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Volumn 79, Issue 5, 2008, Pages 1524-1537

Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can Hinder learning of mathematical equivalence

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COGNITION; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; PRESCHOOL CHILD; PROBLEM SOLVING; TEACHING;

EID: 51949085289     PISSN: 00093920     EISSN: 14678624     Source Type: Journal    
DOI: 10.1111/j.1467-8624.2008.01203.x     Document Type: Article
Times cited : (80)

References (50)
  • 1
    • 0032608342 scopus 로고    scopus 로고
    • How children change their minds: Strategy change can be gradual or abrupt
    • Alibali, M. W 1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35, 127 145.
    • (1999) Developmental Psychology , vol.35 , pp. 127-145
    • Alibali, M.W.1
  • 2
    • 0002530202 scopus 로고    scopus 로고
    • What makes children change their minds? Changes in encoding lead to changes in strategy selection
    • In. M. A. Gernsbacher. S. Derry (. Eds. pp.). Mahwah, NJ: Erlbaum.
    • Alibali, M. W., McNeil, N. M. Perrott, M. A 1998). What makes children change their minds? Changes in encoding lead to changes in strategy selection. In M. A. Gernsbacher S. Derry (Eds Proceedings of the Twentieth Annual Conference of the Cognitive Science Society (pp. 36 41). Mahwah, NJ : Erlbaum.
    • (1998) Proceedings of the Twentieth Annual Conference of the Cognitive Science Society , pp. 36-41
    • Alibali, M.W.1    McNeil, N.M.2    Perrott, M.A.3
  • 3
    • 0001754927 scopus 로고
    • The effects of instruction on children's understanding of the "equals" sign
    • Baroody, A. J. Ginsburg, H. P 1983). The effects of instruction on children's understanding of the "equals" sign. Elementary School Journal, 84, 199 212.
    • (1983) Elementary School Journal , vol.84 , pp. 199-212
    • Baroody, A.J.1    Ginsburg, H.P.2
  • 4
    • 0020021788 scopus 로고
    • Context-independent and context-dependent information in concepts
    • Barsalou, L. W 1982). Context-independent and context-dependent information in concepts. Memory and Cognition, 10, 82 93.
    • (1982) Memory and Cognition , vol.10 , pp. 82-93
    • Barsalou, L.W.1
  • 7
    • 23844440370 scopus 로고    scopus 로고
    • Developing elementary teachers' "algebra eyes and ears."
    • Blanton, M. L. Kaput, J. J 2003). Developing elementary teachers' "algebra eyes and ears." Teaching Children Mathematics, 10, 70 77.
    • (2003) Teaching Children Mathematics , vol.10 , pp. 70-77
    • Blanton, M.L.1    Kaput, J.J.2
  • 8
    • 33746396344 scopus 로고
    • On perceptual readiness
    • Bruner, J. S 1957). On perceptual readiness. Psychological Review, 2, 123 152.
    • (1957) Psychological Review , vol.2 , pp. 123-152
    • Bruner, J.S.1
  • 9
    • 19644389506 scopus 로고    scopus 로고
    • Encouraging conceptual change: The use of bridging analogies in the teaching of action-reaction forces and the "at rest" condition in physics
    • Bryce, T. MacMillan, K 2005). Encouraging conceptual change: The use of bridging analogies in the teaching of action-reaction forces and the "at rest" condition in physics. International Journal of Science Education, 27, 737 763.
    • (2005) International Journal of Science Education , vol.27 , pp. 737-763
    • Bryce, T.1    MacMillan, K.2
  • 12
    • 84873952165 scopus 로고
    • Not all preconceptions are misconceptions: Finding anchoring conceptions for grounding instruction on students' intuition
    • Clement, J., Brown, D. Zeitsman, A 1989). Not all preconceptions are misconceptions: Finding anchoring conceptions for grounding instruction on students' intuition. International Journal of Science Education, 11, 554 565.
    • (1989) International Journal of Science Education , vol.11 , pp. 554-565
    • Clement, J.1    Brown, D.2    Zeitsman, A.3
  • 13
    • 0009414603 scopus 로고
    • An investigation of young children's academic arithmetic contexts
    • Cobb, P 1987). An investigation of young children's academic arithmetic contexts. Educational Studies in Mathematics, 18, 109 124.
    • (1987) Educational Studies in Mathematics , vol.18 , pp. 109-124
    • Cobb, P.1
  • 14
    • 51949089665 scopus 로고
    • Paper presented at the Psychology of Mathematics Education Workshop, Centre for Science Education, Chelsea College, London.
    • Collis, K. F 1974). Cognitive development and mathematics learning. Paper presented at the Psychology of Mathematics Education Workshop, Centre for Science Education, Chelsea College, London.
    • (1974) Cognitive Development and Mathematics Learning
    • Collis, K.F.1
  • 15
    • 51949101249 scopus 로고    scopus 로고
    • The importance of basic number knowledge to advanced mathematical problem solving. Unpublished doctoral dissertation, Carnegie Mellon University, Pittsburgh.
    • Haverty, L. A 1999). The importance of basic number knowledge to advanced mathematical problem solving. Unpublished doctoral dissertation, Carnegie Mellon University, Pittsburgh.
    • (1999)
    • Haverty, L.A.1
  • 16
    • 0008056854 scopus 로고    scopus 로고
    • Solving inductive reasoning problems in mathematics: Not so trivial pursuit
    • Haverty, L. A., Koedinger, K. R., Klahr, D. Alibali, M. W 2000). Solving inductive reasoning problems in mathematics: Not so trivial pursuit. Cognitive Science, 24, 249 298.
    • (2000) Cognitive Science , vol.24 , pp. 249-298
    • Haverty, L.A.1    Koedinger, K.R.2    Klahr, D.3    Alibali, M.W.4
  • 17
    • 51949090237 scopus 로고
    • The spring is wound too tight on our spiral curriculum
    • Jensen, R. J 1990). The spring is wound too tight on our spiral curriculum. Arithmetic Teacher, 38, 4 5.
    • (1990) Arithmetic Teacher , vol.38 , pp. 4-5
    • Jensen, R.J.1
  • 18
    • 38249044009 scopus 로고
    • The development of mathematical cognition
    • Kaye, D. B 1986). The development of mathematical cognition. Cognitive Development, 1, 157 170.
    • (1986) Cognitive Development , vol.1 , pp. 157-170
    • Kaye, D.B.1
  • 19
    • 0001071316 scopus 로고
    • Concepts associated with the equality symbol
    • Kieran, C 1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317 326.
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 317-326
    • Kieran, C.1
  • 20
    • 85085443275 scopus 로고
    • The early learning of algebra: A structural perspective
    • In. S. Wagner. C. Kieran (. Eds. pp.). Reston, VA: NCTM.
    • Kieran, C 1989). The early learning of algebra: A structural perspective. In S. Wagner C. Kieran (Eds Research issues in the learning and teaching of algebra (pp. 33 56). Reston, VA : NCTM.
    • (1989) Research Issues in the Learning and Teaching of Algebra , pp. 33-56
    • Kieran, C.1
  • 22
    • 2442549739 scopus 로고    scopus 로고
    • The real story behind story problems: Effects of representation on quantitative reasoning
    • Koedinger, K. R. Nathan, M. J 2004). The real story behind story problems: Effects of representation on quantitative reasoning. Journal of the Learning Sciences, 13, 129 164.
    • (2004) Journal of the Learning Sciences , vol.13 , pp. 129-164
    • Koedinger, K.R.1    Nathan, M.J.2
  • 24
    • 42149097129 scopus 로고    scopus 로고
    • Sources of differences in children's understandings of mathematical equality: Comparative analysis of teacher guides and student texts in China and the United States
    • Li, X., Ding, M., Capraro, M. M. Capraro, R. M 2008). Sources of differences in children's understandings of mathematical equality: Comparative analysis of teacher guides and student texts in China and the United States. Cognition and Instruction, 26, 195 217.
    • (2008) Cognition and Instruction , vol.26 , pp. 195-217
    • Li, X.1    Ding, M.2    Capraro, M.M.3    Capraro, R.M.4
  • 25
    • 0042027462 scopus 로고    scopus 로고
    • On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal
    • Limon, M 2001). On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. Learning and Instruction, 11, 357 380.
    • (2001) Learning and Instruction , vol.11 , pp. 357-380
    • Limon, M.1
  • 26
    • 0002534515 scopus 로고
    • The influence of encoding and strategic knowledge on children's choices among serial recall strategies
    • McGilly, K. Siegler, R. S 1990). The influence of encoding and strategic knowledge on children's choices among serial recall strategies. Developmental Psychology, 26, 931 941.
    • (1990) Developmental Psychology , vol.26 , pp. 931-941
    • McGilly, K.1    Siegler, R.S.2
  • 27
    • 51949116258 scopus 로고    scopus 로고
    • Talk presented at the American Enterprise Institute for Public Policy Research (AEI). Retrieved June 2005 from
    • McKeown, M 2002). Does two plus two still equal four: What should our children know about math? Talk presented at the American Enterprise Institute for Public Policy Research (AEI). Retrieved June 2005 from http://www.aei.org/ events/eventID.193/event_detail.asp
    • (2002) Does Two Plus Two Still Equal Four: What Should Our Children Know about Math?
    • McKeown, M.1
  • 28
    • 51949095185 scopus 로고    scopus 로고
    • When the basics backfire: The change-resistance account of equation-learning difficulties. Unpublished doctoral dissertation, University of Wisconsin, Madison.
    • McNeil, N. M 2005). When the basics backfire: The change-resistance account of equation-learning difficulties. Unpublished doctoral dissertation, University of Wisconsin, Madison.
    • (2005)
    • McNeil, N.M.1
  • 29
    • 34248396379 scopus 로고    scopus 로고
    • U-shaped development in math: Seven year olds outperform nine year olds on equivalence problems
    • McNeil, N. M 2007). U-shaped development in math: Seven year olds outperform nine year olds on equivalence problems. Developmental Psychology, 43, 687 695.
    • (2007) Developmental Psychology , vol.43 , pp. 687-695
    • McNeil, N.M.1
  • 30
    • 0034347499 scopus 로고    scopus 로고
    • Learning mathematics from procedural instruction: Externally imposed goals influence what is learned
    • McNeil, N. M. Alibali, M. W 2000). Learning mathematics from procedural instruction: Externally imposed goals influence what is learned. Journal of Educational Psychology, 92, 734 744.
    • (2000) Journal of Educational Psychology , vol.92 , pp. 734-744
    • McNeil, N.M.1    Alibali, M.W.2
  • 31
    • 2442675472 scopus 로고    scopus 로고
    • You'll see what you mean: Students encode equations based on their knowledge of arithmetic
    • McNeil, N. M. Alibali, M. W 2004). You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science, 28, 451 466.
    • (2004) Cognitive Science , vol.28 , pp. 451-466
    • McNeil, N.M.1    Alibali, M.W.2
  • 32
    • 33645242498 scopus 로고    scopus 로고
    • Knowledge change as a function of mathematics experience: All contexts are not created equal
    • McNeil, N. M. Alibali, M. W 2005a). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6, 285 306.
    • (2005) Journal of Cognition and Development , vol.6 , pp. 285-306
    • McNeil, N.M.1    Alibali, M.W.2
  • 33
    • 23844468227 scopus 로고    scopus 로고
    • Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations
    • McNeil, N. M. Alibali, M. W 2005b). Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 1 17.
    • (2005) Child Development , vol.76 , pp. 1-17
    • McNeil, N.M.1    Alibali, M.W.2
  • 36
    • 0003865799 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics. Reston, VA: Author.
    • National Council of Teachers of Mathematics 2000). Principles and standards for school mathematics. Reston, VA : Author.
    • (2000) Principles and Standards for School Mathematics.
  • 37
    • 0004254471 scopus 로고    scopus 로고
    • National Research Council. Washington, DC: National Academy Press.
    • National Research Council 2002). Scientific research in education. Washington, DC : National Academy Press.
    • (2002) Scientific Research in Education.
  • 38
    • 0000761881 scopus 로고
    • Learning and transfer: Instructional conditions and conceptual change
    • Perry, M 1991). Learning and transfer: Instructional conditions and conceptual change. Cognitive Development, 6, 449 468.
    • (1991) Cognitive Development , vol.6 , pp. 449-468
    • Perry, M.1
  • 41
    • 0009330261 scopus 로고
    • The child's conception of number (C. Gattegno & F. M. Hadgson, Trans
    • In. H. E. Gruber. J. J. Voneche (. Eds. pp.). Northvale, NJ: Jason Aronson. Original work published 1941)
    • Piaget, J. Szeminska, A 1995). The child's conception of number (C. Gattegno & F. M. Hadgson, Trans In H. E. Gruber J. J. Voneche (Eds The essential Piaget (pp. 298 341). Northvale, NJ : Jason Aronson Original work published 1941)
    • (1995) The Essential Piaget , pp. 298-341
    • Piaget, J.1    Szeminska, A.2
  • 42
    • 0033084379 scopus 로고    scopus 로고
    • Conceptual and procedural knowledge of mathematics: Does one lead to the other?
    • Rittle-Johnson, B. Alibali, M. W 1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175 189.
    • (1999) Journal of Educational Psychology , vol.91 , pp. 175-189
    • Rittle-Johnson, B.1    Alibali, M.W.2
  • 43
    • 0035602865 scopus 로고    scopus 로고
    • Developing conceptual understanding and procedural skill in mathematics: An iterative process
    • 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.
    • (2001) Journal of Educational Psychology , vol.93 , pp. 346-362
    • Rittle-Johnson, B.1    Siegler, R.S.2    Alibali, M.W.3
  • 44
    • 0025382052 scopus 로고
    • Belief revision in children: The role of prior knowledge and strategies for generating evidence
    • Schauble, L 1990). Belief revision in children: The role of prior knowledge and strategies for generating evidence. Journal of Experimental Child Psychology, 49, 31 57.
    • (1990) Journal of Experimental Child Psychology , vol.49 , pp. 31-57
    • Schauble, L.1
  • 45
    • 84909395691 scopus 로고    scopus 로고
    • "you've got to carefully read the math sentence.": Classroom context and children's interpretations of the equals sign
    • In. A. J. Baroody. A. Dowker (. Eds. pp.). Mahwah, NJ: Erlbaum.
    • Seo, K.-H. Ginsburg, H. P 2003). "You've got to carefully read the math sentence.": Classroom context and children's interpretations of the equals sign. In A. J. Baroody A. Dowker (Eds The development of arithmetic concepts and skills (pp. 161 187). Mahwah, NJ : Erlbaum.
    • (2003) The Development of Arithmetic Concepts and Skills , pp. 161-187
    • Seo, K.-H.1    Ginsburg, H.P.2
  • 46
    • 51949084002 scopus 로고    scopus 로고
    • Children's misunderstanding of the equal sign and their adherence to addition schemas: Detecting the effect of prior arithmetic experience and instruction. Unpublished doctoral dissertation, University of Alberta, Edmonton, Alberta, Canada.
    • Sherman, J. L 2007). Children's misunderstanding of the equal sign and their adherence to addition schemas: Detecting the effect of prior arithmetic experience and instruction. Unpublished doctoral dissertation, University of Alberta, Edmonton, Alberta, Canada.
    • (2007)
    • Sherman, J.L.1
  • 47
    • 0033644252 scopus 로고    scopus 로고
    • The rebirth of children's learning
    • Siegler, R. S 2000). The rebirth of children's learning. Child Development, 71, 26 35.
    • (2000) Child Development , vol.71 , pp. 26-35
    • Siegler, R.S.1
  • 48
    • 0031185021 scopus 로고    scopus 로고
    • Beyond competence: The significance of performance for conceptual development
    • Sophian, C 1997). Beyond competence: The significance of performance for conceptual development. Cognitive Development, 12, 281 303.
    • (1997) Cognitive Development , vol.12 , pp. 281-303
    • Sophian, C.1
  • 49
    • 0642283662 scopus 로고    scopus 로고
    • Cognitive skill acquisition
    • VanLehn, K 1996). Cognitive skill acquisition. Annual Review of Psychology, 47, 513 539.
    • (1996) Annual Review of Psychology , vol.47 , pp. 513-539
    • Vanlehn, K.1
  • 50
    • 0029692978 scopus 로고    scopus 로고
    • An age-related dissociation between knowing rules and using them
    • Zelazo, P. D., Frye, D. Rapus, T 1996). An age-related dissociation between knowing rules and using them. Cognitive Development, 11, 37 63.
    • (1996) Cognitive Development , vol.11 , pp. 37-63
    • Zelazo, P.D.1    Frye, D.2    Rapus, T.3


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