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Volumn 38, Issue 6, 2010, Pages 523-550

Productive failure in mathematical problem solving

Author keywords

Classroom based research; Failure in problem solving; Ill structured problems; Mathematical problem solving; Persistence

Indexed keywords


EID: 77958476079     PISSN: 00204277     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11251-009-9093-x     Document Type: Article
Times cited : (188)

References (55)
  • 3
    • 0038504590 scopus 로고    scopus 로고
    • When smart groups fail
    • doi:10.1207/S15327809JLS1203_1
    • Barron, B. (2003). When smart groups fail. Journal of the Learning Sciences, 12(3), 307-359. doi: 10. 1207/S15327809JLS1203_1.
    • (2003) Journal of the Learning Sciences , vol.12 , Issue.3 , pp. 307-359
    • Barron, B.1
  • 4
    • 84935412703 scopus 로고
    • Design experiments
    • doi:10.1207/s15327809jls0202_2
    • Brown, A. L. (1992). Design experiments. Journal of the Learning Sciences, 2(2), 141-178. doi: 10. 1207/s15327809jls0202_2.
    • (1992) Journal of the Learning Sciences , vol.2 , Issue.2 , pp. 141-178
    • Brown, A.L.1
  • 5
    • 84965520752 scopus 로고
    • Situated cognition and the culture of learning
    • Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32-42.
    • (1989) Educational Researcher , vol.18 , Issue.1 , pp. 32-42
    • Brown, J.S.1    Collins, A.2    Duguid, P.3
  • 6
    • 0001790660 scopus 로고
    • Vygotsky: A historical and conceptual perspective
    • J. V. Wertsch (Ed.), Cambridge: Cambridge University Press
    • Bruner, J. S. (1985). Vygotsky: A historical and conceptual perspective. In J. V. Wertsch (Ed.), Culture, communication, and cognition: Vygotskian perspectives (pp. 21-34). Cambridge: Cambridge University Press.
    • (1985) Culture, Communication, and Cognition: Vygotskian Perspectives , pp. 21-34
    • Bruner, J.S.1
  • 7
    • 58149410841 scopus 로고
    • Categorization and representation of physics problems by experts and novices
    • doi:10.1207/s15516709cog0502_2
    • Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152. doi: 10. 1207/s15516709cog0502_2.
    • (1981) Cognitive Science , vol.5 , pp. 121-152
    • Chi, M.T.H.1    Feltovich, P.J.2    Glaser, R.3
  • 9
    • 0036436003 scopus 로고    scopus 로고
    • The effects of argumentation scaffolds on argumentation and problem solving
    • doi:10.1007/BF02505022
    • Cho, K. L., & Jonassen, D. H. (2002). The effects of argumentation scaffolds on argumentation and problem solving. Educational Technology Research and Development, 50(3), 5-22. doi: 10. 1007/BF02505022.
    • (2002) Educational Technology Research and Development , vol.50 , Issue.3 , pp. 5-22
    • Cho, K.L.1    Jonassen, D.H.2
  • 10
    • 0000871266 scopus 로고
    • Thoughts on a theory of constructive failure
    • Clifford, M. M. (1984). Thoughts on a theory of constructive failure. Educational Psychologist, 19(2), 108-120.
    • (1984) Educational Psychologist , vol.19 , Issue.2 , pp. 108-120
    • Clifford, M.M.1
  • 12
    • 1542780181 scopus 로고    scopus 로고
    • Over-scripting CSCL: The risks of blending collaborative learning with instructional design
    • P. A. Kirschner (Ed.), Heerlen: Open Universiteit Nederland
    • Dillenbourg, P. (2002). Over-scripting CSCL: The risks of blending collaborative learning with instructional design. In P. A. Kirschner (Ed.), Three worlds of CSCL. Can we support CSCL (pp. 61-91). Heerlen: Open Universiteit Nederland.
    • (2002) Three Worlds of CSCL. Can We Support CSCL , pp. 61-91
    • Dillenbourg, P.1
  • 13
    • 2442695430 scopus 로고    scopus 로고
    • On the spontaneous discovery of a mathematical relation during problem solving
    • Dixon, J. A., & Bangert, A. S. (2004). On the spontaneous discovery of a mathematical relation during problem solving. Cognitive Science, 28, 433-449.
    • (2004) Cognitive Science , vol.28 , pp. 433-449
    • Dixon, J.A.1    Bangert, A.S.2
  • 14
    • 0032336889 scopus 로고    scopus 로고
    • Factors involved in linking representations of functions
    • doi:10.1016/S0732-3123(99)80063-7
    • Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17(1), 105-121. doi: 10. 1016/S0732-3123(99)80063-7.
    • (1998) The Journal of Mathematical Behavior , vol.17 , Issue.1 , pp. 105-121
    • Even, R.1
  • 15
    • 1042303002 scopus 로고    scopus 로고
    • Creating a framework for research on systemic technology innovations
    • doi:10.1207/s15327809jls1301_3
    • Fishman, B., Marx, R., Blumenfeld, P., Krajcik, J. S., & Soloway, E. (2004). Creating a framework for research on systemic technology innovations. Journal of the Learning Sciences, 13(1), 43-76. doi: 10. 1207/s15327809jls1301_3.
    • (2004) Journal of the Learning Sciences , vol.13 , Issue.1 , pp. 43-76
    • Fishman, B.1    Marx, R.2    Blumenfeld, P.3    Krajcik, J.S.4    Soloway, E.5
  • 17
    • 0037262271 scopus 로고    scopus 로고
    • Scaffolding students' problem-solving processes in an ill-structured task using question prompts and peer interactions
    • doi:10.1007/BF02504515
    • Ge, X., & Land, S. M. (2003). Scaffolding students' problem-solving processes in an ill-structured task using question prompts and peer interactions. Educational Technology Research and Development, 51(1), 21-38. doi: 10. 1007/BF02504515.
    • (2003) Educational Technology Research and Development , vol.51 , Issue.1 , pp. 21-38
    • Ge, X.1    Land, S.M.2
  • 18
    • 34249290925 scopus 로고
    • Perceptual learning: Differentiation or enrichment?
    • doi:10.1037/h0048826
    • Gibson, J. J., & Gibson, E. J. (1955). Perceptual learning: Differentiation or enrichment? Psychological Review, 62, 32-41. doi: 10. 1037/h0048826.
    • (1955) Psychological Review , vol.62 , pp. 32-41
    • Gibson, J.J.1    Gibson, E.J.2
  • 19
    • 0000527318 scopus 로고
    • The structure of design problem spaces
    • Goel, V., & Pirolli, P. (1992). The structure of design problem spaces. Cognitive Science, 16, 395-429.
    • (1992) Cognitive Science , vol.16 , pp. 395-429
    • Goel, V.1    Pirolli, P.2
  • 20
    • 3843146632 scopus 로고    scopus 로고
    • Representation in mathematical learning and problem solving
    • L. D. English (Ed.), Mahwah: Erlbaum
    • Goldin, G. A. (2002). Representation in mathematical learning and problem solving. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 197-218). Mahwah: Erlbaum.
    • (2002) Handbook of International Research in Mathematics Education , pp. 197-218
    • Goldin, G.A.1
  • 21
    • 0000327148 scopus 로고    scopus 로고
    • Practicing representation: Learning with and about representational forms
    • Greeno, J. G., & Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78(5), 361-367.
    • (1997) Phi Delta Kappan , vol.78 , Issue.5 , pp. 361-367
    • Greeno, J.G.1    Hall, R.P.2
  • 23
    • 0024729760 scopus 로고
    • The relation between problem categorization and problem solving among experts and novices
    • Hardiman, P. T., Dufresne, R., & Mestre, J. P. (1989). The relation between problem categorization and problem solving among experts and novices. Memory & Cognition, 17(5), 627-638.
    • (1989) Memory & Cognition , vol.17 , Issue.5 , pp. 627-638
    • Hardiman, P.T.1    Dufresne, R.2    Mestre, J.P.3
  • 24
    • 0002050269 scopus 로고
    • Two courses of expertise
    • H. Stevenson, H. Azuma, and K. Hakuta (Eds.), New York: Freeman
    • Hatano, G., & Inagaki, K. (1986). Two courses of expertise. In H. Stevenson, H. Azuma, & K. Hakuta (Eds.), Child development and education in Japan (pp. 262-272). New York: Freeman.
    • (1986) Child Development and Education in Japan , pp. 262-272
    • Hatano, G.1    Inagaki, K.2
  • 25
    • 3142678927 scopus 로고    scopus 로고
    • Problem-based learning: What and how do students learn?
    • doi:10.1023/B:EDPR.0000034022.16470.f3
    • Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266. doi: 10. 1023/B: EDPR. 0000034022. 16470. f3.
    • (2004) Educational Psychology Review , vol.16 , Issue.3 , pp. 235-266
    • Hmelo-Silver, C.E.1
  • 27
    • 0034551957 scopus 로고    scopus 로고
    • Towards a design theory of problem solving
    • doi:10.1007/BF02300500
    • Jonassen, D. H. (2000). Towards a design theory of problem solving. Educational Technology Research and Development, 48(4), 63-85. doi: 10. 1007/BF02300500.
    • (2000) Educational Technology Research and Development , vol.48 , Issue.4 , pp. 63-85
    • Jonassen, D.H.1
  • 29
    • 46849100254 scopus 로고    scopus 로고
    • Productive failure
    • doi:10.1080/07370000802212669
    • Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379-424. doi: 10. 1080/07370000802212669.
    • (2008) Cognition and Instruction , vol.26 , Issue.3 , pp. 379-424
    • Kapur, M.1
  • 30
    • 58149331293 scopus 로고    scopus 로고
    • Productive failure in mathematical problem solving
    • B. C. Love, K. McRae, and V. M. Sloutsky (Eds.), Austin: Cognitive Science Society
    • Kapur, M., Dickson, L., & Toh, P. Y. (2008). Productive failure in mathematical problem solving. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society (pp. 1717-1722). Austin: Cognitive Science Society.
    • (2008) Proceedings of the 30th Annual Conference of the Cognitive Science Society , pp. 1717-1722
    • Kapur, M.1    Dickson, L.2    Toh, P.Y.3
  • 32
    • 0242372441 scopus 로고    scopus 로고
    • Representations, inscriptions, descriptions and learning: A kaleidoscope of windows
    • doi:10.1016/S0364-0213(99)80062-7
    • Kaput, J. (1999). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. The Journal of Mathematical Behavior, 17(2), 265-281. doi: 10. 1016/S0364-0213(99)80062-7.
    • (1999) The Journal of Mathematical Behavior , vol.17 , Issue.2 , pp. 265-281
    • Kaput, J.1
  • 33
    • 33744807434 scopus 로고    scopus 로고
    • Why minimal guidance during instruction does not work
    • doi:10.1207/s15326985ep4102_1
    • Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work. Educational Psychologist, 41(2), 75-86. doi: 10. 1207/s15326985ep4102_1.
    • (2006) Educational Psychologist , vol.41 , Issue.2 , pp. 75-86
    • Kirschner, P.A.1    Sweller, J.2    Clark, R.E.3
  • 37
    • 84993661184 scopus 로고    scopus 로고
    • How design experiments can inform a rethinking of transfer and vice versa
    • doi:10.3102/0013189X032001017
    • Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher, 32(1), 17-20. doi: 10. 3102/0013189X032001017.
    • (2003) Educational Researcher , vol.32 , Issue.1 , pp. 17-20
    • Lobato, J.1
  • 38
    • 33751506977 scopus 로고    scopus 로고
    • Sameness and difference in transfer
    • doi:10.1207/s15327809jls1504_3
    • Marton, F. (2007). Sameness and difference in transfer. Journal of the Learning Sciences, 15(4), 499-535. doi: 10. 1207/s15327809jls1504_3.
    • (2007) Journal of the Learning Sciences , vol.15 , Issue.4 , pp. 499-535
    • Marton, F.1
  • 39
    • 0035290114 scopus 로고    scopus 로고
    • Reading both high-coherence and low-coherence texts: Effects of text sequence and prior knowledge
    • doi:10.1037/h0087352
    • McNamara, D. S. (2001). Reading both high-coherence and low-coherence texts: Effects of text sequence and prior knowledge. Canadian Journal of Experimental Psychology, 55(1), 51-62. doi: 10. 1037/h0087352.
    • (2001) Canadian Journal of Experimental Psychology , vol.55 , Issue.1 , pp. 51-62
    • McNamara, D.S.1
  • 41
    • 15944396939 scopus 로고    scopus 로고
    • Tools for scaffolding students in a complex learning environment: What have we gained and what have we missed?
    • doi:10.1207/s15326985ep4001_1
    • Puntambekar, S., & Hübscher, R. (2005). Tools for scaffolding students in a complex learning environment: What have we gained and what have we missed? Educational Psychologist, 40(1), 1-12. doi: 10. 1207/s15326985ep4001_1.
    • (2005) Educational Psychologist , vol.40 , Issue.1 , pp. 1-12
    • Puntambekar, S.1    Hübscher, R.2
  • 42
    • 4043178469 scopus 로고    scopus 로고
    • Scaffolding complex learning: The mechanisms of structuring and problematizing student work
    • doi:10.1207/s15327809jls1303_2
    • Reiser, B. J. (2004). Scaffolding complex learning: The mechanisms of structuring and problematizing student work. Journal of the Learning Sciences, 13(3), 423-451. doi: 10. 1207/s15327809jls1303_2.
    • (2004) Journal of the Learning Sciences , vol.13 , Issue.3 , pp. 423-451
    • Reiser, B.J.1
  • 43
    • 0346859968 scopus 로고    scopus 로고
    • Knowledge building
    • J. W. Guthrie (Ed.), New York: Macmillan Reference
    • Scardamalia, M., & Bereiter, C. (2003). Knowledge building. In J. W. Guthrie (Ed.), Encyclopedia of education. New York: Macmillan Reference.
    • (2003) Encyclopedia of Education
    • Scardamalia, M.1    Bereiter, C.2
  • 44
    • 84965393809 scopus 로고
    • New conceptualizations of practice: Common principles in three paradigms suggest new concepts for training
    • doi:10.1111/j.1467-9280.1992.tb00029.x
    • Schmidt, R. A., & Bjork, R. A. (1992). New conceptualizations of practice: Common principles in three paradigms suggest new concepts for training. Psychological Science, 3(4), 207-217. doi: 10. 1111/j. 1467-9280. 1992. tb00029. x.
    • (1992) Psychological Science , vol.3 , Issue.4 , pp. 207-217
    • Schmidt, R.A.1    Bjork, R.A.2
  • 45
    • 0000130954 scopus 로고    scopus 로고
    • A time for telling
    • doi:10.1207/s1532690xci1604_4
    • Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475-522. doi: 10. 1207/s1532690xci1604_4.
    • (1998) Cognition and Instruction , vol.16 , Issue.4 , pp. 475-522
    • Schwartz, D.L.1    Bransford, J.D.2
  • 46
    • 3042583333 scopus 로고    scopus 로고
    • Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction
    • doi:10.1207/s1532690xci2202_1
    • Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129-184. doi: 10. 1207/s1532690xci2202_1.
    • (2004) Cognition and Instruction , vol.22 , Issue.2 , pp. 129-184
    • Schwartz, D.L.1    Martin, T.2
  • 49
    • 84986478033 scopus 로고
    • Inquiry processes in program development
    • doi:10.1002/1520-6629(198204)10:2<103::AID-JCOP2290100202>3.0.CO;2-9
    • Tharp, R. G., & Gallimore, R. (1982). Inquiry processes in program development. Journal of Community Psychology, 10, 103-118. doi: 10. 1002/1520-6629(198204)10: 2< 103:: AID-JCOP2290100202> 3. 0. CO; 2-9.
    • (1982) Journal of Community Psychology , vol.10 , pp. 103-118
    • Tharp, R.G.1    Gallimore, R.2
  • 50
    • 0041760343 scopus 로고    scopus 로고
    • Why do only some events cause learning during human tutoring?
    • doi:10.1207/S1532690XCI2103_01
    • VanLehn, K., Siler, S., Murray, C., Yamauchi, T., & Baggett, W. B. (2003). Why do only some events cause learning during human tutoring? Cognition and Instruction, 21(3), 209-249. doi: 10. 1207/S1532690XCI2103_01.
    • (2003) Cognition and Instruction , vol.21 , Issue.3 , pp. 209-249
    • Vanlehn, K.1    Siler, S.2    Murray, C.3    Yamauchi, T.4    Baggett, W.B.5
  • 51
    • 0002643259 scopus 로고
    • Problem solving and reasoning in ill-structured domains
    • C. Antaki (Ed.), London: Sage Publications
    • Voss, J. F. (1988). Problem solving and reasoning in ill-structured domains. In C. Antaki (Ed.), Analyzing everyday explanation: A casebook of methods. London: Sage Publications.
    • (1988) Analyzing Everyday Explanation: A Casebook of Methods
    • Voss, J.F.1
  • 52
    • 33644542430 scopus 로고    scopus 로고
    • Toulmin's model and the solving of ill-structured problems
    • doi:10.1007/s10503-005-4419-6
    • Voss, J. F. (2005). Toulmin's model and the solving of ill-structured problems. Argumentation, 19, 321-329. doi: 10. 1007/s10503-005-4419-6.
    • (2005) Argumentation , vol.19 , pp. 321-329
    • Voss, J.F.1
  • 53
    • 0004115808 scopus 로고
    • Cambridge: Harvard University Press
    • Vygotsky, L. S. (1978). Mind in society. Cambridge: Harvard University Press.
    • (1978) Mind in Society
    • Vygotsky, L.S.1


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