元认知监测与算术知识制约小学儿童心算策略运用能力的发展:一年纵向考察
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摘要
为探究元认知监测与算术知识对儿童心算策略运用能力的影响如何随个体发展而变化,采用计算机任务与纸笔测量的方法,对85名小学三、五年级儿童进行了历时一年的纵向追踪研究。研究发现:(1)两组儿童的元认知监测和算术知识均呈增长趋势,算术知识的增长速度五年级显著快于三年级,且元认知监测增长速度与算术知识增长速度显著相关;(2)两组儿童中,元认知监测与算术知识增长速度更快的个体策略执行反应时与错误率的减少速度也更快;(3)五年级儿童的算术知识在元认知监测影响策略选择发展中起着完全中介作用。
It is very fast for the development of a high level of math ability in primary school. So it is necessary to investigate how metacognitive monitoring and arithmetic knowledge impact the performance of strategy use in arithmetic problem solving from the longitudinal perspective. Total 85 primary school age children from two classes( third and fifth graders) took part in the present longitudinal study. Three measures on them in a whole year were administered. Results showed that( 1) metacognitive monitoring showed linear growth trends in two groups. The growth of arithmetic knowledge in fifth grade was much faster than in third grade. And the growth of metacognitive monitoring can predict the growth of arithmetic knowledge significantly;( 2) Both the growth of metacognitive monitoring and arithmetic knowledge can predict the growth of strategy execution adaptability in both two groups on RTs and error rates;( 3) In accurate mental calculation,the effect of metacognitive monitoring on strategy selection is via the complete mediating effect of arithmetic knowledge in fifth grade.
It is very fast for the development of a high level of math ability in primary school. So it is necessary to investigate how metacognitive monitoring and arithmetic knowledge impact the performance of strategy use in arithmetic problem solving from the longitudinal perspective. Total 85 primary school age children from two classes( third and fifth graders) took part in the present longitudinal study. Three measures on them in a whole year were administered. Results showed that( 1) metacognitive monitoring showed linear growth trends in two groups. The growth of arithmetic knowledge in fifth grade was much faster than in third grade. And the growth of metacognitive monitoring can predict the growth of arithmetic knowledge significantly;( 2) Both the growth of metacognitive monitoring and arithmetic knowledge can predict the growth of strategy execution adaptability in both two groups on RTs and error rates;( 3) In accurate mental calculation,the effect of metacognitive monitoring on strategy selection is via the complete mediating effect of arithmetic knowledge in fifth grade.
引文
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Braver,T.S.,Gray,J.R.,&Burgess,G.C.(2007).Explaining the many varieties of working memory variation:Dual mechanisms of cognitive control.In A.R.A.Conway,C.Jarrold,M.J.Kane,A.Miyake,&J.N.Towse(Eds.),Variation in working memory(pp.76-106).New York,NY,USA:Oxford University Press.
Campbell,J.I.D.(2005).Handbook of mathematical cognition.New York:Psychology Press.
Chevalier,N.,Martis,S.B.,Curran,T.,&Munakata,Y.(2015).Metacognitive processes in executive control development:The case of reactive and proactive control.Journal of Cognitive Neuroscience,27(6),1125-1136.
Chu,F,W.,vanMarle,K.,Rouder,Jeffrey.,&Geary,D.C.(2018).Children’s early understanding of number predicts their later problem-solving sophistication in addition.Journal of Experimental Child Psychology,169,73-92.
Desoete,A.,Roeyers,H.,&Buysse,A.(2001).Metacognition and mathematical problem solving in grade 3.Journal of Learning Disabilities,34(5),435-449.
Duncan,T.E.,Duncan,S.C.,&Li,F.Z.(1998).A comparison of model-and multiple imputation-based approaches to longitudinal analyses with partial missingness.Structural Equation Modelling,5(1),1-21.
Dunlosky,J.,&Hertzog,C.(2000).Updating knowledge about strategy effectiveness:A componential analysis of learning about strategy effectiveness from task experience.Psychology and Aging,15(3),462-474.
Dunlosky,J.,&Metcalfe,J.(2009).Metacognition.Thousand Oaks,CA:Sage Publications,Inc.
Fan,X.,&Konold,T.R.(2009).Latent growth curve analysis in structural equation modeling:Concepts and implementations.In T.Teo,&M.S.Khine(Eds.),Structural equation modeling:Concepts and applications in educational research(pp.29-58).Rotterdam,Netherlands:Sense Publishers.
Fehr,T.,Code,C.,&Herrmann,M.(2007).Common brain regions underlying different arithmetic operations as revealed by conjunct f MRI-BOLD activation.Brain Research,1172,93-102.
Georghiades,P.(2004).From the general to the situated:Three decades of metacognition.International Journal of Science Education,26(3),365-383.
Geurten,M,&Lemaire,P.(2017).Age-related differences in strategic monitoring during arithmetic problem solving.Acta Psychologica,180,105-116.
Geurten,M,&Lemaire,P.(2018).Metacognition for strategy selection during arithmetic problem-solving in young and older adults.Aging Neuropsychology and Cognition,1-23
Hertzog,C.(2016).Aging and metacognitive control.In J.Dunlosky&S.K.Tauber(Eds.),Oxford handbook of metacognition,Oxford,UK:Oxford University Press.
Klein,E.,Nuerk,H.,Wood,G.,Knops,A.,&Willmes,K.(2009).The exact vs.approximate distinction in numerical cognition may not be exact,but only approximate:How different processes work together in multidigit addition.Brain and Cognition,69(2),369-381.
Kraemer,H.C.,Yesavage,J.A.,Taylor,J.L.,&Kupfer,D.(2000).How can we learn about developmental processes from crosssectional studies,or can we?American Journal of Psychiatry,157(2),163-171.
Lemaire,P.,&Callies,S.(2009).Children’s strategies in complex arithmetic.Journal of Experimental Child Psychology,103(1),49-65.
Lemaire,P.,&Hinault,T.(2014).Age-related differences in sequential modulations of poorer-strategy effects:A study in arithmetic problem solving.Experimental Psychology,61(4):253-262.
Lemaire,P.,&Lecacheur,M.(2010).Strategy switch costs in arithmetic problem solving.Memory and Cognition,38(3),322-332.
Lemaire,P.,&Lecacheur,M.(2011).Age-related changes in children’s executive functions and strategy selection:A study in computational estimation.Cognitive Development,26(3),282-294.
Lovett,M.C.,&Schunn,C.D.(1999).Task representations,strategy variability and base-rate neglect.Journal of Experimental Psychology:General,128(2),107-130.
Nelson,T.O.(1996).Consciousness and metacognition.American Psychologist,51,102-116.doi:10.1037/0003-066X.51.2.102
Pennequin,V.,Sorel,O.,Nanty,I.,&Fontaine,R.(2010).Metacognition and low achievement in mathematics:The effect of training in the use of metacognitive skills to solve mathematical word problems.Thinking and Reasoning,16(3),198-220.
Rieskamp,J.,&Otto,P.E.(2006).SSL:A theory of how people learn to select strategies.Journal of Experimental Psychology:General,135(2),207-236.
Rittle-Johnson,B.,&Star,J.R.(2007).Do comparing solution methods facilitate conceptual and procedural knowledge?An experimental study on learning to solve equations.Journal of Educational Psychology,99(3),561-574.
Schmitt,M.C.,&Sha,S.(2009).The developmental nature of metacognition and the relationship between knowledge and control over time.Journal of Research in Reading,32(2),254-271.
Siegler,R.S.,&Araya,R.(2005).A computational model of conscious and unconscious strategy discovery.In R.V.Kail(Ed.),Advances in child development and behavior(Vol.33,pp.1-42).Oxford,UK:Elsevier.
Siegler,R.S.,&Booth,J.(2005).Development of numerical estimation:A review.In J.I.D.Campbell(Ed.),Handbook of mathematical cognition(pp.197-212).New York:Psychology Press.
Taillan,J.,Ardiale,E.,&Lemaire,P.(2015).Relationships between strategy switching and strategy switch costs in young and older adults:A study in arithmetic problem solving.Experimental Aging Research,41(2),136-156.
Tiberghien,K.,Notebaert,W.,De Smedt,B.,&Fias,W.(2017).Reactive and proactive control in arithmetical strategy selection.Journal of Numerical Cognition,3(3),598-619.
Veenman,M.,Van Hout-Wolters,B.,&Afflerbach,P.(2006).Metacognition and learning:Conceptual and methodological considerations.Metacognition and Learning,1(1),3-14.
Vígh-Kiss,E.R.(2013).Adaptive strategy use in mathematics education.In J.T.Karlovitz(Eds.),Questions and perspectives in education(pp.342-352).Komárno:International Research Institute.
陈英和,韩瑽瑽.(2012).儿童青少年元认知的发展特点及作用的心理机制.心理科学,35(3),537-543.
刘伟方,华晓腾,封洪敏,胡冬梅,司继伟.(2014).算术策略运用能力的年龄差异:元认知监测与算术知识的作用.心理发展与教育,30(3),234-243.
刘伟方,司继伟,王玉璇.(2011).认知策略选择的元认知因素.心理科学进展,19(9),1328-1338.
吴灵丹,刘电芝.(2006).儿童计算的元认知监测及其对策略选择的影响.心理科学,29(2),354-357.
Braver,T.S.,Gray,J.R.,&Burgess,G.C.(2007).Explaining the many varieties of working memory variation:Dual mechanisms of cognitive control.In A.R.A.Conway,C.Jarrold,M.J.Kane,A.Miyake,&J.N.Towse(Eds.),Variation in working memory(pp.76-106).New York,NY,USA:Oxford University Press.
Campbell,J.I.D.(2005).Handbook of mathematical cognition.New York:Psychology Press.
Chevalier,N.,Martis,S.B.,Curran,T.,&Munakata,Y.(2015).Metacognitive processes in executive control development:The case of reactive and proactive control.Journal of Cognitive Neuroscience,27(6),1125-1136.
Chu,F,W.,vanMarle,K.,Rouder,Jeffrey.,&Geary,D.C.(2018).Children’s early understanding of number predicts their later problem-solving sophistication in addition.Journal of Experimental Child Psychology,169,73-92.
Desoete,A.,Roeyers,H.,&Buysse,A.(2001).Metacognition and mathematical problem solving in grade 3.Journal of Learning Disabilities,34(5),435-449.
Duncan,T.E.,Duncan,S.C.,&Li,F.Z.(1998).A comparison of model-and multiple imputation-based approaches to longitudinal analyses with partial missingness.Structural Equation Modelling,5(1),1-21.
Dunlosky,J.,&Hertzog,C.(2000).Updating knowledge about strategy effectiveness:A componential analysis of learning about strategy effectiveness from task experience.Psychology and Aging,15(3),462-474.
Dunlosky,J.,&Metcalfe,J.(2009).Metacognition.Thousand Oaks,CA:Sage Publications,Inc.
Fan,X.,&Konold,T.R.(2009).Latent growth curve analysis in structural equation modeling:Concepts and implementations.In T.Teo,&M.S.Khine(Eds.),Structural equation modeling:Concepts and applications in educational research(pp.29-58).Rotterdam,Netherlands:Sense Publishers.
Fehr,T.,Code,C.,&Herrmann,M.(2007).Common brain regions underlying different arithmetic operations as revealed by conjunct f MRI-BOLD activation.Brain Research,1172,93-102.
Georghiades,P.(2004).From the general to the situated:Three decades of metacognition.International Journal of Science Education,26(3),365-383.
Geurten,M,&Lemaire,P.(2017).Age-related differences in strategic monitoring during arithmetic problem solving.Acta Psychologica,180,105-116.
Geurten,M,&Lemaire,P.(2018).Metacognition for strategy selection during arithmetic problem-solving in young and older adults.Aging Neuropsychology and Cognition,1-23
Hertzog,C.(2016).Aging and metacognitive control.In J.Dunlosky&S.K.Tauber(Eds.),Oxford handbook of metacognition,Oxford,UK:Oxford University Press.
Klein,E.,Nuerk,H.,Wood,G.,Knops,A.,&Willmes,K.(2009).The exact vs.approximate distinction in numerical cognition may not be exact,but only approximate:How different processes work together in multidigit addition.Brain and Cognition,69(2),369-381.
Kraemer,H.C.,Yesavage,J.A.,Taylor,J.L.,&Kupfer,D.(2000).How can we learn about developmental processes from crosssectional studies,or can we?American Journal of Psychiatry,157(2),163-171.
Lemaire,P.,&Callies,S.(2009).Children’s strategies in complex arithmetic.Journal of Experimental Child Psychology,103(1),49-65.
Lemaire,P.,&Hinault,T.(2014).Age-related differences in sequential modulations of poorer-strategy effects:A study in arithmetic problem solving.Experimental Psychology,61(4):253-262.
Lemaire,P.,&Lecacheur,M.(2010).Strategy switch costs in arithmetic problem solving.Memory and Cognition,38(3),322-332.
Lemaire,P.,&Lecacheur,M.(2011).Age-related changes in children’s executive functions and strategy selection:A study in computational estimation.Cognitive Development,26(3),282-294.
Lovett,M.C.,&Schunn,C.D.(1999).Task representations,strategy variability and base-rate neglect.Journal of Experimental Psychology:General,128(2),107-130.
Nelson,T.O.(1996).Consciousness and metacognition.American Psychologist,51,102-116.doi:10.1037/0003-066X.51.2.102
Pennequin,V.,Sorel,O.,Nanty,I.,&Fontaine,R.(2010).Metacognition and low achievement in mathematics:The effect of training in the use of metacognitive skills to solve mathematical word problems.Thinking and Reasoning,16(3),198-220.
Rieskamp,J.,&Otto,P.E.(2006).SSL:A theory of how people learn to select strategies.Journal of Experimental Psychology:General,135(2),207-236.
Rittle-Johnson,B.,&Star,J.R.(2007).Do comparing solution methods facilitate conceptual and procedural knowledge?An experimental study on learning to solve equations.Journal of Educational Psychology,99(3),561-574.
Schmitt,M.C.,&Sha,S.(2009).The developmental nature of metacognition and the relationship between knowledge and control over time.Journal of Research in Reading,32(2),254-271.
Siegler,R.S.,&Araya,R.(2005).A computational model of conscious and unconscious strategy discovery.In R.V.Kail(Ed.),Advances in child development and behavior(Vol.33,pp.1-42).Oxford,UK:Elsevier.
Siegler,R.S.,&Booth,J.(2005).Development of numerical estimation:A review.In J.I.D.Campbell(Ed.),Handbook of mathematical cognition(pp.197-212).New York:Psychology Press.
Taillan,J.,Ardiale,E.,&Lemaire,P.(2015).Relationships between strategy switching and strategy switch costs in young and older adults:A study in arithmetic problem solving.Experimental Aging Research,41(2),136-156.
Tiberghien,K.,Notebaert,W.,De Smedt,B.,&Fias,W.(2017).Reactive and proactive control in arithmetical strategy selection.Journal of Numerical Cognition,3(3),598-619.
Veenman,M.,Van Hout-Wolters,B.,&Afflerbach,P.(2006).Metacognition and learning:Conceptual and methodological considerations.Metacognition and Learning,1(1),3-14.
Vígh-Kiss,E.R.(2013).Adaptive strategy use in mathematics education.In J.T.Karlovitz(Eds.),Questions and perspectives in education(pp.342-352).Komárno:International Research Institute.
陈英和,韩瑽瑽.(2012).儿童青少年元认知的发展特点及作用的心理机制.心理科学,35(3),537-543.
刘伟方,华晓腾,封洪敏,胡冬梅,司继伟.(2014).算术策略运用能力的年龄差异:元认知监测与算术知识的作用.心理发展与教育,30(3),234-243.
刘伟方,司继伟,王玉璇.(2011).认知策略选择的元认知因素.心理科学进展,19(9),1328-1338.
吴灵丹,刘电芝.(2006).儿童计算的元认知监测及其对策略选择的影响.心理科学,29(2),354-357.