4～6岁儿童加减法反演律概念的发展与影响因素

心理发展与教育 ›› 2012, Vol. 28 ›› Issue (2): 121-130.

4～6岁儿童加减法反演律概念的发展与影响因素

韩瑽瑽¹, 曹仕莹², 陈英和¹

1. 京师范大学发展心理研究所, 北京100875;
2. 河北正定中学, 石家庄050800

出版日期:2012-03-15 发布日期:2012-03-15
通讯作者: 陈英和,E-mail:chenyinghe@bnu.edu.cn E-mail:chenyinghe@bnu.edu.cn
基金资助:
北京市教育科学十一五规划课题(ACA08017);北京师范大学研究生院优秀博士学位论文培育基金项目(019-10421203GK)

Four to Six-Year-Old Children’s Understanding of Inversion Concept about Addition and Subtraction and Its Influencing Factors

HAN Cong-cong¹, CAO Shi-ying², CHEN Ying-he¹

1. Institute of Developmental Psychology, Beijing Normal University, Beijing 100875;
2. Zhengding Middle School of Hebei Province, Shijiazhuang 050800

Online:2012-03-15 Published:2012-03-15

摘要/Abstract

摘要： 儿童对加法和减法逆反关系的理解在加法概念和减法概念的学习中具有十分重要的作用。研究采用代数推理任务、给数取物任务、数量比较任务和记忆刷新任务,对83名4到6岁幼儿进行施测,考察4到6岁儿童加减法反演律概念的发展特点,探讨儿童的基数概念、数量比较、记忆刷新能力在反演律概念发展中的作用。结果发现:(1)5岁到6岁是儿童掌握和运用加减法反演律概念的快速发展时期。幼儿的加减法反演律概念表现出数量大小效应以及问题情境效应,小数反演问题的成绩优于大数反演问题的成绩,符号化数量反演的成绩优于集合数量反演的成绩。(2)基数概念掌握组儿童加减法反演律概念的发展显著优于未掌握组;但儿童基数概念的掌握情况并不显著预测儿童反演律概念的发展。(3)数量比较、记忆刷新对儿童加减法反演律概念的发展具有显著的正向预测作用。

关键词: 反演律, 加减法, 基数概念, 数量比较, 记忆刷新

Abstract: The reverse relationship of addition and subtraction is critical in children's learning of addition and subtraction.83 children aged 4 to 6 participated in this study.Algebraic Reasoning Paradigm,Cardinal tasks,Magnitude Comparison task,and Running Memory task were administered to examine the developmental trend of 4 to 6year-old preschooler's inversion concept about addition and subtraction,and how this trajectory influenced by Cardinal,Quantity Comparison and Memory Updating.Results showed that:(1)neither in non-symbolic nor symbolic inverse problems,4 and 5-year-old children's accuracy was above chance level.Few 4 and 5-year-old children passed the inverse problems.However,6-year-old kids had a great progress in both non-symbolic and symbolic inverse problems.Almost half of the 6-year-old children passed the symbolic inverse problems.4 to 6-year-old preschooler's accuracy was higher in small number problems than in large number problems,and higher in symbolic quantity problems than analog quantity problems.(2)Preschoolers,those who had already grasped cardinals were much better in the development of inversion concept than those who hadn't.However,according to children's knowledge of cardinal,we cannot predict their understanding about inversion concept.(3)Magnitude Comparison and Memory Updating had salient and positive prediction to children understands of inversion concept.

Key words: inversion, addition, subtraction, magnitude comparison, updating

中图分类号:

B844.1

韩瑽瑽, 曹仕莹, 陈英和. 4～6岁儿童加减法反演律概念的发展与影响因素[J]. 心理发展与教育, 2012, 28(2): 121-130.

HAN Cong-cong, CAO Shi-ying, CHEN Ying-he. Four to Six-Year-Old Children’s Understanding of Inversion Concept about Addition and Subtraction and Its Influencing Factors[J]. Psychological Development and Education, 2012, 28(2): 121-130.

参考文献

[1] Baddeley,A.D.(2002).Human memory:theory and practice.4th. East Sussex:Psychology Press.
[2] Bisanz,J.,Watchorn,R.P.D.,&Piatt,C.(2009).On"under-standing"children's developing use of inversion.Mathematical Thinking and Learning,11,10-24.
[3] Canobi,K.H.,&Bethune,N.E.(2008).Number words in young children conceptual and procedural knowledge of addition,subtraction and inversion.Cognition,108,675-686.
[4] Carey,S.(2001).Cognitive foundations of arithmetic:Evolution and ontogenesis.Mind&Language,16,37-55.
[5] Carey,S.(2004).Bootstrapping and the origins of concepts.Daedalus,133(1),59-68.
[6] Carey,S.,&Sarnecka,B.W.(2006).The development of human conceptual representations.In M.Johnson&Y.Munakata(Eds.), Processes of change in brain and cognitive development:Attention and performance XXI(pp.473-496).New York:Academic Press. Dehaene,S.(1992).Varieties of numerical abilities.Cognition,44,1-42.
[7] Deschuyteneer,M.,Vandierendonck,A.,&Muyllaert,I.(2006).Does Solution of mental arithmetic problems such as 2+6 and 3×8 rely on the process of "memory updating"?Experimental Psychology,53(3),198-208.
[8] Feigenson,L.,Dehaene,S.,&Spelke,E.(2004).Core systems of number.Trends in Cognitive Science,8(7),307-314.
[9] Gilmore,C.K.(2005).Children's understanding of the inverse relationship between addition and subtraction.Doctoral dissertation,University of Oxford,UK.
[10] Gilmore,C.K.(2006).Investigating children's understanding of inversion using the missing number paradigm.Cognitive Development,21,301-316.
[11] Gilmore,C.K.,&Bryant,P.(2006).Individual differences in children's understanding of inversion and arithmetical skill.British Journal of Educational Psychology,76,309-331.
[12] Gilmore,C.K.,&Papadatou-Pastou,M.(2009).Patterns of individual differences in conceptual understanding and arithmetical skill:A meta-analysis.Mathematical Thinking and Learning,11,25-40.
[13] Gilmore,C.K.,&Spelke,E.S.(2008).Children's understanding of the relationship between addition and subtraction.Cognition,107,932-945.
[14] Lai,M.L.,Baroody,A.J.,&Johnson,A.R.(2008).Fostering Taiwanese preschoolers'understanding of the addition-subtraction inverse principle.Cognitive Development,23,216-235.
[15] Logan,G.D.,&Zbrodoff,N.J.(2003).Subitizing and similarity:Toward a pattern-matching theory of enumeration.Psychonomic Bulletin &Review.3(7),676-682.
[16] Mix,K.S.,Hutternlocher,J.,&Levine,S.C.(2002).Multiple cues for quantification in infancy:Is number one of them?Psychological Bulletin,128(2),278-294.
[17] Passolunghi,M.C.,&Pazzaglia,F.P.(2004).Individual differences in memory updating in relation to arithemtic problem solving.Learning and Individual Differences,14,219-230.
[18] Piaget,J.(1952).The child's conception of number.London:Routledge&Kegan Paul.
[19] Resnick,L.B.(1992).From protoquantities to operators:Building mathematical competence on a foundation of everyday knowledge.In G.Leinhardt,R.Putnam,&R.A.Hattrup(Eds.),Analysis of arithmetic for mathematics teaching(pp.373-425).Hillsdale,NJ: Erlbaum.
[20] Sherman,J.,&Bisanz,J.(2007).Evidence for use of mathematical inversion by three-year-old children.Journal of Cognition and Development,8,333-344.
[21] Vilette,B.(2002).Do young children grasp the inverse relationship between addition and subtraction?Cognitive Development,17,1365-1383.
[22] Wynn,K.(1992).Addition and subtraction by human infants.Nature,358,749-750.
[23] 刘锋,陈旭.(2009).婴儿的数认知核心系统.心理科学进展,17(1),78-85.
[24] 王乃弋,罗跃嘉,李红.(2006).两种数量表征系统.心理科学进展,14(4),610-617.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed