幼儿心理数线的发展：估计准确率与模式背后的策略

摘要/Abstract

摘要： 通过对81名3～5岁幼儿心理数线发展特点及其在数线估计任务中使用策略的研究，探究幼儿数线估计策略的发展特点，数线估计策略与估计准确率、估计模式的关系，从而为促进幼儿心理数线发展提供启示。结果发现：（1）幼儿在数线估计任务中表现出丰富多样的估计策略；（2）估计策略具有年龄、估计情景差异和数线范围的差异；（3）估计策略与数线估计准确率、数线估计模式密切相关。幼儿在1～20数线范围内的估计准确率存在显著的策略差异。幼儿数线估计策略能够影响估计模式，各种估计模式中使用比例较高的是“数字关系”和“数数”策略，“标准线性模式”中各种有效策略运用的比例最高。

关键词: 幼儿, 心理数线, 估计策略

Abstract: Based on the study of 81 children aged 3～5, children’s mental number line development characteristics and estimation strategies used in the number line task were explored to find the developmental characteristics of children’s number line estimation strategy, and the relationship between number line estimation strategy, estimation accuracy and estimation model, so as to provide enlightenment for measures to promote the development of children’s mental number line. The results showed that: 1) Children showed a rich variety of estimation strategies. 2) There were differences between estimation strategy and age, estimation situation as well as number line range. 3) The estimation strategy was closely related to the accuracy of the number line estimation and the number line estimation model. There existed significant difference in the estimation strategies of children’s estimation accuracy in the range of 1～20 number lines. Children’s number line estimation strategy could affect the estimation model. The "number relation" and "counting number" strategies were used in a high proportion in various estimation models, and the "standard linear model" had the highest proportion of effective strategies.

Key words: children, mental number line, estimation strategy

中图分类号:

B844

臧蓓蕾, 张俊, 顾荣芳. 幼儿心理数线的发展：估计准确率与模式背后的策略[J]. 心理与行为研究, 2019, 17(6): 795-802.

ZANG Beilei, ZHANG Jun, GU Rongfang. The Development of Children’s Mental Number Line: Strategies Behind the Estimation Accuracy and Model[J]. Studies of Psychology and Behavior, 2019, 17(6): 795-802.

参考文献

刘国芳, 辛自强. (2012). 数字线估计研究:"模型"背后的策略. 心理研究, 5(2), 27-33, doi:10.3969/j.issn.2095-1159.2012.02.004
Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189-201, doi:10.1037/0012-1649.41.6.189.
Bouwmeester, S., & Verkoeijen, P. P. J. L. (2012). Multiple representations in number line estimation:A developmental shift or classes of representations? Cognition and Instruction, 30(3), 246-260, doi:10.1080/07370008.2012.689384.
Crites, T. (1992). Skilled and less skilled estimators' strategies for estimating discrete quantities. The Elementary School Journal, 92(5), 601-619, doi:10.1086/461709.
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology:General, 122(3), 371-396, doi:10.1037/0096-3445.122.3.371.
Ebersbach, M., Luwel, K., Frick, A., Onghena, P., & Verschaffel, L. (2008). The relationship between the shape of the mental number line and familiarity with numbers in 5-to 9-year old children:Evidence for a segmented linear model. Journal of Experimental Child Psychology, 99(1), 1-17, doi:10.1016/j.jecp.2007.08.006.
Laski, E. V., & Yu, Q. Y. (2014). Number line estimation and mental addition:Examining the potential roles of language and education. Journal of Experimental Child Psychology, 117, 29-44, doi:10.1016/j.jecp.2013.08.007.
Link, T., Huber, S., Nuerk, H. C., & Moeller, K. (2014). Unbounding the mental number line-New evidence on children's spatial representation of numbers. Frontiers in Psychology, 4, 1021.
Muthén, L. K., & Muthén, B. O. (2012). Mplus user's guide (7th ed.). Los Angeles, CA:Muthén & Muthén.
Opfer, J. E., Thompson, C. A., & Kim, D. (2016). Free versus anchored numerical estimation:A unified approach. Cognition, 149, 11-17, doi:10.1016/j.cognition.2015.11.015.
Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. Child Development, 79(2), 375-394, doi:10.1111/j.1467-8624.2007.01131.x.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research:Learning trajectories for young children. New York:Routledge.
Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement:Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372, doi:10.1037/a0013840.
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444, doi:10.1111/cdev.2004.75.issue-2.
Siegler, R. S., & Mu, Y. (2008). Chinese children excel on novel mathematics problems even before elementary school. Psychological Science, 19(8), 759-763, doi:10.1111/j.1467-9280.2008.02153.x.
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation:Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237-250, doi:10.1111/1467-9280.02438.
Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children's numerical development. Developmental Science, 11(5), 655-661, doi:10.1111/desc.2008.11.issue-5.
Simms, V., Clayton, S., Cragg, L., Gilmore, C., & Johnson, S. (2016). Explaining the relationship between number line estimation and mathematical achievement:The role of visuomotor integration and visuospatial skills. Journal of Experimental Child Psychology, 145, 22-33, doi:10.1016/j.jecp.2015.12.004.
Simms, V., Muldoon, K., & Towse, J. (2013). Plane thinking:Mental representations in number line estimation as a function of orientation, scale, and counting proficiency. Journal of Experimental Child Psychology, 115(3), 468-480, doi:10.1016/j.jecp.2013.03.011.
Slusser, E. B., Santiago, R. T., & Barth, H. C. (2013). Developmental change in numerical estimation. Journal of Experimental Psychology:General, 142(1), 193-208, doi:10.1037/a0028560.
Xu, X. H., Chen, C. S., Pan, M. M., & Li, N. (2013). Development of numerical estimation in Chinese preschool children. Journal of Experimental Child Psychology, 116(2), 351-366, doi:10.1016/j.jecp.2013.06.009.

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