Psychological Development and Education ›› 2012, Vol. 28 ›› Issue (2): 121-130.

Previous Articles     Next Articles

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. 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

PDF (PC)

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

CLC Number: 

  • B844.1
[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.
[1] CHEN Jianwen, LIU Yan, TAN Qianbao. The Relationship of Cumulative Ecological Risk and Higher Vocational College Students’ Learning Burnout: The Mediation Effect of Negative Self-schema and Internet Addiction [J]. Psychological Development and Education, 2022, 38(4): 576-583.
[2] XU Junting, BAO Wei, LUO Junlong. Unstable Control Deprivation Impairs Working Memory Updating [J]. Psychological Development and Education, 2022, 38(1): 1-9.
[3] NIU Yubai, SHI Ranran, CAO Xiancai. Preschool Children's Approximate Number System Acuity and Symbolic Number Abilities [J]. Psychological Development and Education, 2016, 32(2): 129-138.
[4] DAI Man, LIU Ru-de, DI Miao-ci, MA Xue-ying, XU Le. The Effects of Working Memory Load and Automatic Retrieval on Elementary School Students Mental Addition Strategy Execution [J]. Psychological Development and Education, 2014, 30(4): 420-426.
[5] WEN Ping, ZHANG Li, LI Hong, LIULI Xiang-jun, ZHANG Xue-yi. Model of Executive Functioning As Predictor of Children’s Mathematical Ability [J]. Psychological Development and Education, 2007, 23(3): 13-18.
[6] CHEN Shang-bao, WO Jian-zhong, LUO Liang. The Developmental Characteristics of 8～11 Year-old Strategy in Solving Addition Comparison Problems [J]. Psychological Development and Education, 2005, 21(2): 17-23.
[7] YING He-chen, GENG Liu-na. The Developmental Characteristics of Children Addition and Subtraction Strategy Selection in Grade 1～3 Primary Students [J]. Psychological Development and Education, 2005, 21(2): 11-16.
[8] WO Jian-zhong, LI Feng, CHEN Shang-bao. The Developmental Characteristics of Children Addition Strategy in 5-7 year-old [J]. Psychological Development and Education, 2002, 18(4): 26-30.
[9] ZHANG Qi, LIN Chong-de. The Developmental Study of the Speeds and Spans of Mental Addition of Pupils [J]. Psychological Development and Education, 2002, 18(1): 16-21.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of Psychological Development and Education
Supported by Beijing Magtech Co.Ltd