Psychological Development and Education ›› 2014, Vol. 30 ›› Issue (5): 449-456.

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Representation Patterns of Children’s and Adults’ Fraction Estimation on Different Number Lines

LU Chun, GUO Hong-Li, SI Ji-wei, SUN Yan   

  1. School of Psychology, Shandong Normal University, Jinan 250014, China
  • Online:2014-09-15 Published:2014-09-15

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Abstract: 44 sixth-graders and 40 college students were tested by Number-Position task (NP) and Position-Number task (PN) on 0-1 and 1/100-1/10 number lines to explore children's and adults' representation patterns of fractions estimation. Results showed that:1)Two groups followed a linear pattern in both NP and PN tasks on 0-1 number line, and followed a logarithmic pattern on NP task and an exponential pattern on PN task on 1/100-1/10 number line.; 2) the percentage of error for NP task was higher than PN task for children and adults,and sixth-graders made more error than the adults did on the 0-1 and 1/100-1/10 number lines.

Key words: number line estimation, linear representation, fractions estimation, NP task, PN task

CLC Number: 

  • B844.1
Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189-201.
Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.
Gibbon, J., & Church, R. M. (1981). Time left: Linear versus logarithmic subjective time. Journal of the Experimental Analysis of Behavior, 7(2), 87-107.
Mix, K. S., Huttenlocher, J., & Levine, S.C.(200). Quantitative development in infancy and early childhood. New York: Oxford University Press.
Ischebeck, A., Schocke, M., & Delazer, M. (2009). The processing and representation of fractions within the brain: An fMRI investigation. NeuroImage, 47(1), 403-413.
Kallai, A. Y., & Tzelgov, J. (2009). A generalized fraction: An entity smaller than one on the mental number line. Journal of Experimental Psychology: Human Perception and Performance, 35 (6), 1845-1864.
Nieder, D., & Deheane, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32(1), 185-208.
Opfer, J. E., & Devries, J. M. (2008). Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults. Cognition, 108(3), 843-849.
Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227-1238.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). New York: Taylor & Francis.
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296.
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237-243.
Siegler, R. S., & Pyke, A. A. (2012). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994-2004.
Vallentin, D., & Nieder, A. (2010). Representations of visual proportions in the primate posterior parietal and prefrontal cortices. European Journal of Neuroscience, 32(8), 1380-1387.
Zhang, L., Xin, Z., Li, F., Wang, Q., Ding, C., & Li, H. (2012). An ERP study on the processing of common fractions. Experimental Brain Research, 217(1), 25-34.
郭红力. (2010). 小学高年级儿童的分数数量表征. 硕士论文. 山东师范大学.
刘春晖, 辛自强. (2010). 分数认知的"整数偏向"研究:理论与方法. 心理科学进展, 18(1), 65-74.
卢彩芳. (2013). 三至六年级儿童整数数量表征与分数数量表征的关系. 硕士论文. 西南大学.
莫雷, 周广东, 温红博. (2010). 儿童数字估计中的心理长度. 心理学报, 42(5), 569-580.
倪玉菁. (1999). 五、六年级小学生对分数的意义和性质的理解. 心理发展与教育, 15(4), 26-30.
汪运起. (2013). 儿童的分数和小数数量表征及其发展. 博士论文. 浙江大学
辛自强, 李丹. (2013). 小学生在非符号材料上的分数表征方式. 心理科学, 36(2), 364-371.
辛自强, 刘国芳. (2011). 非符号分数与整数计算能力的发展及其与数字记忆的关系. 心理科学, 34(3). 520-526.
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