메뉴 건너뛰기




Volumn 63, Issue 3, 2009, Pages 193-200

A microgenetic study of the multiplication and division inversion concept

Author keywords

Arithmetic; Conceptual knowledge; Inversion; Microgenetic

Indexed keywords

ADOLESCENT; ARTICLE; CHILD; CONCEPT FORMATION; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; PHYSIOLOGY; PROBLEM SOLVING; REACTION TIME;

EID: 70349611718     PISSN: 11961961     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0013908     Document Type: Article
Times cited : (18)

References (30)
  • 1
    • 38149145223 scopus 로고
    • An evaluation of evidence supporting fact-retrieval models
    • Baroody, A. J. (1994). An evaluation of evidence supporting fact-retrieval models. Learning and Individual Differences, 6, 1-36.
    • (1994) Learning and Individual Differences , vol.6 , pp. 1-36
    • Baroody, A.J.1
  • 2
    • 84908959608 scopus 로고    scopus 로고
    • The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge
    • A. J. Baroody & A. Dowker (Eds.), Mahwah, NJ: Erlbaum.
    • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1-33). Mahwah, NJ: Erlbaum.
    • (2003) The Development of Arithmetic Concepts and Skills , pp. 1-33
    • Baroody, A.J.1
  • 3
    • 85065689686 scopus 로고
    • The relationship between initial meaningful and mechanical knowledge of arithmetic
    • J. Hiebert (Ed.), Hillsdale, NJ: Erlbaum.
    • Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75-112). Hillsdale, NJ: Erlbaum.
    • (1986) Conceptual and Procedural Knowledge: the Case of Mathematics , pp. 75-112
    • Baroody, A.J.1    Ginsburg, H.P.2
  • 4
    • 38949198927 scopus 로고    scopus 로고
    • Preschoolers' understanding of the addition-subtraction inversion principle: A Taiwanese sample
    • Baroody, A. J., & Lai, M. (2007). Preschoolers' understanding of the addition-subtraction inversion principle: A Taiwanese sample. Mathematical Thinking and Learning, 9, 131-171.
    • (2007) Mathematical Thinking and Learning , vol.9 , pp. 131-171
    • Baroody, A.J.1    Lai, M.2
  • 5
    • 84909106688 scopus 로고    scopus 로고
    • Two perspectives on addition development
    • A. J. Aroody & A. Dowker (Eds.), Mahwah, NJ: Erlbaum.
    • Baroody, A. J., & Tiilikainen, S. H. (2003). Two perspectives on addition development. In A. J. Aroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 75-126). Mahwah, NJ: Erlbaum.
    • (2003) The Development of Arithmetic Concepts and Skills , pp. 75-126
    • Baroody, A.J.1    Tiilikainen, S.H.2
  • 6
    • 0002445611 scopus 로고
    • Strategic and nonstrategic processing in the development of mathematical cognition
    • D. F. Bjorklund (Ed.), Hillsdale, NJ: Erlbaum.
    • Bisanz, J., & LeFevre, J.-A. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D. F. Bjorklund (Ed.), Children's strategies: Contemporary views of cognitive development (pp. 213-244). Hillsdale, NJ: Erlbaum.
    • (1990) Children's Strategies: Contemporary Views of Cognitive Development , pp. 213-244
    • Bisanz, J.1    Lefevre, J.A.2
  • 7
    • 0742289073 scopus 로고    scopus 로고
    • Individual differences in children's addition and subtraction knowledge
    • DOI 10.1016/j.cogdev.2003.10.001, PII S0885201403000662
    • Canobi, K. H. (2004). Individual differences in children's addition and subtraction knowledge. Cognitive Development, 19, 81-93. (Pubitemid 38148377)
    • (2004) Cognitive Development , vol.19 , Issue.1 , pp. 81-93
    • Canobi, K.H.1
  • 8
    • 84868266019 scopus 로고    scopus 로고
    • Do they know what they are doing? Children's use of economical addition strategies and knowledge of commutativity
    • Cowan, R., & Renton, M. (1996). Do they know what they are doing? Children's use of economical addition strategies and knowledge of commutativity. Educational Psychology, 16, 407-420.
    • (1996) Educational Psychology , vol.16 , pp. 407-420
    • Cowan, R.1    Renton, M.2
  • 9
    • 33744522327 scopus 로고    scopus 로고
    • Investigating children's understanding of inversion using the missing number paradigm
    • Gilmore, C. K. (2006). Investigating children's understanding of inversion using the missing number paradigm. Cognitive Development, 21, 301-316.
    • (2006) Cognitive Development , vol.21 , pp. 301-316
    • Gilmore, C.K.1
  • 10
    • 42249115841 scopus 로고    scopus 로고
    • Children's understanding of the relationship between addition and subtraction
    • Gilmore, C. K., & Spelke, E. S. (2008). Children's understanding of the relationship between addition and subtraction. Cognition, 107, 932-945.
    • (2008) Cognition , vol.107 , pp. 932-945
    • Gilmore, C.K.1    Spelke, E.S.2
  • 11
    • 0034199374 scopus 로고    scopus 로고
    • Preschoolers doing arithmetic: The concepts are willing but the working memory is weak
    • Klein, J. S., & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal of Experimental Psychology, 54, 105-115.
    • (2000) Canadian Journal of Experimental Psychology , vol.54 , pp. 105-115
    • Klein, J.S.1    Bisanz, J.2
  • 12
    • 0020390439 scopus 로고
    • The development of problem solving strategies
    • H. Reese (Ed.), New York: Academic.
    • Kuhn, D., & Phelps, E. (1982). The development of problem solving strategies. In H. Reese (Ed.), Advances in child development and behavior (Vol. 17, pp. 1-44). New York: Academic.
    • (1982) Advances in Child Development and Behavior , vol.17 , pp. 1-44
    • Kuhn, D.1    Phelps, E.2
  • 13
    • 0036400919 scopus 로고    scopus 로고
    • An analysis of students' initial statistical understandings: Developing a conjectured learning trajectory
    • McGatha, M., Cobb, P., & McClain, K. (2002). An analysis of students' initial statistical understandings: Developing a conjectured learning trajectory. Journal of Mathematical Behavior, 21, 339-355.
    • (2002) Journal of Mathematical Behavior , vol.21 , pp. 339-355
    • McGatha, M.1    Cobb, P.2    McClain, K.3
  • 16
    • 0035602865 scopus 로고    scopus 로고
    • Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process
    • DOI 10.1037//0022-0663.93.2.346
    • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-362. (Pubitemid 33375073)
    • (2001) Journal of Educational Psychology , vol.93 , Issue.2 , pp. 346-362
    • Rittle-Johnson, B.1    Siegler, R.S.2    Alibali, M.W.3
  • 17
    • 0035579746 scopus 로고    scopus 로고
    • The validity of verbal reports in children's subtraction
    • Robinson,K.M.(2001).Thevalidityofverbalreportsinchildren'ssubtraction. JournalofEducationalPsychology,93,211-222.(Pubitemid33242814)
    • (2001) Journal of Educational Psychology , vol.93 , Issue.1 , pp. 211-222
    • Robinson, K.M.1
  • 19
    • 0347588516 scopus 로고    scopus 로고
    • Adults' understanding of inversion concepts: How does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?
    • Robinson, K. M., & Ninowski, J. E. (2003). Adults' understanding of inversion concepts: How does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems? Canadian Journal of Experimental Psychology, 57, 321-330.
    • (2003) Canadian Journal of Experimental Psychology , vol.57 , pp. 321-330
    • Robinson, K.M.1    Ninowski, J.E.2
  • 20
    • 33745969503 scopus 로고    scopus 로고
    • Children's understanding of the arithmetic concepts of inversion and associativity
    • DOI 10.1016/j.jecp.2006.03.004, PII S0022096506000415, Reflections
    • Robinson, K. M., Ninowski, J. E., & Gray, M. L. (2006). Children's understanding of the arithmetic concepts of inversion and associativity. Journal of Experimental Child Psychology, 94, 349-362. (Pubitemid 44063832)
    • (2006) Journal of Experimental Child Psychology , vol.94 , Issue.4 , pp. 349-362
    • Robinson, K.M.1    Ninowski, J.E.2    Gray, M.L.3
  • 21
    • 34848874734 scopus 로고    scopus 로고
    • Evidence for use of mathematical inversion by three-year-old children
    • Sherman,J.,&Bisanz,J.(2007). Evidenceforuseofmathematicalinversionbythree-year-oldchildren. JournalofCognitionandDevelopment,8,333-344.(Pubitemid47490680)
    • (2007) Journal of Cognition and Development , vol.8 , Issue.3 , pp. 333-344
    • Sherman, J.1    Bisanz, J.2
  • 22
    • 0000933783 scopus 로고
    • The perils of averaging data over strategies: An example from children's addition
    • Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 116, 250-264.
    • (1987) Journal of Experimental Psychology: General , vol.116 , pp. 250-264
    • Siegler, R.S.1
  • 23
    • 0000078422 scopus 로고
    • Hazards of mental chronometry: An example from children's subtraction
    • Siegler, R. S. (1989). Hazards of mental chronometry: An example from children's subtraction. Journal of Educational Psychology, 81, 497-506.
    • (1989) Journal of Educational Psychology , vol.81 , pp. 497-506
    • Siegler, R.S.1
  • 24
    • 33644805402 scopus 로고    scopus 로고
    • Microgenetic analyses of learning
    • W. Damon & R. M. Lerner (Series Eds.) and D. Kuhn & R. S. Siegler (Vol. Eds.), Hoboken, NJ: Wiley.
    • Siegler, R. S. (2006). Microgenetic analyses of learning. In W. Damon & R. M. Lerner (Series Eds.) and D. Kuhn & R. S. Siegler (Vol. Eds.), Handbook of child psychology: Vol.2: Cognition, perception, and language (6th ed., pp. 464-510). Hoboken, NJ: Wiley.
    • (2006) Handbook of Child Psychology: Cognition, perception, and language 6th ed , vol.2 , pp. 464-510
    • Siegler, R.S.1
  • 25
    • 26944466870 scopus 로고    scopus 로고
    • A computational model of conscious and unconscious strategy discovery
    • R. V. Kail (Ed.), Oxford: Elsevier.
    • 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: Elsevier.
    • (2005) Advances in Child Development and Behavior , vol.33 , pp. 1-42
    • Siegler, R.S.1    Araya, R.2
  • 26
    • 0026176902 scopus 로고
    • The microgenetic method: A direct means for studying cognitive development
    • Siegler, R. S., & Crowley, K. (1991). The microgenetic method: A direct means for studying cognitive development. American Psychologist, 46, 606-620.
    • (1991) American Psychologist , vol.46 , pp. 606-620
    • Siegler, R.S.1    Crowley, K.2
  • 27
    • 0032253286 scopus 로고    scopus 로고
    • Conscious and unconscious strategy discoveries: A microgenetic analysis
    • Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127, 377-397.
    • (1998) Journal of Experimental Psychology: General , vol.127 , pp. 377-397
    • Siegler, R.S.1    Stern, E.2
  • 28
    • 10244221168 scopus 로고    scopus 로고
    • Does the cue help? Children's understanding of multiplicative concepts in different problem contexts
    • DOI 10.1348/0007099042376364
    • Squire, S., Davies, C., & Bryant, P. (2004). Does the cue help? Children's understanding of multiplicative concepts in different problem contexts. British Journal of Educational Psychology, 74, 515-532. (Pubitemid 39620957)
    • (2004) British Journal of Educational Psychology , vol.74 , Issue.4 , pp. 515-532
    • Squire, S.1    Davies, C.2    Bryant, P.3
  • 29
    • 38249012377 scopus 로고
    • Spontaneous use of conceptual mathematical knowledge in elementary school children
    • Stern, E. (1992). Spontaneous use of conceptual mathematical knowledge in elementary school children. Contemporary Educational Psychology, 17, 266-277.
    • (1992) Contemporary Educational Psychology , vol.17 , pp. 266-277
    • Stern, E.1
  • 30
    • 0141791183 scopus 로고    scopus 로고
    • Multiway frequency analysis for experimental psychologists
    • Vokey, J. R. (2005). Multiway frequency analysis for experimental psychologists. Canadian Journal of Experimental Psychology, 57, 257-264.
    • (2005) Canadian Journal of Experimental Psychology , vol.57 , pp. 257-264
    • Vokey, J.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.