1.1912375
26. Luck, S. J., & Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature, 390(6657), 279-281. doi: 10.1038/36846
27. Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology, 111(1), 1-22. doi:10.1037/0096-3445.111.1.1
28. Menninger, K. (1969). Number words and number symbols: A cultural history of numbers. Cambridge, MA: MIT Press.
29. Miller, K. F., & Stigler, J. W. (1991). Meanings of skill: Effects of abacus expertise on number representation. Cognition and Instruction, 8(1), 29-67. doi:10.1207/s1532690xci0801_2
30. Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499-503. doi:10.1126/science.1102085
31. Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. New York, NY: Springer.
32. Stigler, J. W. (1984). "Mental abacus": The effect of abacus training on Chinese children's mental calculation. Cognitive Psychology, 16(2), 145-176. doi:10.1016/0010-0285(84)90006-9
33. Stigler, J. W., Chalip, L., & Miller, K. F. (1986). Consequences of skill: The case of abacus training in Taiwan. American Journal of Education, 94(4), 447-479. doi:10.1086/443862
34. Tanaka, S., Michimata, C., Kaminaga, T., Honda, M., & Sadato, N. (2002). Superior digit memory of abacus experts: An event-related functional MRI study. NeuroReport, 13(17), 2187-2191. doi:10.1097/00001756-200212030-00005
35. Van Oeffelen, M. P., & Vos, P. G. (1982). Configurational effects on the enumeration of dots: Counting by groups. Memory & Cognition, 10(4), 396-404. doi:10.3758/BF03202432
36. Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal counting in humans: The psychophysics of number representation. Psychological Science, 10(2), 130-137. doi:10.1111/1467-9280.00120
37. Wynn, K. (1990). Children's understanding of counting. Cognition, 36(2), 155-193. doi:10.1016/0010-0277(90)90003-3
38. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1-B11. doi:10.1016/S0010-0277(99) 00066-9