心理发展与教育 ›› 2024, Vol. 40 ›› Issue (6): 761-773.doi: 10.16187/j.cnki.issn1001-4918.2024.06.01

• 认知与社会性发展 •    

幼儿数量敏锐度的个体差异及其对数轴估计表现与策略使用的影响

梁渊1,2, 张丽锦2,3,4, 冀婷1, 李博艺1, 卜凡1   

  1. 1. 西安外国语大学人工智能与语言认知神经科学重点实验室, 西安 710128;
    2. 陕西师范大学心理学院, 西安 710062;
    3. 陕西省儿童青少年心理与行为健康哲学社会科学 重点研究基地, 西安 710062;
    4. 陕西省行为与认知神经科学重点实验室, 西安 710062
  • 发布日期:2024-11-13
  • 通讯作者: 梁渊,E-mail:liangyuan0219@126.com;张丽锦,E-mail:zhangljin2013@snnu.edu.cn E-mail:liangyuan0219@126.com;zhangljin2013@snnu.edu.cn
  • 基金资助:
    中国博士后科学基金(2022M722563);陕西省社会科学基金年度项目(2022P001);陕西省教育科学“十四五”规划课题(SGH21Y0118);奕阳教育研究院青年学者项目(SEI-QXZ-2021-05)。

Individual Differences of Numerical Acuity and Its Impact on the Performance Patterns and Strategy Use among Preschool Children

LIANG Yuan1,2, ZHANG Lijin2,3,4, JI Ting1, LI Boyi1, BU Fan1   

  1. 1. Key Laboratory of Artificial Intelligence and Language Cognitive Neuroscience, Xi'an International Studies University, Xi'an 710128;
    2. School of Psychology, Shaanxi Normal University, Xi'an 710062;
    3. Shaanxi Key Research Center of Child Mental and Behavioral Health, Xi'an 710062;
    4. Shaanxi Key Laboratory of Behavior and Cognitive Neuroscience, Xi'an 710062
  • Published:2024-11-13

摘要: 以“自动关注数量信息(SFON)”倾向为指标考查4、5岁幼儿的数量敏锐度,探讨不同数量敏锐度水平的幼儿在三种形式的数轴估计(非符号面积、数字-位置(NP)和位置-数字(PN))任务上的表现及策略使用情况。结果发现:(1)4岁幼儿敏锐度可分为次高、中、低三个水平,5岁幼儿敏锐度可分为高、中两个水平,幼儿捕捉数量信息的敏锐度水平从4岁到5岁明显提升,由依赖参考提示逐渐转变为独立自发感知;(2)幼儿数轴估计表现受情境的影响,在非符号数轴估计任务上的表现显著优于在符号NP和PN任务上的表现;(3)数量敏锐度在一定程度上影响数轴估计表现及策略使用,高数量敏锐度幼儿的数轴估计成绩更好,大多数5岁幼儿基本可以在不同形式的数轴估计任务上灵活地选用合适的数轴估计策略。本研究结果揭示了幼儿心理数量表征的内部机制,证实了数量认知的四步发展模型,为鉴别、预测和筛选出低敏锐度的数学风险幼儿提供参考依据。

关键词: 幼儿, 数量敏锐度, 数轴估计, 表征模式

Abstract: This study investigated the effect of numerical acuity levels on the performance and estimation patterns in non-symbolic and symbolic number line estimation (NLE) tasks among 4- and 5-year-old children. One hundred and fifty two 4-year-old children and 102 5-year-old children completed two types of SFON task (one is imitation SFON, and the other is automatic SFON) and three types of NLE tasks (non-symbolic area, number-to-position (NP), and position-to-number (PN)). We found three important results: Firstly, latent profile analysis showed that the levels of numerical acuity were classified as high, average, and poor for 4-year-old children, and that were classified as top and average for children aged 5 years. Children's perceptual acuity in capturing numerical information increased significantly from 4 to 5 years old, experiencing a process from relying on reference cue to independent and spontaneous acquisition. Secondly, there existed a context effect on the performance of NLE for 4- and 5-year-old children. All children performed better on non-symbolic area NLE task than that on symbolic NP and PN NLE tasks. Thirdly, the numerical acuity affected performance patterns and strategy use of NLE. Most 5-year-olds can choose appropriate estimation strategies on either non-symbolic NLE or symbolic NLE tasks flexibly. These findings confirm the hypothesis of four-step developmental model, uncover the internal mechanism of children’s mental numerical representation, and provide a theoretical reference for identifying, predicting and screening preschool children with risk of low numerical acuity.

Key words: preschool children, numerical acuity, number line estimation, estimation patterns

中图分类号: 

  • B844
Ashcraft, M. H., & Moore, A. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111(2), 246-267.
Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14(1), 125-135.
Batchelor, S., Inglis, M., & Gilmore, C. (2015). Spontaneous focusing on numerosity and the arithmetic advantage. Learning and Instruction, 40(2-3), 116-135.
Bojorque, G., Torbeyns, J., Hannula-Sormunen, M., Van Nijlen, D., & Verschaffel, L. (2017). Development of SFON in Ecuadorian kindergartners. European Journal of Psychology of Education, 32, 449-462.
Cantlon, J. F., Safford, K. E., & Brannon, E. M. (2010). Spontaneous analog number representations in 3-year-old children. Developmental Science, 13(2), 289-297.
Chan, J. Y., & Mazzocco, M. M. (2017). Competing features influence children's attention to number. Journal of Experimental Child Psychology, 156, 62-81.
Chen, C., & Stevenson, H. W. (1988). Cross-linguistic differences in digit span of preschool children.Journal of Experimental Child Psychology, 46(1), 150-158.
Cicchini, G. M., Anobile, G., & Burr, D. C. (2014). Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform.Proceedings of the National Academy of Sciences, 111(21), 7867-7872.
Cicchini, G. M., Anobile, G., & Burr, D. C. (2019). Spontaneous representation of numerosity in typical and dyscalculic development. Cortex, 114, 151-163.
Deng, C., Silinskas, G., Wei, W., & Georgiou, G. (2015). Cross-lagged relationships between home literacy/numeracy environment and academic achievement in Chinese.Early Childhood Research Quarterly, 33, 12-20.
Ebersbach, M. (2016). Development of children's estimation skills: The ambiguous role of their familiarity with numerals. Child Development Perspectives, 10(2), 116-121.
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.
Fuhs, M. W., Nesbitt, K. T., & Connor, D. O. (2018). Approximate number system task performance: Associations with domain-general and domain-specific cognitive skills in young children.Journal of Numerical Cognition, 4(3), 590-612.
Gelman, R. (2009). Learning in core and noncore domains. In L. Tommasi, M. A. Peterson, & L. Nadal (Eds.),Cognitive biology: Evolutionary and developmental perspectives on mind, brain, and behavior (pp. 247-260). MIT Press.
Gelman, R., & Williams, E. M. (1998). Enabling constraints for cognitive development and learning: Domain specificity and epigenesis. In W. Damon, D. Kuhn, & R. S. Siegler (Eds.).Handbook of child psychology: Cognition, perception, and language (5th ed., Vol. 1, pp. 575-630). Wiley.
Gray, S. A., & Reeve, R. A. (2016). Number-specific and general cognitive markers of preschoolers’ math ability profiles. Journal of Experimental Child Psychology, 147, 1-21.
Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15(3), 237-256.
Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Preschool children's spontaneous focusing on numerosity, subitizing and counting skills as predictors of their mathematical performance 7 years later at school.Mathematical Thinking and Learning, 17(2-3), 155-177.
Hannula, M. M., Lepola, J., & Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107(4), 394-406.
Hannula-Sormunen, M.(2014). Spontaneous focusing on numerosity and its relation to counting and arithmetic. In R. Cohen-Kadosh & A. Dowker (Eds.), Handbook of Numerical Cognition (pp.275-290). Oxford University Press.
Hollands, J. G. & Dyre, B. P. (2000). Bias in proportion judgments:The cyclical power model. Psychological Review, 107(3), 500-524.
Jung, T., & Wickrama, K. (2008). An introduction to latent class growth analysis and growth mixture modeling.Social and Personality Psychology Compass, 2(1), 302-317.
Kucian, K., Ashkenazi, S. S., Hänggi, J., Rotzer, S., Jäncke, L., Martin, E., & von Aster, M. (2014). Developmental dyscalculia: A dysconnection syndrome? Brain Structure and Function, 219(5), 1721-1733.
Lanza, S. T., Collins, J. L., Lemmon, D., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis.Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 671-694.
Lehtinen, E., Hannula-Sormunen, M., McMullen, J., & Gruber, H. (2017). Cultivating mathematical skills: From drill-and-practice to deliberate practice.ZDM Mathematics Education, 49, 625-636.
Liang Y., Zhang, L., Long, Y., Deng, Q., & Liu, Y. (2020). Promoting effects of RTI-based mathematical play training on number sense growth among low-SES preschool children. Early Education and Development, 31(3), 335-353.
Magidson, J., & Vermunt, J. K. (2003). Comparing latent class factor analysis with traditional approach in data mining. In H. Bozdogan (Ed.),Statistical data mining and knowledge discovery (pp. 373-383). Chapman and Hall/CRC Press.
McMullen, J., Chan, J. Y.-C., Mazzocco, M. M. M., & Hannula-Sormunen, M. M. (2019). Spontaneous mathematical focusing tendencies in mathematical development and education. In A. Norton & M. W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education (pp. 69-86). Springer International Publishing.
Miller, K., Major, S. M., Shu, H., & Zhang, H. (2000). Ordinal knowledge: Number names and number concepts in Chinese and English.Canadian Journal of Experimental Psychology, 54, 129-140.
Nanu, C. E., McMullen, J., Munck, P., & Hannula-Sormunen, M. M. (2018). Spontaneous focusing on numerosity in preschool as a predictor of mathematical skills and knowledge in the fifth grade. Journal of Experimental Child Psychology, 169, 42-58.
Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study.Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 535-569.
Odic, D., Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Developmental change in the acuity of approximate number and area representations. Developmental Psychology, 49(6), 1103-1112.
Opfer, J. E., Siegler, R. S., & Young, C. J. (2011). The powers of noise-fitting: Reply to Barth and Paladino. Developmental Science, 14(5), 1194-1204.
Peeters, D., Degrande, T., Ebersbach, M., Verschaffel, L., & Luwel, K. (2016). Children’s use of number line estimation strategies.European Journal of Psychology of Education, 31(2), 117-134.
Rathé, S., Torbeyns, J., Hannula-Sormunen, M. M., De Smedt, B., & Verschaffel, L. (2016). Spontaneous focusing on numerosity: A review of recent research.Mediterrean Journal for Research in Mathematics Education, 15, 1-25.
Rathé, S., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Spontaneous focusing on Arabic number symbols and its association with early mathematical competencies.Early Childhood Research Quarterly, 48, 111-121.
Rathé, S., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2022). Longitudinal associations between spontaneous number focusing tendencies, numerical abilities, and mathematics achievement in 4- to 7-year-olds. Journal of Educational Psychology, 114(1), 37-55.
Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Child Psychology: General, 141(4), 649-666.
Schneider, M., Merz, S., Stricker, J., De Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89(5), 1467-1484.
Sella, F., Berteletti, I., Lucangeli, D., & Zorzi, M. (2015). Varieties of quantity estimation in children. Developmental Psychology, 51(6), 758-770.
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.
Siegler, R. S., Thompson, C. A., & Opfer, J. E. (2010). The logarithmic-to-linear shift: One learning sequence, many tasks, many time scales. Mind Brain & Education, 3(3), 143-150.
Slusser, E. B., Santiago, R. T., & Barth, H. C. (2013). Developmental change in numerical estimation. Journal of Experimental Psychology: General, 142(1), 193-200.
Slusser, E., & Barth, H. (2011).An Excel worksheet for proportion-judgment analyses of number-line data. Department of Psychology, Wesleyan University, Middletown, CT. Hilary Barth. https://hbarth.faculty.wesleyan.edu
Slusser, E., & Barth, H. (2017). Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks. Journal of Experimental Child Psychology, 162, 181-198.
Spelke, E. S. (2017). Core knowledge, language, and number.Language Learning and Development, 13(2), 147-170.
Stoianov, I. P., & Zorzi, M. (2012). The abstraction of visual numerosity from continous visual properties. Perception ECVP Abstract, 41, 256.
Torbeyns, J., Bojorque, G., Van Hoof, J., Van Nijlen, D., & Verschaffel, L. (2018). Unique contribution of Ecuadorian kindergartners' spontaneous focusing on numerosity to their early numerical abilities.British Journal of Developmental Psychology, 36(2), 299-312.
Vermunt, J. K., & Magidson, J. (2013). Technical guide for Latent GOLD 5.0: Basic, advanced, and syntax. Statistical Innovations.
Verschaffel, L., Rathé, S., Wijns, N., Degrande, T., Van Dooren, W., De Smedt, B., & Torbeyns, J. (2020). Young children's early mathematical competencies: The role of mathematical focusing tendencies. In M. Carlsen, I. Erfjord & P. Hundeland (Eds.),Mathematics education in the early years (pp. 23-42). Springer-Cham.
von Aster, R. S., & Shalev, S. S. (2007). Number development and developmental dyscalculia.Developmental Medicine & Child Neurology, 49(11), 868-873.
Wong, T. T.-Y., & Chan, W. W. L. (2019). Identifying children with persistent low math achievement: The role of number-magnitude mapping and symbolic numerical processing.Learning and Instruction, 60, 29-40.
崔爽, 高亚茹, 王阳阳, 黄碧娟, 司继伟. (2020). 非正式学习环境中幼儿的自发数量聚焦. 心理科学进展, 28(12), 2064-2075.
张洁婷, 焦璨, 张敏强. (2010). 潜在类别分析技术在心理学研究中的应用. 心理科学进展, 18(12), 1991-1998.
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