메뉴 건너뛰기




Volumn 41, Issue 7, 2013, Pages 1079-1095

An eye for relations: Eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence

Author keywords

Einstellung; Eye tracking; Mathematical equivalence; Mental set; Problem solving

Indexed keywords

ADULT; EDUCATION; EYE MOVEMENT; HUMAN; MATHEMATICAL PHENOMENA; OCULOGRAPHY; PHYSIOLOGY; PROBLEM SOLVING; YOUNG ADULT;

EID: 84884568632     PISSN: 0090502X     EISSN: 15325946     Source Type: Journal    
DOI: 10.3758/s13421-013-0315-8     Document Type: Article
Times cited : (30)

References (47)
  • 1
    • 0032608342 scopus 로고    scopus 로고
    • How children change their minds: Strategy change can be gradual or abrupt
    • doi:10.1037/0012-1649.35.1.127
    • Alibali, M. W. (1999). How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology, 35, 127-145. doi: 10. 1037/0012-1649. 35. 1. 127.
    • (1999) Developmental Psychology , vol.35 , pp. 127-145
    • Alibali, M.W.1
  • 3
    • 0001754927 scopus 로고
    • The effects of instruction on children's understanding of the "equals" sign
    • doi:10.1086/461356
    • Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the "equals" sign. The Elementary School Journal, 84, 199-212. doi: 10. 1086/461356.
    • (1983) The Elementary School Journal , vol.84 , pp. 199-212
    • Baroody, A.J.1    Ginsburg, H.P.2
  • 5
    • 38149030153 scopus 로고    scopus 로고
    • Inflexibility of experts - Reality or myth? Quantifying the Einstellung effect in chess masters
    • doi:10.1016/j.cogpsych.2007.02.001
    • Bilalić, M., McLeod, P., & Gobet, F. (2008a). Inflexibility of experts - Reality or myth? Quantifying the Einstellung effect in chess masters. Cognitive Psychology, 56, 73-102. doi: 10. 1016/j. cogpsych. 2007. 02. 001.
    • (2008) Cognitive Psychology , vol.56 , pp. 73-102
    • Bilalić, M.1    McLeod, P.2    Gobet, F.3
  • 6
    • 51249097724 scopus 로고    scopus 로고
    • Why good thoughts block better ones: The mechanism of the pernicious Einstellung (set) effect
    • doi:10.1016/j.cognition.2008.05.005
    • Bilalić, M., McLeod, P., & Gobet, F. (2008b). Why good thoughts block better ones: The mechanism of the pernicious Einstellung (set) effect. Cognition, 108, 652-661. doi: 10. 1016/j. cognition. 2008. 05. 005.
    • (2008) Cognition , vol.108 , pp. 652-661
    • Bilalić, M.1    McLeod, P.2    Gobet, F.3
  • 8
    • 37249041941 scopus 로고    scopus 로고
    • Gesture makes learning last
    • doi:10.1016/j.cognition.2007.04.010
    • Cook, S. W., Mitchell, Z., & Goldin-Meadow, S. (2008). Gesture makes learning last. Cognition, 106, 1047-1058. doi: 10. 1016/j. cognition. 2007. 04. 010.
    • (2008) Cognition , vol.106 , pp. 1047-1058
    • Cook, S.W.1    Mitchell, Z.2    Goldin-Meadow, S.3
  • 9
    • 0041853567 scopus 로고    scopus 로고
    • The importance of cognitive errors in diagnosis and strategies to minimize them
    • Croskerry, P. (2003). The importance of cognitive errors in diagnosis and strategies to minimize them. Academic Medicine, 78, 775-780.
    • (2003) Academic Medicine , vol.78 , pp. 775-780
    • Croskerry, P.1
  • 10
    • 17444368113 scopus 로고    scopus 로고
    • Not quite as grown-up as we like to think: Parallels between cognition in childhood and adulthood
    • doi:10.1111/j.0956-7976.2005.01530.x
    • Diamond, A., & Kirkham, N. Z. (2005). Not quite as grown-up as we like to think: Parallels between cognition in childhood and adulthood. Psychological Science, 16, 291-297. doi: 10. 1111/j. 0956-7976. 2005. 01530. x.
    • (2005) Psychological Science , vol.16 , pp. 291-297
    • Diamond, A.1    Kirkham, N.Z.2
  • 11
    • 0001467771 scopus 로고
    • On problem solving
    • (Whole No. 270)
    • Duncker, K. (1945). On problem solving. Psychological Monographs, 58 (Whole No. 270).
    • (1945) Psychological Monographs , vol.58
    • Duncker, K.1
  • 12
    • 80051670013 scopus 로고    scopus 로고
    • Eye movements real solution knowledge prior to insight
    • doi:10.1016/j.concog.2010.12.007
    • Ellis, J. J., Glaholt, M. G., & Reingold, E. M. (2011). Eye movements real solution knowledge prior to insight. Consciousness and Cognition, 20, 768-776. doi: 10. 1016/j. concog. 2010. 12. 007.
    • (2011) Consciousness and Cognition , vol.20 , pp. 768-776
    • Ellis, J.J.1    Glaholt, M.G.2    Reingold, E.M.3
  • 13
    • 0027584733 scopus 로고
    • Transitions in concept acquisition: Using the hand to read the mind
    • doi:10.1037/0033-295X.100.2.279
    • Goldin-Meadow, S., Alibali, M. W., & Church, R. B. (1993). Transitions in concept acquisition: Using the hand to read the mind. Psychological Review, 100, 279-297. doi: 10. 1037/0033-295X. 100. 2. 279.
    • (1993) Psychological Review , vol.100 , pp. 279-297
    • Goldin-Meadow, S.1    Alibali, M.W.2    Church, R.B.3
  • 14
    • 62349108992 scopus 로고    scopus 로고
    • Gesturing gives children new ideas about math
    • doi:10.1111/j.1467-9280.2009.02297.x
    • Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267-272. doi: 10. 1111/j. 1467-9280. 2009. 02297. x.
    • (2009) Psychological Science , vol.20 , Issue.3 , pp. 267-272
    • Goldin-Meadow, S.1    Cook, S.W.2    Mitchell, Z.A.3
  • 15
    • 0142118595 scopus 로고    scopus 로고
    • Eye movements and problem solving: Guiding attention guides thought
    • doi:10.1111/1467-9280.02454
    • Grant, E. R., & Spivey, M. J. (2003). Eye movements and problem solving: Guiding attention guides thought. Psychological Science, 14(5), 462-466. doi: 10. 1111/1467-9280. 02454.
    • (2003) Psychological Science , vol.14 , Issue.5 , pp. 462-466
    • Grant, E.R.1    Spivey, M.J.2
  • 17
    • 77952888496 scopus 로고    scopus 로고
    • Learning about the equal sign: Does comparing with inequality symbols help?
    • doi:10.1016/j.jecp.2010.03.004
    • Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help? Journal of Experimental Child Psychology, 107, 15-30. doi: 10. 1016/j. jecp. 2010. 03. 004.
    • (2010) Journal of Experimental Child Psychology , vol.107 , pp. 15-30
    • Hattikudur, S.1    Alibali, M.W.2
  • 20
    • 34249876473 scopus 로고    scopus 로고
    • Methods for the behavioral, educational, and social science: An R package
    • doi:10.3758/BF03192966
    • Kelley, K. (2007a). Methods for the behavioral, educational, and social science: An R package. Behavior Research Methods, 39(4), 979-984. doi: 10. 3758/BF03192966.
    • (2007) Behavior Research Methods , vol.39 , Issue.4 , pp. 979-984
    • Kelley, K.1
  • 21
    • 34249875735 scopus 로고    scopus 로고
    • Confidence intervals for standardized effect sizes: Theory, application, and implementation
    • Kelley, K. (2007b). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1-24.
    • (2007) Journal of Statistical Software , vol.20 , Issue.8 , pp. 1-24
    • Kelley, K.1
  • 23
    • 0035710228 scopus 로고    scopus 로고
    • An eye movement study of insight problem solving
    • doi:10.3758/BF03195762
    • Knoblich, G., Ohlsson, S., & Raney, E. G. (2001). An eye movement study of insight problem solving. Memory & Cognition, 29, 1000-1009. doi: 10. 3758/BF03195762.
    • (2001) Memory & Cognition , vol.29 , pp. 1000-1009
    • Knoblich, G.1    Ohlsson, S.2    Raney, E.G.3
  • 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
    • doi:10.1080/07370000801980845
    • 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. doi: 10. 1080/07370000801980845.
    • (2008) Cognition and Instruction , vol.26 , pp. 195-217
    • Li, X.1    Ding, M.2    Capraro, M.M.3    Capraro, R.M.4
  • 25
    • 0028528867 scopus 로고
    • Rule governed performance and sensitivity to contingencies: What's new?
    • doi:10.1080/00221309.1994.9921209
    • Lippman, L. G. (1994). Rule governed performance and sensitivity to contingencies: What's new? The Journal of General Psychology, 121, 353-360. doi: 10. 1080/00221309. 1994. 9921209.
    • (1994) The Journal of General Psychology , vol.121 , pp. 353-360
    • Lippman, L.G.1
  • 26
    • 21444436489 scopus 로고    scopus 로고
    • History of success and current context in problem solving: Combined influences on operator selection
    • doi:10.1006/cogp.1996.0016
    • Lovett, M. C., & Anderson, J. R. (1996). History of success and current context in problem solving: Combined influences on operator selection. Cognitive Psychology, 31, 168-217. doi: 10. 1006/cogp. 1996. 0016.
    • (1996) Cognitive Psychology , vol.31 , pp. 168-217
    • Lovett, M.C.1    Anderson, J.R.2
  • 27
    • 0003333569 scopus 로고
    • Mechanization in problem solving - The effect of Einstellung
    • Luchins, A. S. (1942). Mechanization in problem solving - The effect of Einstellung. Psychological Monographs, 54(6), i-95.
    • (1942) Psychological Monographs , vol.54 , Issue.6
    • Luchins, A.S.1
  • 28
    • 0001331331 scopus 로고
    • Reasoning in humans: II. The solution of a problem and its appearance in consciousness
    • doi:10.1037/h0071361
    • Maier, N. R. F. (1931). Reasoning in humans: II. The solution of a problem and its appearance in consciousness. Journal of Comparative Psychology, 12, 181-194. doi: 10. 1037/h0071361.
    • (1931) Journal of Comparative Psychology , vol.12 , pp. 181-194
    • Maier, N.R.F.1
  • 29
    • 34248396379 scopus 로고    scopus 로고
    • U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems
    • doi:10.1037/0012-1649.43.3.687
    • McNeil, N. M. (2007). U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology, 43, 687-695. doi: 10. 1037/0012-1649. 43. 3. 687.
    • (2007) Developmental Psychology , vol.43 , pp. 687-695
    • McNeil, N.M.1
  • 30
    • 2442675472 scopus 로고    scopus 로고
    • You'll see what you mean: Students encode equations based on their knowledge of arithmetic
    • doi:10.1207/s15516709cog2803_7
    • 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. doi: 10. 1207/s15516709cog2803_7.
    • (2004) Cognitive Science , vol.28 , pp. 451-466
    • McNeil, N.M.1    Alibali, M.W.2
  • 31
    • 33645242498 scopus 로고    scopus 로고
    • Knowledge change as a function of mathematics experience: All contexts are not created equal
    • doi:10.1207/s15327647jcd0602_6
    • 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. doi: 10. 1207/s15327647jcd0602_6.
    • (2005) Journal of Cognition and Development , vol.6 , pp. 285-306
    • McNeil, N.M.1    Alibali, M.W.2
  • 32
    • 23844468227 scopus 로고    scopus 로고
    • Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations
    • doi:10.1111/j.1467-8624.2005.00884.x
    • 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, 883-899. doi: 10. 1111/j. 1467-8624. 2005. 00884. x.
    • (2005) Child Development , vol.76 , pp. 883-899
    • McNeil, N.M.1    Alibali, M.W.2
  • 34
    • 80052585224 scopus 로고    scopus 로고
    • Benefits of practicing 4 = 2 + 2: Nontraditional problem formats facilitate children's understanding of mathematical equivalence
    • doi:10.1111/j.1467-8624.2011.01622.x
    • McNeil, N. M., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Brletic-Shipley, H. (2011). Benefits of practicing 4 = 2 + 2: Nontraditional problem formats facilitate children's understanding of mathematical equivalence. Child Development, 82(5), 1620-1633. doi: 10. 1111/j. 1467-8624. 2011. 01622. x.
    • (2011) Child Development , vol.82 , Issue.5 , pp. 1620-1633
    • McNeil, N.M.1    Fyfe, E.R.2    Petersen, L.A.3    Dunwiddie, A.E.4    Brletic-Shipley, H.5
  • 35
    • 78149392989 scopus 로고    scopus 로고
    • Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates' algebraic problem solving
    • doi:10.1080/15248372.2010.516421
    • McNeil, N. M., Rittle-Johnson, B., Hattikudur, S., & Petersen, L. A. (2010). Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates' algebraic problem solving. Journal of Cognition and Development, 11(4), 437-457. doi: 10. 1080/15248372. 2010. 516421.
    • (2010) Journal of Cognition and Development , vol.11 , Issue.4 , pp. 437-457
    • McNeil, N.M.1    Rittle-Johnson, B.2    Hattikudur, S.3    Petersen, L.A.4
  • 36
    • 0000612150 scopus 로고    scopus 로고
    • Infant perseveration and implications for object permanence theories: A PDP model of the AB task
    • doi:10.1111/1467-7687.00021
    • Munakata, Y. (1998). Infant perseveration and implications for object permanence theories: A PDP model of the AB task. Developmental Science, 1(2), 161-184. doi: 10. 1111/1467-7687. 00021.
    • (1998) Developmental Science , vol.1 , Issue.2 , pp. 161-184
    • Munakata, Y.1
  • 37
    • 60649108086 scopus 로고    scopus 로고
    • Resubsumption: A possible mechanism for conceptual change and belief revision
    • doi:10.1080/00461520802616267
    • Ohlsson, S. (2009). Resubsumption: A possible mechanism for conceptual change and belief revision. Educational Psychologist, 44, 20-40. doi: 10. 1080/00461520802616267.
    • (2009) Educational Psychologist , vol.44 , pp. 20-40
    • Ohlsson, S.1
  • 38
    • 84863304598 scopus 로고    scopus 로고
    • R Development Core Team, Vienna, Austria: F Foundation for Statistical Computing
    • R Development Core Team. (2012). R: A language and environment for statistical computing. Vienna, Austria: F Foundation for Statistical Computing.
    • (2012) R: A Language and Environment for Statistical Computing
  • 40
    • 0030518312 scopus 로고    scopus 로고
    • Preservation of pavlovian associations through extinction
    • doi:10.1080/713932629
    • Rescorla, R. A. (1996). Preservation of pavlovian associations through extinction. The Quarterly Journal of Experimental Psychology. B, 49(3), 245-258. doi: 10. 1080/713932629.
    • (1996) The Quarterly Journal of Experimental Psychology. B , vol.49 , Issue.3 , pp. 245-258
    • Rescorla, R.A.1
  • 41
    • 0025382052 scopus 로고
    • Belief revision in children: The role of prior knowledge and strategies for generating evidence
    • doi:10.1016/0022-0965(90)90048-D
    • Schauble, L. (1990). Belief revision in children: The role of prior knowledge and strategies for generating evidence. Journal of Experimental Child Psychology, 49(1), 31-57. doi: 10. 1016/0022-0965(90)90048-D.
    • (1990) Journal of Experimental Child Psychology , vol.49 , Issue.1 , pp. 31-57
    • Schauble, L.1
  • 42
    • 0036584469 scopus 로고    scopus 로고
    • Rigidity of thought and behavior: 100 years of research
    • doi:10.1024/1421-0185/a000070
    • Schultz, P. W., & Searleman, A. (2002). Rigidity of thought and behavior: 100 years of research. Genetic, Social, and General Psychology Monographs, 128(2), 165-207. doi: 10. 1024/1421-0185/a000070.
    • (2002) Genetic, Social, and General Psychology Monographs , vol.128 , Issue.2 , pp. 165-207
    • Schultz, P.W.1    Searleman, A.2
  • 43
    • 60849128815 scopus 로고    scopus 로고
    • Equivalence in symbolic and non-symbolic contexts: Benefits of solving problems with manipulatives
    • doi:10.1037/a0013156
    • Sherman, J., & Bisanz, J. (2009). Equivalence in symbolic and non-symbolic contexts: Benefits of solving problems with manipulatives. Journal of Educational Psychology, 101, 88-100. doi: 10. 1037/a0013156.
    • (2009) Journal of Educational Psychology , vol.101 , pp. 88-100
    • Sherman, J.1    Bisanz, J.2
  • 44
    • 72449211751 scopus 로고    scopus 로고
    • The dynamics of insight: Mathematical discovery as a phase transition
    • doi:10.3758/MC.37.8.1132
    • Stephen, D. G., Boncoddo, R. A., Magnuson, J. S., & Dixon, J. A. (2009). The dynamics of insight: Mathematical discovery as a phase transition. Memory & Cognition, 37(8), 1132-1149. doi: 10. 3758/MC. 37. 8. 1132.
    • (2009) Memory & Cognition , vol.37 , Issue.8 , pp. 1132-1149
    • Stephen, D.G.1    Boncoddo, R.A.2    Magnuson, J.S.3    Dixon, J.A.4
  • 45
    • 35348871477 scopus 로고    scopus 로고
    • Moving eyes and moving thought: On spatial compatibility between eye movements and cognition
    • doi:10.3758/BF03196818
    • Thomas, L. E., & Lleras, A. (2007). Moving eyes and moving thought: On spatial compatibility between eye movements and cognition. Psychonomic Bulletin & Review, 14(4), 663-668. doi: 10. 3758/BF03196818.
    • (2007) Psychonomic Bulletin & Review , vol.14 , Issue.4 , pp. 663-668
    • Thomas, L.E.1    Lleras, A.2
  • 46
    • 0031879214 scopus 로고    scopus 로고
    • Expertise as mental set: The effects of domain knowledge in creative problem solving
    • doi:10.3758/BF03211392
    • Wiley, J. (1998). Expertise as mental set: The effects of domain knowledge in creative problem solving. Memory & Cognition, 26(4), 716-730. doi: 10. 3758/BF03211392.
    • (1998) Memory & Cognition , vol.26 , Issue.4 , pp. 716-730
    • Wiley, J.1
  • 47
    • 0029692978 scopus 로고    scopus 로고
    • An age-related dissociation between knowing rules and using them
    • doi:10.1016/S0885-2014(96)90027-1
    • Zelazo, P. D., Frye, D., & Rapus, T. (1996). An age-related dissociation between knowing rules and using them. Cognitive Development, 11(1), 37-63. doi: 10. 1016/S0885-2014(96)90027-1.
    • (1996) Cognitive Development , vol.11 , Issue.1 , pp. 37-63
    • Zelazo, P.D.1    Frye, D.2    Rapus, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.