珠心算的数字表征机制及珠心算练习对儿童数量加工的影响
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摘要
学习是人类与生俱来的一种能力,是人类全面发展的基础。学习是个体在特别情境下,由于练习或反复体验而产生的行为、能力或倾向上的比较持久的变化及其过程。学习的过程实际上就是对某一个特定程序或操作进行不断练习或者训练的过程。珠心算是指对算盘的练习时间较长后,练习者能够在脑海中虚拟出一个算盘,从而脱离实际的算盘操作,用这个虚拟的算盘来实现对数字的操作的计算方法。珠心算训练可以使人在不借助任何工具的情况下进行快速、准确地计算。与传统的心算相比,珠心算能够处理更加复杂的计算任务,也更加快速、准确。脑功能磁共振成像在空间维度上的研究发现,珠心算专家在大脑中是以“虚拟珠像”的方式来对数字进行表征的。本研究以事件相关电位技术为手段,从时间维度对经过珠心算训练后儿童的数字认知能力进行系统的研究。
本研究由三部分组成,第一部分以接受近两年和四年珠心算训练的儿童为研究对象,与接受常规教育的对照组儿童(不接受任何珠算训练)进行比较,通过不同表现形式的数字与5进行比较的实验,考察了珠心算训练对数字加工的符号效应和距离效应的影响。第二部分通过数字的Stroop实验范式考察了经过珠心算训练后儿童对阿拉伯数字和珠像数字的自动加工。第三部分考察了经过近两年珠心算训练后,儿童基本数学能力的变化以及执行功能与数学能力的关系。
本研究主要得到以下结论：
(1)中国儿童对数字的加工存在符号效应和距离效应；对数量加工的距离效应是普遍的,依赖于数量的表现形式；珠心算的训练并没有使距离效应消失或发生明显改变。
(2)经过近两年的珠心算训练后,珠心算组儿童对数字的加工与对照组儿童存在差异,他们可能采取了视觉加工的策略；经过四年的珠心算训练后,儿童建立了珠像与其代表的数值之间的联系,能够对珠像数字进行自动加工。
(3)珠心算组与对照组儿童的数学运算能力、逻辑思维与空间-视觉能力、总数学能力都存在显著差异；珠心算组与对照组儿童都存在空间兼容效应；经过近两年的珠心算训练后,儿童对冲突的抑制能力有减弱的趋势；珠心算的训练与儿童的转换能力密切相关。
Human beings are born with the ability of learning, which is the basis of human development. Learning is a course that individual repeats a practice or experience in a specifically instance, and the course can make the behavior, ability or tendency of the human change for long. Actually, the process of learning is a continuously process of practice or learning toward a given procedure. Abacus-based mental calculation(AMC) is a method of calculation that users can calculate by manipulating a imagery abacus in the brain. The imagery abacus was formed in the brain of AMC trainees after a long period of training. The training can make people calculate rapidly and exactly without the help of any actual tools. Comparing to traditional mental calculations, the tasks that the AMC processed are more complex, rapid and nicety. The functional magnetic image(fMRI) studies, which concerned the spatial dimension have found that the AMC trainees represent numbers by an imagery abacus in the brain. The present study attempts to explore the ability of numerical cognition of children from the temporal dimension after a long term AMC training, by adopting the event-related potentials(ERP) technology.
This study was composed of three parts. The first part investigated the notion effect and the influence to the magnitude processing after long term AMC practice. Children that accepted about2and4years'AMC trainings participated in the experiment, and they were asked to compare numbers to5with numbers in different notations. In the second part, we investigated the automatic process to Arabic numbers and abacus numbers of children after AMC trainings by adopting the numerical Stroop paradigm. In the third part,we investigated the changes of the mathematics ability and the relation between executive function and mathematics ability of children after about two years'training of AMC.
The main findings of our study were as follows:
(1) We found the notation effect and distance effect in the Chinese children when they process magnitudes; the distance effect of the magnitude was universal and notation-dependent; the practice of AMC didn't make the distance effect disappear or change dramatically.
(2) The Chinese children can process Arabic numbers automatically in the second grade; the strategy of number processing of the children changed after about2years' AMC trainings; children have developed a direct connection between the abacus beads and magnitudes, and they processed the abacus numbers automatically after4years'AMC trainings.
(3) The mathematics ability of the AMC group was significantly different from the control; the AMC children and the control both showed the spatial compatibility effect; the ability of inhibition to the conflict attribute was tend to be decreased after about2years' AMC trainings; the ability of transfer between tasks was related a lot to the AMC trainings for the AMC children.
本研究由三部分组成,第一部分以接受近两年和四年珠心算训练的儿童为研究对象,与接受常规教育的对照组儿童(不接受任何珠算训练)进行比较,通过不同表现形式的数字与5进行比较的实验,考察了珠心算训练对数字加工的符号效应和距离效应的影响。第二部分通过数字的Stroop实验范式考察了经过珠心算训练后儿童对阿拉伯数字和珠像数字的自动加工。第三部分考察了经过近两年珠心算训练后,儿童基本数学能力的变化以及执行功能与数学能力的关系。
本研究主要得到以下结论：
(1)中国儿童对数字的加工存在符号效应和距离效应；对数量加工的距离效应是普遍的,依赖于数量的表现形式；珠心算的训练并没有使距离效应消失或发生明显改变。
(2)经过近两年的珠心算训练后,珠心算组儿童对数字的加工与对照组儿童存在差异,他们可能采取了视觉加工的策略；经过四年的珠心算训练后,儿童建立了珠像与其代表的数值之间的联系,能够对珠像数字进行自动加工。
(3)珠心算组与对照组儿童的数学运算能力、逻辑思维与空间-视觉能力、总数学能力都存在显著差异；珠心算组与对照组儿童都存在空间兼容效应；经过近两年的珠心算训练后,儿童对冲突的抑制能力有减弱的趋势；珠心算的训练与儿童的转换能力密切相关。
Human beings are born with the ability of learning, which is the basis of human development. Learning is a course that individual repeats a practice or experience in a specifically instance, and the course can make the behavior, ability or tendency of the human change for long. Actually, the process of learning is a continuously process of practice or learning toward a given procedure. Abacus-based mental calculation(AMC) is a method of calculation that users can calculate by manipulating a imagery abacus in the brain. The imagery abacus was formed in the brain of AMC trainees after a long period of training. The training can make people calculate rapidly and exactly without the help of any actual tools. Comparing to traditional mental calculations, the tasks that the AMC processed are more complex, rapid and nicety. The functional magnetic image(fMRI) studies, which concerned the spatial dimension have found that the AMC trainees represent numbers by an imagery abacus in the brain. The present study attempts to explore the ability of numerical cognition of children from the temporal dimension after a long term AMC training, by adopting the event-related potentials(ERP) technology.
This study was composed of three parts. The first part investigated the notion effect and the influence to the magnitude processing after long term AMC practice. Children that accepted about2and4years'AMC trainings participated in the experiment, and they were asked to compare numbers to5with numbers in different notations. In the second part, we investigated the automatic process to Arabic numbers and abacus numbers of children after AMC trainings by adopting the numerical Stroop paradigm. In the third part,we investigated the changes of the mathematics ability and the relation between executive function and mathematics ability of children after about two years'training of AMC.
The main findings of our study were as follows:
(1) We found the notation effect and distance effect in the Chinese children when they process magnitudes; the distance effect of the magnitude was universal and notation-dependent; the practice of AMC didn't make the distance effect disappear or change dramatically.
(2) The Chinese children can process Arabic numbers automatically in the second grade; the strategy of number processing of the children changed after about2years' AMC trainings; children have developed a direct connection between the abacus beads and magnitudes, and they processed the abacus numbers automatically after4years'AMC trainings.
(3) The mathematics ability of the AMC group was significantly different from the control; the AMC children and the control both showed the spatial compatibility effect; the ability of inhibition to the conflict attribute was tend to be decreased after about2years' AMC trainings; the ability of transfer between tasks was related a lot to the AMC trainings for the AMC children.
引文
Abel, S., Rushworth, M.,& Walsh, V. (2001). rTMS disrupts the representation of small numbers in supramarginal gyrus. Neurolmage,13(6, Supplement),409.
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.
Antell, S. E.;& Keating, D. P. (1983). Perception of numerical invariance in neonates. Child development,54(3),695-701.
Ashcraft, M. H. (1992). Cognitive arithmetic:a review of data and theory. Cognition, 44(1-2),75-106.
Awh, E.,& Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. Trends in cognitive sciences,5(3),119-126.
Barrouillet, P., Fayol, M.,& Lathuliere, E. (1997). Selecting between Competitors in Multiplication Tasks:An Explanation of the Errors Produced by Adolescents with Learning Difficulties. International Journal of Behavioral Development, 21(2),253-275.
Barth, H., Kanwisher, N.,& Spelke, E. (2003). The construction of large number representations in adults. Cognition,86(3),201-221.
Berch, D. B., Foley, E. J., Hill, R. J.,& Ryan, P. M. (1999). Extracting Parity and Magnitude from Arabic Numerals:Developmental Changes in Number Processing and Mental Representation. Journal of Experimental Child Psychology,74(4),286-308.
Bijeljac-Babic, R., Bertoncini, J., Mehler,& J. (1993). How do 4-day-old infants categorize multisyllabic utterances? (Vol.29). Washington, DC, ETATS-UNIS: American Psychological Association.
Brannon, E. M.,& Terrace, H. S. (2000). Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). Journal of experimental psychology. Animal behavior processes,26(1),31-49.
Bull, R.,& Scerif, G. (2001). Executive Functioning as a Predictor of Children's Mathematics Ability:Inhibition, Switching, and Working Memory. Developmental Neuropsychology,19(3),273-293.
Campbell, J. I. D. (Ed.). (2005). Handbook of mathematical cognition. New York and Hove:Psychology Press Ltd.,57-66.
Campbell, J. I. D. (Ed.). (2005). Handbook of mathematical cognition:Psychology Pr.
Campbell, J. I. D.,& Oliphant, M. (1992). Representation And Retrieval Of Arithmetic Facts:A Network-Interference Model And Simulation. In I. D. C. Jamie (Ed.), Advances in Psychology (Vol. Volume 91, pp.331-364):North-Holland.
Cao, B., Li, F.,& Li, H. (2010). Notation-dependent processing of numerical magnitude:Electrophysiological evidence from Chinese numerals. Biological Psychology,83(1),47-55.
Cepeda, N. J., Kramer, A. F.,& Gonzalez de Sather, J. C. (2001). Changes in executive control across the life span:examination of task-switching performance. Developmental psychology,37(5),715-730.
Chen; C. L., Wu, T. H., Cheng, M. C, Huang, Y. H., Sheu, C. Y., Hsieh, J. C., et al. (2006). Prospective demonstration of brain plasticity after intensive abacus-based mental calculation training:An fMRI study. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,569(2),567-571.
Chen, F., Hu, Z., Zhao, X., Wang, R., Yang, Z., Wang, X., et al. (2006). Neural correlates of serial abacus mental calculation in children:A functional MRI study. Neuroscience Letters,403(1-2),46-51.
Church, R. M. (1984). Properties of the internal clock. Annals of the New York Academy of Sciences,423,566-582.
Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A.,& Goebel, R. (2007). Notation-Dependent and-Independent Representations of Numbers in the Parietal Lobes. Neuron,53(2),307-314.
Davidson, M. C., Amso, D., Anderson, L. C.,& Diamond, A. (2006). Development of cognitive control and executive functions from 4 to 13 years:Evidence from manipulations of memory, inhibition, and task switching. Neuropsychologia, 44(11),2037-2078.
Dehaene, S., Bossini, S., Giraux,& P. (1993). The mental representation of parity and number magnitude (Vol.122). Washington, DC, ETATS-UNIS:American Psychological Association.
Dehaene, S. (1989). The psychophysics of numerical comparison:A reexamination of apparently incompatible data. Attention, Perception,& Psychophysics,45(6), 557-566.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition,44(1-2),1-42.
Dehaene, S. (1996). The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method. Journal of Cognitive Neuroscience,8(1),47-68.
Dehaene, S., Dehaene-Lambertz, G.,& Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences,21(8), 355-361.
Dehaene, S., Dupoux, E.,& 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(3), 626-641.
Dehaene, S., Molko, N., Cohen, L.,& Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology,14(2),218-224.
Dehaene, S., Piazza, M., Pinel, P.,& Cohen, L. (2003). THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING. Cognitive Neuropsychology,20(3-6),487-506.
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.
Draganski, B., Gaser, C., Busch, V., Schuierer, G., Bogdahn, U.,& May, A. (2004). Neuroplasticity:changes in grey matter induced by training. Nature, 427(6972),311-312.
Duncan, E.,& McFarland, C. (1980). Isolating the effects of symbolic distance, and semantic congruity in comparative judgments:An additive-factors analysis. Memory & Cognition,8(6),612-622.
Feigenson, L. (2008). Parallel non-verbal enumeration is constrained by a set-based limit. Cognition,107(1),1-18.
Feigenson, L., Dehaene, S.,& Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences,8(7),307-314.
Fias, W. (2001). Two routes for the processing of verbal numbers:Evidence from the SNARC effect.
Fias, W., Reynvoet, B.,& Brysbaert, M. (2001). Are Arabic numerals processed as pictures in a Stroop interference task? PSYCHOLOGICAL RESEARCH-PSYCHOLOGISCHE FORSCHUNG,65(4),242-249.
Fischer, M. (2003). Spatial representations in number processing--evidence from a pointing task. Visual Cognition,10(4),493-508.
Frank, M. C.,& Barner, D. Constructing exact visual representations of number (unpublished).
Gobel, S., Walsh, V.,& Rushworth, M. F. S. (2001). The Mental Number Line and the Human Angular Gyrus. Neurolmage,14(6),1278-1289.
Gallistel, C. R.,& Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition,44(1-2),43-74.
Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of experimental child psychology,49(3),363-383.
Geary, D. C. (1993). Mathematical disabilities:Cognitive,neuropsychological,and genetic components. Psychological Bulletin,114.
Geary, D. C., Hamson, C. O.,& Hoard, M. K. (2000). Numerical and arithmetical cognition:a longitudinal study of process and concept deficits in children with learning disability. Journal of experimental child psychology,77(3), 236-263.
Gebuis, T,, Kenemans, J. L., de Haan, E. H. F.,& van der Smagt, M. J. (2010). Conflict processing of symbolic and non-symbolic numerosity. Neuropsychologia, 48(2),394-401.
Gevers, W., Reynvoet, B.,& Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition,87(3), B87-B95.
Girelli, L., Lucangeli, D.,& Butterworth, B. (2000). The Development of Automaticity in Accessing Number Magnitude. Journal of Experimental Child Psychology, 76(2),104-122.
Gracia-Bafalluy, M.,& Noel, M.-P. (2008). Does finger training increase young children's numerical performance? Cortex,44(4),368-375.
Gross-Tsur, V., Manor,O.,& Shalev, R. S. (1996). Developmental dyscalculia: prevalence and demographic features. Developmental medicine and child neurology,38(1),25-33.
Halberda, J.,Sires, S. F.,& Feigenson, L. (2006). Multiple Spatially Overlapping Sets Can Be Enumerated in Parallel. Psychological science,17(7),572-576.
Hanakawa, T., Honda, M., Okada, T., Fukuyama, H.,& Shibasaki, H. (2003). Neural correlates underlying mental calculation in abacus experts:a functional magnetic resonance imaging study. Neurolmage,19(2),296-307.
Hanich, L. B. (2001). Performance across different areas of mathematical cognition in children with learning difficulties.
Hatano, G., Miyake, Y.,& Binks; M. G. (1977). Performance of expert abacus operators. Cognition,5(1),47-55.
Hatano, G.,& Osawa, K. (1983). Digit memory of grand experts in abacus-derived mental calculation. Cognition,15(1-3),95-110.
Hatta, T.,& Ikeda, K. (1988). Hemispheric specialization of abacus experts in mental calculation:Evidence from the results of time-sharing tasks. Neuropsychologia,26(6),877-893.
Hauser, M., Macneilage, P.,& Ware, M. (1996). Numerical representations in primates. PNAS,93(4),1514-1517.
Hauser, M. D., Carey, S.,& Hauser, L. B. (2000). Spontaneous number representation in semi-free-ranging rhesus monkeys. Proceedings. Biological sciences/The Royal Society,267(1445),829-833.
Hauser, M. D., Dehaene, S., Dehaene-Lambertz, G.,& Patalano, A. L. (2002). Spontaneous number discrimination of multi-format auditory stimuli in cotton-top tamarins (Saguinus oedipus). Cognition,86(2), B23-B32.
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. Biological sciences/The Royal Society,270(1523), 1441-1446.
Henik, A.,& Tzelgov, J. (1982). Is three greater than five:The relation between physical and semantic size in comparison tasks. Memory & Cognition,10(4), 389-395.
Hishitani, S. (1990). Imagery experts:How do expert abacus operators process imagery? Applied Cognitive Psychology,4(1),33-46.
Hu, Y., Geng, F., Tao, L, Hu, N., Du, F., Fu, K., et al. (2011). Enhanced white matter tracts integrity in children with abacus training. Human Brain Mapping,32(1), 10-21.
Hyde, K. L, Lerch, J., Norton, A., Forgeard, M., Winner, E., Evans, A. C., et al. (2009). Musical training shapes structural brain development. The Journal of neuroscience:the official journal of the Society for Neuroscience,29(10), 3019-3025.
Iguchi, Y.,& Hashimoto, I. (2000). Sequential information processing during a mental arithmetic is reflected in the time course of event-related brain potentials. Clinical Neurophysiology,111(2),204-213.
Imbo, I.,& Vandierendonck, A. (2008). Practice effects on strategy selection and strategy efficiency in simple mental arithmetic. Psychological Research,72(5), 528-541.
Jasper H, H. (1958). The ten twenty electrode system of the international federation. Electroencephalography and Clinical Neurophysiology,10,371-375.
Jordan, N. C.,Hanich, L. B.,& Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child development,74(3),834-850.
Jordan, N. C.,& Montani, T.0. (1997). Cognitive arithmetic and problem solving:a comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities,30(6),624-634,684.
Kilian, A., Yaman, S., von Fersen, L.,& Gunturkun, O. (2003). A bottlenose dolphin discriminates visual stimuli differing in numerosity. Learning & Behavior, 31(2),133-142.
Kray, J., Eber, J.,& Lindenberger, U. (2004). Age differences in executive functioning across the lifespan:The role of verbalization in task preparation. Acta Psychologica,115(2-3),143-165.
Lee, K. M.,& Kang, S. Y. (2002). Arithmetic operation and working memory: differential suppression in dual tasks. Cognition,83(3),63-68.
LeFevre, JA., Bisanz, J., Daley, KE., et al. (1996). Multiple routes to solution of single-digit multiplication problems (Vol.125). Washington, DC, ETATS-UNIS: American Psychological Association.
LeFevre, JA., Sadesky, GS., Bisanz,& J. (1996). Selection of procedures in mental addition:Reassessing the problem size effect in adults (Vol.22). Washington, DC, ETATS-UNIS:American Psychological Association.
Libertus, M., Woldorff, M.,& Brannon, E. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions,3(1),1-15.
Loosbroek, V., E., Smitsman,& W., A. (1990). Visual perception of numerosity in infancy (Vol.26). Washington, DC, ETATS-UNIS:American Psychological Association.
Luck, S. J.,& Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature,390(6657),279-281.
Mandler, G.,& Shebo, B. J. (1982). Subitizing:an analysis of its component processes. Journal of experimental psychology. General,111(1),1-22.
Mazzocco, M. M. M.,& Kover, S. T. (2007). A Longitudinal Assessment of Executive Function Skills and Their Association with Math Performance. Child Neuropsychology,13(1),18-45.
McComb, K., Packer, C.,& Pusey, A. (1994). Roaring and numerical assessment in contests between groups of female lions, Panthera leo. Animal Behaviour, 47(2),379-387.
McLean, J. F.,& Hitch, G. J. (1999). Working Memory Impairments in Children with Specific Arithmetic Learning Difficulties. Journal of experimental child psychology,74(3),240-260.
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A.,& Wager, T. D. (2000). The Unity and Diversity of Executive Functions and Their Contributions to Complex "Frontal Lobe" Tasks:A Latent Variable Analysis. Cognitive Psychology,41(1),49-100.
Moyer, R. S.,& Landauer, T. K. (1967). Time required for Judgements of Numerical Inequality. [10.1038/2151519a0]. Nature,215(5109),1519-1520.
Mundy, E.,& Gilmore, C. K. (2009). Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology,103(4),490-502.
Nieder, A.,.& Dehaene, S. (2009). Representation of number in the brain. Annual review of neuroscience,32,185-208.
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(1), B25-B33.
Nuerk, H. C., Iversen, W.,& Willmes, K. (2004). Notational modulation, of the SNARC and the MARC (linguistic markedness of response codes) effect. The Quarterly Journal of Experimental Psychology Section A,57(5),835-863.,
Ohlsson, S.,& Rees, E. (1991). The Function of Conceptual Understanding in the Learning of Arithmetic Procedures. Cognition and Instruction,8(2),103-179.
Pansky, A.,& Algom, D. (2002a). Comparative judgment of numerosity and numerical magnitude:attention preempts automaticity. Journal of experimental psychology. Learning, memory, and cognition,28(2),259-274.
Pansky, A.,& Algom,. D. (2002b). Comparative judgment of numerosity and numerical magnitude:Attention preempts automaticity. J Exp Psychol Learn Mem Cogn,28(2),259-274.
Pavese, A.,& Umilta, C. (1999). Symbolic distance between numerosity and identity modulates Stroop-like interference.
Pavese, A.,& Umilta, C. (1998). Symbolic distance between numerosity and identity modulates Stroop interference. J EXP PSYCHOL HUMAN 24(5),1535-1545.
Petersen, S. E., van Mier, H., Fiez, J. A.,& Raichle, M. E. (1998). The effects of practice on the functional anatomy of task performance. Proceedings of the National Academy of Sciences,95(3),853-860.
Pinel, P., Dehaene, S., Riviere, D.,& LeBihan, D. (2001). Modulation of Parietal Activation by Semantic Distance in a Number Comparison Task. Neurolmage, 14(5),1013-1026.
Plodowski, A., Swainson, R., Jackson, G. M., Rorden, C.,& Jackson, S. R. (2003). Mental Representation of Number in Different Numerical Forms. Current Biology,13(23),2045-2050.
Reimers, S.,& Maylor, E. A. (2005). Task switching across the life span:effects of age on general and specific switch costs. Developmental psychology,41(4), 661-671.
Reynvoet, B.,& Brysbaert, M. (1999). Single-digit and two-digit Arabic numerals address the same semantic number line. Cognition,72(2),191-201.
Robinson, D. A. (1976). Adaptive gain control of vestibuloocular reflex by the cerebellum. Journal of neurophysiology,39(5),954-969.
Rourke, B. P.,& Conway, J. A. (1997). Disabilities of Arithmetic and Mathematical Reasoning. Journal of Learning Disabilities,30(1),34-46.
Rubinsten, O., Henik, A., Berger, A.,& Shahar-Shalev, S. (2002). The Development of Internal Representations of Magnitude and Their Association with Arabic Numerals. Journal of Experimental Child Psychology,81(1),74-92.
Rumbaugh, M., D., Aavage-Rumbaugh, S., Hegel,& T., M. (1987). Summation in the chimpanzee (Pan troglodytes) (Vol.13). Washington, DC, ETATS-UNIS: American Psychological Association.
Schneider, W., Eschmann, A.,& Zuccolotto, A. (Eds.). (2002). E-Prime reference guide. Pittsburgh,PA:Psychology Software Tools.
Soltesz, F., Goswami, U.,White, S.,& Szucs, D. (2011). Executive function effects and numerical development in children:Behavioural and ERP evidence from a numerical Stroop paradigm. Learning and Individual Differences,21(6), 662-671.
Soltesz, F., Szucs, D., Dekany, J., Markus, A.,& Csepe, V. (2007). A combined event-related potential and neuropsychological investigation of developmental dyscalculia. Neuroscience Letters,417(2),181-186.
Starkey, P.,& Cooper, R. G. (1980). Perception of numbers by human infants. Science (New York, N.Y.),210(4473),1033-1035.
Starkey, P., Spelke, E.,& Gelman, R. (1983). Detection of intermodal numerical correspondences by human infants. Science,222(4620),179-181.
Stigler, J. W. (1984). "Mental abacus":The effect of abacus training on Chinese children's mental calculation. Cognitive Psychology,16(2),145-176.
Strauss, M. S.,& Curtis, L. E. (1981). Infant perception of numerosity. Child development,52(4),1146-1152.
Stroop, J. R. (1935). Studies of interference in serial verbal reactions. J EXP PSYCHOL, 18(6),643-662.
Szucs, D.,& Soltesz, F. (2008). The interaction of task-relevant and task-irrelevant stimulus features in the number/size congruency paradigm:An ERP study. Brain Research,1190(0),143-158.
Szucs, D., Soltesz, F., Jarmi, E.,& Csepe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children:an electro-encephalography study. Behavioral and Brain Functions,3(1),1-20.
Szucs, D., Soltesz, F., Jarmi, E.,& Csepe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children:an electro-encephalography study. Behavioral and brain functions:BBF,3,23.
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.
Temple, C. M.,& Sherwood, S. (2002). Representation and retrieval of arithmetical facts:Developmental difficulties. The Quarterly Journal of Experimental Psychology A,55(3),733-752.
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,95(13),7836-7841.
Turconi, E., Jemel, B., Rossion, B.,& Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research,21(1),22-38.
Uller, C., Jaeger, R., Guidry, G.,& Martin, C. (2003). Salamanders (Plethodon cinereus) go for more:rudiments of number in an amphibian. Animal Cognition,6.(2),105-112.
van Galen, M. S.,& Reitsma, P. (2008). Developing access to number magnitude:A study of the SNARC effect in 7-to 9-year-olds. Journal of Experimental Child Psychology,101(2),99-113.
van Mier, H.,& Hulstijn, W. (1993). The effects of motor complexity and practice on initiation time in writing and drawing. Acta Psychologica,84(3),231-251.
Verguts, T., Fias, W.,& Stevens, M. (2005). A model of exact small-number representation. Psychonomic bulletin& review,12(1),66-80.
Wakeley, A., Rivera, S.,& Langer, J. (2000). Can young infants add and subtract? Child development,71(6),1525-1534.
Wei, J., Zhao, L., Yan, G., Duan, R.,& Li, D. (1998). The temporal and spatial features of event-related EEG spectral changes in 4 mental conditions. Electroencephalography and clinical neurophysiology,106(5),416-423.
Wender, K. F.,& Rothkegel, R. (2000). Subitizing and its subprocesses. Psychological Research,64(2),81-92.
Whalen, J., Gallistel, C. R.,& Gelman, R. (1999). Nonverbal Counting in Hur lans:The Psychophysics of Number Representation. Psychological science,10(2), 130-137.
Wu, T.-H., Chen, C.-L., Huang, Y.-H., Liu, R.-S., Hsieh, J.-C.,& Lee, J. (2009). Effects of long-term practice and task complexity on brain activities when performing abacus-based mental calculations:a PET study. European Journal of Nuclear Medicine and Molecular Imaging,36(3),436-445.
Wynn, K. (1992). Addition and subtraction by human infants. Nature,358(6389), 749-750.
Wynn, K. (1996). Infants'Individuation and Enumeration of Actions. Psychological Science,7(3),164-169.
Wynn, K. (1998). Psychological foundations of number:numerical competence in human infants. Trends in cognitive sciences,2(8),296-303.
Xu, F.,& Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition,74(1), B1-B11.
Zhou, X., Chen, C., Chen, L.,& Dong, Q. (2008). Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task. Cognition,106(3),1525-1536.
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H.,& Dong, Q. (2007). Chinese kindergartners'automatic processing on numerical magnitude in Stroop-like tasks. Memory & amp;amp; cognition,35(3),7.
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H.,& Dong, Q. (2007). Chinese kindergartners' automatic processing of numerical magnitude in Stroop-like tasks. Memory & Cognition,35(3),464-470.
文萍,张莉,李红,刘莉湘君,＆张雪怡.(2007)).儿童执行功能对数学能力的预测模型.心理发展与教育，23(3),6.
李丽,&吴汉荣.(2004).中国小学生基本数学能力测试量表常模的建立.尹国学校卫生,25(5),3.
胡玉正.(2011).“珠心算的神经机制及珠心算练习对儿童脑发育的影响”.[D].
高卫星,＆李秀艳.(2009).珠心算训练对儿童数字认知能力的影响研究.中国科技信息,no.15(20090914),252-253.
甄玉青,李秀艳,＆李平.(2007).“珠心算练习对儿童数字记忆能力的影响.中国健康心理学杂志，15,no.11(20071126)：1024-1025.
吴汉荣,李丽,＆约翰.哈夫纳.(2003).小学生数学能力测试的应用研究.中国学校卫生,24(4),3.
罗跃嘉主编.(2006).认知神经科学教程：北京大学出版社.
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.
Antell, S. E.;& Keating, D. P. (1983). Perception of numerical invariance in neonates. Child development,54(3),695-701.
Ashcraft, M. H. (1992). Cognitive arithmetic:a review of data and theory. Cognition, 44(1-2),75-106.
Awh, E.,& Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. Trends in cognitive sciences,5(3),119-126.
Barrouillet, P., Fayol, M.,& Lathuliere, E. (1997). Selecting between Competitors in Multiplication Tasks:An Explanation of the Errors Produced by Adolescents with Learning Difficulties. International Journal of Behavioral Development, 21(2),253-275.
Barth, H., Kanwisher, N.,& Spelke, E. (2003). The construction of large number representations in adults. Cognition,86(3),201-221.
Berch, D. B., Foley, E. J., Hill, R. J.,& Ryan, P. M. (1999). Extracting Parity and Magnitude from Arabic Numerals:Developmental Changes in Number Processing and Mental Representation. Journal of Experimental Child Psychology,74(4),286-308.
Bijeljac-Babic, R., Bertoncini, J., Mehler,& J. (1993). How do 4-day-old infants categorize multisyllabic utterances? (Vol.29). Washington, DC, ETATS-UNIS: American Psychological Association.
Brannon, E. M.,& Terrace, H. S. (2000). Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). Journal of experimental psychology. Animal behavior processes,26(1),31-49.
Bull, R.,& Scerif, G. (2001). Executive Functioning as a Predictor of Children's Mathematics Ability:Inhibition, Switching, and Working Memory. Developmental Neuropsychology,19(3),273-293.
Campbell, J. I. D. (Ed.). (2005). Handbook of mathematical cognition. New York and Hove:Psychology Press Ltd.,57-66.
Campbell, J. I. D. (Ed.). (2005). Handbook of mathematical cognition:Psychology Pr.
Campbell, J. I. D.,& Oliphant, M. (1992). Representation And Retrieval Of Arithmetic Facts:A Network-Interference Model And Simulation. In I. D. C. Jamie (Ed.), Advances in Psychology (Vol. Volume 91, pp.331-364):North-Holland.
Cao, B., Li, F.,& Li, H. (2010). Notation-dependent processing of numerical magnitude:Electrophysiological evidence from Chinese numerals. Biological Psychology,83(1),47-55.
Cepeda, N. J., Kramer, A. F.,& Gonzalez de Sather, J. C. (2001). Changes in executive control across the life span:examination of task-switching performance. Developmental psychology,37(5),715-730.
Chen; C. L., Wu, T. H., Cheng, M. C, Huang, Y. H., Sheu, C. Y., Hsieh, J. C., et al. (2006). Prospective demonstration of brain plasticity after intensive abacus-based mental calculation training:An fMRI study. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,569(2),567-571.
Chen, F., Hu, Z., Zhao, X., Wang, R., Yang, Z., Wang, X., et al. (2006). Neural correlates of serial abacus mental calculation in children:A functional MRI study. Neuroscience Letters,403(1-2),46-51.
Church, R. M. (1984). Properties of the internal clock. Annals of the New York Academy of Sciences,423,566-582.
Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A.,& Goebel, R. (2007). Notation-Dependent and-Independent Representations of Numbers in the Parietal Lobes. Neuron,53(2),307-314.
Davidson, M. C., Amso, D., Anderson, L. C.,& Diamond, A. (2006). Development of cognitive control and executive functions from 4 to 13 years:Evidence from manipulations of memory, inhibition, and task switching. Neuropsychologia, 44(11),2037-2078.
Dehaene, S., Bossini, S., Giraux,& P. (1993). The mental representation of parity and number magnitude (Vol.122). Washington, DC, ETATS-UNIS:American Psychological Association.
Dehaene, S. (1989). The psychophysics of numerical comparison:A reexamination of apparently incompatible data. Attention, Perception,& Psychophysics,45(6), 557-566.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition,44(1-2),1-42.
Dehaene, S. (1996). The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method. Journal of Cognitive Neuroscience,8(1),47-68.
Dehaene, S., Dehaene-Lambertz, G.,& Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences,21(8), 355-361.
Dehaene, S., Dupoux, E.,& 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(3), 626-641.
Dehaene, S., Molko, N., Cohen, L.,& Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology,14(2),218-224.
Dehaene, S., Piazza, M., Pinel, P.,& Cohen, L. (2003). THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING. Cognitive Neuropsychology,20(3-6),487-506.
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.
Draganski, B., Gaser, C., Busch, V., Schuierer, G., Bogdahn, U.,& May, A. (2004). Neuroplasticity:changes in grey matter induced by training. Nature, 427(6972),311-312.
Duncan, E.,& McFarland, C. (1980). Isolating the effects of symbolic distance, and semantic congruity in comparative judgments:An additive-factors analysis. Memory & Cognition,8(6),612-622.
Feigenson, L. (2008). Parallel non-verbal enumeration is constrained by a set-based limit. Cognition,107(1),1-18.
Feigenson, L., Dehaene, S.,& Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences,8(7),307-314.
Fias, W. (2001). Two routes for the processing of verbal numbers:Evidence from the SNARC effect.
Fias, W., Reynvoet, B.,& Brysbaert, M. (2001). Are Arabic numerals processed as pictures in a Stroop interference task? PSYCHOLOGICAL RESEARCH-PSYCHOLOGISCHE FORSCHUNG,65(4),242-249.
Fischer, M. (2003). Spatial representations in number processing--evidence from a pointing task. Visual Cognition,10(4),493-508.
Frank, M. C.,& Barner, D. Constructing exact visual representations of number (unpublished).
Gobel, S., Walsh, V.,& Rushworth, M. F. S. (2001). The Mental Number Line and the Human Angular Gyrus. Neurolmage,14(6),1278-1289.
Gallistel, C. R.,& Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition,44(1-2),43-74.
Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of experimental child psychology,49(3),363-383.
Geary, D. C. (1993). Mathematical disabilities:Cognitive,neuropsychological,and genetic components. Psychological Bulletin,114.
Geary, D. C., Hamson, C. O.,& Hoard, M. K. (2000). Numerical and arithmetical cognition:a longitudinal study of process and concept deficits in children with learning disability. Journal of experimental child psychology,77(3), 236-263.
Gebuis, T,, Kenemans, J. L., de Haan, E. H. F.,& van der Smagt, M. J. (2010). Conflict processing of symbolic and non-symbolic numerosity. Neuropsychologia, 48(2),394-401.
Gevers, W., Reynvoet, B.,& Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition,87(3), B87-B95.
Girelli, L., Lucangeli, D.,& Butterworth, B. (2000). The Development of Automaticity in Accessing Number Magnitude. Journal of Experimental Child Psychology, 76(2),104-122.
Gracia-Bafalluy, M.,& Noel, M.-P. (2008). Does finger training increase young children's numerical performance? Cortex,44(4),368-375.
Gross-Tsur, V., Manor,O.,& Shalev, R. S. (1996). Developmental dyscalculia: prevalence and demographic features. Developmental medicine and child neurology,38(1),25-33.
Halberda, J.,Sires, S. F.,& Feigenson, L. (2006). Multiple Spatially Overlapping Sets Can Be Enumerated in Parallel. Psychological science,17(7),572-576.
Hanakawa, T., Honda, M., Okada, T., Fukuyama, H.,& Shibasaki, H. (2003). Neural correlates underlying mental calculation in abacus experts:a functional magnetic resonance imaging study. Neurolmage,19(2),296-307.
Hanich, L. B. (2001). Performance across different areas of mathematical cognition in children with learning difficulties.
Hatano, G., Miyake, Y.,& Binks; M. G. (1977). Performance of expert abacus operators. Cognition,5(1),47-55.
Hatano, G.,& Osawa, K. (1983). Digit memory of grand experts in abacus-derived mental calculation. Cognition,15(1-3),95-110.
Hatta, T.,& Ikeda, K. (1988). Hemispheric specialization of abacus experts in mental calculation:Evidence from the results of time-sharing tasks. Neuropsychologia,26(6),877-893.
Hauser, M., Macneilage, P.,& Ware, M. (1996). Numerical representations in primates. PNAS,93(4),1514-1517.
Hauser, M. D., Carey, S.,& Hauser, L. B. (2000). Spontaneous number representation in semi-free-ranging rhesus monkeys. Proceedings. Biological sciences/The Royal Society,267(1445),829-833.
Hauser, M. D., Dehaene, S., Dehaene-Lambertz, G.,& Patalano, A. L. (2002). Spontaneous number discrimination of multi-format auditory stimuli in cotton-top tamarins (Saguinus oedipus). Cognition,86(2), B23-B32.
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. Biological sciences/The Royal Society,270(1523), 1441-1446.
Henik, A.,& Tzelgov, J. (1982). Is three greater than five:The relation between physical and semantic size in comparison tasks. Memory & Cognition,10(4), 389-395.
Hishitani, S. (1990). Imagery experts:How do expert abacus operators process imagery? Applied Cognitive Psychology,4(1),33-46.
Hu, Y., Geng, F., Tao, L, Hu, N., Du, F., Fu, K., et al. (2011). Enhanced white matter tracts integrity in children with abacus training. Human Brain Mapping,32(1), 10-21.
Hyde, K. L, Lerch, J., Norton, A., Forgeard, M., Winner, E., Evans, A. C., et al. (2009). Musical training shapes structural brain development. The Journal of neuroscience:the official journal of the Society for Neuroscience,29(10), 3019-3025.
Iguchi, Y.,& Hashimoto, I. (2000). Sequential information processing during a mental arithmetic is reflected in the time course of event-related brain potentials. Clinical Neurophysiology,111(2),204-213.
Imbo, I.,& Vandierendonck, A. (2008). Practice effects on strategy selection and strategy efficiency in simple mental arithmetic. Psychological Research,72(5), 528-541.
Jasper H, H. (1958). The ten twenty electrode system of the international federation. Electroencephalography and Clinical Neurophysiology,10,371-375.
Jordan, N. C.,Hanich, L. B.,& Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child development,74(3),834-850.
Jordan, N. C.,& Montani, T.0. (1997). Cognitive arithmetic and problem solving:a comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities,30(6),624-634,684.
Kilian, A., Yaman, S., von Fersen, L.,& Gunturkun, O. (2003). A bottlenose dolphin discriminates visual stimuli differing in numerosity. Learning & Behavior, 31(2),133-142.
Kray, J., Eber, J.,& Lindenberger, U. (2004). Age differences in executive functioning across the lifespan:The role of verbalization in task preparation. Acta Psychologica,115(2-3),143-165.
Lee, K. M.,& Kang, S. Y. (2002). Arithmetic operation and working memory: differential suppression in dual tasks. Cognition,83(3),63-68.
LeFevre, JA., Bisanz, J., Daley, KE., et al. (1996). Multiple routes to solution of single-digit multiplication problems (Vol.125). Washington, DC, ETATS-UNIS: American Psychological Association.
LeFevre, JA., Sadesky, GS., Bisanz,& J. (1996). Selection of procedures in mental addition:Reassessing the problem size effect in adults (Vol.22). Washington, DC, ETATS-UNIS:American Psychological Association.
Libertus, M., Woldorff, M.,& Brannon, E. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions,3(1),1-15.
Loosbroek, V., E., Smitsman,& W., A. (1990). Visual perception of numerosity in infancy (Vol.26). Washington, DC, ETATS-UNIS:American Psychological Association.
Luck, S. J.,& Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature,390(6657),279-281.
Mandler, G.,& Shebo, B. J. (1982). Subitizing:an analysis of its component processes. Journal of experimental psychology. General,111(1),1-22.
Mazzocco, M. M. M.,& Kover, S. T. (2007). A Longitudinal Assessment of Executive Function Skills and Their Association with Math Performance. Child Neuropsychology,13(1),18-45.
McComb, K., Packer, C.,& Pusey, A. (1994). Roaring and numerical assessment in contests between groups of female lions, Panthera leo. Animal Behaviour, 47(2),379-387.
McLean, J. F.,& Hitch, G. J. (1999). Working Memory Impairments in Children with Specific Arithmetic Learning Difficulties. Journal of experimental child psychology,74(3),240-260.
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A.,& Wager, T. D. (2000). The Unity and Diversity of Executive Functions and Their Contributions to Complex "Frontal Lobe" Tasks:A Latent Variable Analysis. Cognitive Psychology,41(1),49-100.
Moyer, R. S.,& Landauer, T. K. (1967). Time required for Judgements of Numerical Inequality. [10.1038/2151519a0]. Nature,215(5109),1519-1520.
Mundy, E.,& Gilmore, C. K. (2009). Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology,103(4),490-502.
Nieder, A.,.& Dehaene, S. (2009). Representation of number in the brain. Annual review of neuroscience,32,185-208.
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(1), B25-B33.
Nuerk, H. C., Iversen, W.,& Willmes, K. (2004). Notational modulation, of the SNARC and the MARC (linguistic markedness of response codes) effect. The Quarterly Journal of Experimental Psychology Section A,57(5),835-863.,
Ohlsson, S.,& Rees, E. (1991). The Function of Conceptual Understanding in the Learning of Arithmetic Procedures. Cognition and Instruction,8(2),103-179.
Pansky, A.,& Algom, D. (2002a). Comparative judgment of numerosity and numerical magnitude:attention preempts automaticity. Journal of experimental psychology. Learning, memory, and cognition,28(2),259-274.
Pansky, A.,& Algom,. D. (2002b). Comparative judgment of numerosity and numerical magnitude:Attention preempts automaticity. J Exp Psychol Learn Mem Cogn,28(2),259-274.
Pavese, A.,& Umilta, C. (1999). Symbolic distance between numerosity and identity modulates Stroop-like interference.
Pavese, A.,& Umilta, C. (1998). Symbolic distance between numerosity and identity modulates Stroop interference. J EXP PSYCHOL HUMAN 24(5),1535-1545.
Petersen, S. E., van Mier, H., Fiez, J. A.,& Raichle, M. E. (1998). The effects of practice on the functional anatomy of task performance. Proceedings of the National Academy of Sciences,95(3),853-860.
Pinel, P., Dehaene, S., Riviere, D.,& LeBihan, D. (2001). Modulation of Parietal Activation by Semantic Distance in a Number Comparison Task. Neurolmage, 14(5),1013-1026.
Plodowski, A., Swainson, R., Jackson, G. M., Rorden, C.,& Jackson, S. R. (2003). Mental Representation of Number in Different Numerical Forms. Current Biology,13(23),2045-2050.
Reimers, S.,& Maylor, E. A. (2005). Task switching across the life span:effects of age on general and specific switch costs. Developmental psychology,41(4), 661-671.
Reynvoet, B.,& Brysbaert, M. (1999). Single-digit and two-digit Arabic numerals address the same semantic number line. Cognition,72(2),191-201.
Robinson, D. A. (1976). Adaptive gain control of vestibuloocular reflex by the cerebellum. Journal of neurophysiology,39(5),954-969.
Rourke, B. P.,& Conway, J. A. (1997). Disabilities of Arithmetic and Mathematical Reasoning. Journal of Learning Disabilities,30(1),34-46.
Rubinsten, O., Henik, A., Berger, A.,& Shahar-Shalev, S. (2002). The Development of Internal Representations of Magnitude and Their Association with Arabic Numerals. Journal of Experimental Child Psychology,81(1),74-92.
Rumbaugh, M., D., Aavage-Rumbaugh, S., Hegel,& T., M. (1987). Summation in the chimpanzee (Pan troglodytes) (Vol.13). Washington, DC, ETATS-UNIS: American Psychological Association.
Schneider, W., Eschmann, A.,& Zuccolotto, A. (Eds.). (2002). E-Prime reference guide. Pittsburgh,PA:Psychology Software Tools.
Soltesz, F., Goswami, U.,White, S.,& Szucs, D. (2011). Executive function effects and numerical development in children:Behavioural and ERP evidence from a numerical Stroop paradigm. Learning and Individual Differences,21(6), 662-671.
Soltesz, F., Szucs, D., Dekany, J., Markus, A.,& Csepe, V. (2007). A combined event-related potential and neuropsychological investigation of developmental dyscalculia. Neuroscience Letters,417(2),181-186.
Starkey, P.,& Cooper, R. G. (1980). Perception of numbers by human infants. Science (New York, N.Y.),210(4473),1033-1035.
Starkey, P., Spelke, E.,& Gelman, R. (1983). Detection of intermodal numerical correspondences by human infants. Science,222(4620),179-181.
Stigler, J. W. (1984). "Mental abacus":The effect of abacus training on Chinese children's mental calculation. Cognitive Psychology,16(2),145-176.
Strauss, M. S.,& Curtis, L. E. (1981). Infant perception of numerosity. Child development,52(4),1146-1152.
Stroop, J. R. (1935). Studies of interference in serial verbal reactions. J EXP PSYCHOL, 18(6),643-662.
Szucs, D.,& Soltesz, F. (2008). The interaction of task-relevant and task-irrelevant stimulus features in the number/size congruency paradigm:An ERP study. Brain Research,1190(0),143-158.
Szucs, D., Soltesz, F., Jarmi, E.,& Csepe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children:an electro-encephalography study. Behavioral and Brain Functions,3(1),1-20.
Szucs, D., Soltesz, F., Jarmi, E.,& Csepe, V. (2007). The speed of magnitude processing and executive functions in controlled and automatic number comparison in children:an electro-encephalography study. Behavioral and brain functions:BBF,3,23.
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.
Temple, C. M.,& Sherwood, S. (2002). Representation and retrieval of arithmetical facts:Developmental difficulties. The Quarterly Journal of Experimental Psychology A,55(3),733-752.
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,95(13),7836-7841.
Turconi, E., Jemel, B., Rossion, B.,& Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research,21(1),22-38.
Uller, C., Jaeger, R., Guidry, G.,& Martin, C. (2003). Salamanders (Plethodon cinereus) go for more:rudiments of number in an amphibian. Animal Cognition,6.(2),105-112.
van Galen, M. S.,& Reitsma, P. (2008). Developing access to number magnitude:A study of the SNARC effect in 7-to 9-year-olds. Journal of Experimental Child Psychology,101(2),99-113.
van Mier, H.,& Hulstijn, W. (1993). The effects of motor complexity and practice on initiation time in writing and drawing. Acta Psychologica,84(3),231-251.
Verguts, T., Fias, W.,& Stevens, M. (2005). A model of exact small-number representation. Psychonomic bulletin& review,12(1),66-80.
Wakeley, A., Rivera, S.,& Langer, J. (2000). Can young infants add and subtract? Child development,71(6),1525-1534.
Wei, J., Zhao, L., Yan, G., Duan, R.,& Li, D. (1998). The temporal and spatial features of event-related EEG spectral changes in 4 mental conditions. Electroencephalography and clinical neurophysiology,106(5),416-423.
Wender, K. F.,& Rothkegel, R. (2000). Subitizing and its subprocesses. Psychological Research,64(2),81-92.
Whalen, J., Gallistel, C. R.,& Gelman, R. (1999). Nonverbal Counting in Hur lans:The Psychophysics of Number Representation. Psychological science,10(2), 130-137.
Wu, T.-H., Chen, C.-L., Huang, Y.-H., Liu, R.-S., Hsieh, J.-C.,& Lee, J. (2009). Effects of long-term practice and task complexity on brain activities when performing abacus-based mental calculations:a PET study. European Journal of Nuclear Medicine and Molecular Imaging,36(3),436-445.
Wynn, K. (1992). Addition and subtraction by human infants. Nature,358(6389), 749-750.
Wynn, K. (1996). Infants'Individuation and Enumeration of Actions. Psychological Science,7(3),164-169.
Wynn, K. (1998). Psychological foundations of number:numerical competence in human infants. Trends in cognitive sciences,2(8),296-303.
Xu, F.,& Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition,74(1), B1-B11.
Zhou, X., Chen, C., Chen, L.,& Dong, Q. (2008). Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task. Cognition,106(3),1525-1536.
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H.,& Dong, Q. (2007). Chinese kindergartners'automatic processing on numerical magnitude in Stroop-like tasks. Memory & amp;amp; cognition,35(3),7.
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H.,& Dong, Q. (2007). Chinese kindergartners' automatic processing of numerical magnitude in Stroop-like tasks. Memory & Cognition,35(3),464-470.
文萍,张莉,李红,刘莉湘君,＆张雪怡.(2007)).儿童执行功能对数学能力的预测模型.心理发展与教育，23(3),6.
李丽,&吴汉荣.(2004).中国小学生基本数学能力测试量表常模的建立.尹国学校卫生,25(5),3.
胡玉正.(2011).“珠心算的神经机制及珠心算练习对儿童脑发育的影响”.[D].
高卫星,＆李秀艳.(2009).珠心算训练对儿童数字认知能力的影响研究.中国科技信息,no.15(20090914),252-253.
甄玉青,李秀艳,＆李平.(2007).“珠心算练习对儿童数字记忆能力的影响.中国健康心理学杂志，15,no.11(20071126)：1024-1025.
吴汉荣,李丽,＆约翰.哈夫纳.(2003).小学生数学能力测试的应用研究.中国学校卫生,24(4),3.
罗跃嘉主编.(2006).认知神经科学教程：北京大学出版社.