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Volumn 25, Issue , 2013, Pages 24-34

Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples

Author keywords

Algebra; Conceptual understanding; Learning from errors; Self explanation; Worked examples

Indexed keywords


EID: 84872442697     PISSN: 09594752     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.learninstruc.2012.11.002     Document Type: Article
Times cited : (161)

References (54)
  • 2
    • 0036210232 scopus 로고    scopus 로고
    • An effective metacognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor
    • Aleven V., Koedinger K.R. An effective metacognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science 2002, 26:147-179. 10.1016/S0364-0213(02)00061-7.
    • (2002) Cognitive Science , vol.26 , pp. 147-179
    • Aleven, V.1    Koedinger, K.R.2
  • 3
    • 53349152273 scopus 로고    scopus 로고
    • A longitudinal look at middle-school students' understanding of the equal sign and equivalent equations
    • Alibali M.W., Knuth E.J., Hattikudur S., McNeil N.M., Stephens A.C. A longitudinal look at middle-school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning 2007, 9:221-247. 10.1080/10986060701360902.
    • (2007) Mathematical Thinking and Learning , vol.9 , pp. 221-247
    • Alibali, M.W.1    Knuth, E.J.2    Hattikudur, S.3    McNeil, N.M.4    Stephens, A.C.5
  • 4
    • 77951238231 scopus 로고    scopus 로고
    • Middle-school mathematics teachers' knowledge of students' understanding of core algebraic concepts: equal sign and variable
    • Asquith P.S., Stephens A.C., Knuth E.J., Alibali M.W. Middle-school mathematics teachers' knowledge of students' understanding of core algebraic concepts: equal sign and variable. Mathematical Thinking and Learning 2007, 9:247-270. 10.1080/10986060701360910.
    • (2007) Mathematical Thinking and Learning , vol.9 , pp. 247-270
    • Asquith, P.S.1    Stephens, A.C.2    Knuth, E.J.3    Alibali, M.W.4
  • 6
    • 0001754927 scopus 로고
    • The effects of instructions on children's understanding of the equals sign
    • Baroody A., Ginsburg H. The effects of instructions on children's understanding of the equals sign. The Elementary School Journal 1983, 84:199-212. 10.1086/461356.
    • (1983) The Elementary School Journal , vol.84 , pp. 199-212
    • Baroody, A.1    Ginsburg, H.2
  • 8
    • 84872448567 scopus 로고    scopus 로고
    • The role of problem representation and feature knowledge in algebraic equation-solving
    • (submitted for publication)
    • Booth, J. L., & Davenport, J. L. (submitted for publication). The role of problem representation and feature knowledge in algebraic equation-solving. Journal of Mathematical Behavior.
    • Journal of Mathematical Behavior
    • Booth, J.L.1    Davenport, J.L.2
  • 9
    • 79958275191 scopus 로고    scopus 로고
    • Key misconceptions in algebraic problem solving
    • Cognitive Science Society, Austin, TX, B.C. Love, K. McRae, V.M. Sloutsky (Eds.)
    • Booth J.L., Koedinger K.R. Key misconceptions in algebraic problem solving. Proceedings of the 30th Annual Cognitive Science Society 2008, 571-576. Cognitive Science Society, Austin, TX. B.C. Love, K. McRae, V.M. Sloutsky (Eds.).
    • (2008) Proceedings of the 30th Annual Cognitive Science Society , pp. 571-576
    • Booth, J.L.1    Koedinger, K.R.2
  • 10
    • 84872457369 scopus 로고    scopus 로고
    • Does practice alone make perfect? Taking example-based assignments for a test drive in real-world classrooms
    • (submitted for publication)
    • Booth, J. L., Koedinger, K. R., & Paré-Blagoev, E. J. (submitted for publication). Does practice alone make perfect? Taking example-based assignments for a test drive in real-world classrooms. Journal of Educational Psychology.
    • Journal of Educational Psychology
    • Booth, J.L.1    Koedinger, K.R.2    Paré-Blagoev, E.J.3
  • 11
    • 84872451498 scopus 로고    scopus 로고
    • The effect of prior conceptual knowledge on procedural performance and learning in algebra
    • Poster presented at the 29th Annual Meeting of the Cognitive Science Society in Nashville, TN.
    • Booth, J. L., Koedinger, K. R., & Siegler, R. S. (2007). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Meeting of the Cognitive Science Society in Nashville, TN.
    • (2007)
    • Booth, J.L.1    Koedinger, K.R.2    Siegler, R.S.3
  • 13
    • 21844506281 scopus 로고
    • Using worked examples as an instructional support in the algebra classroom
    • Carroll W.M. Using worked examples as an instructional support in the algebra classroom. Journal of Educational Psychology 1994, 86(3):360-367. 10.1037/0022-0663.86.3.360.
    • (1994) Journal of Educational Psychology , vol.86 , Issue.3 , pp. 360-367
    • Carroll, W.M.1
  • 14
    • 33646033737 scopus 로고    scopus 로고
    • Acquisition of procedures: the effects of example elaborations and active learning exercises
    • Catrambone R., Yuasa M. Acquisition of procedures: the effects of example elaborations and active learning exercises. Learning and Instruction 2006, 16:139-153. 10.1016/j.learninstruc.2006.02.002.
    • (2006) Learning and Instruction , vol.16 , pp. 139-153
    • Catrambone, R.1    Yuasa, M.2
  • 15
    • 0002929633 scopus 로고    scopus 로고
    • Self-explaining expository texts: the dual processes of generating inferences and repairing mental models
    • Lawrence Erlbaum Associates, Mahwah, NJ, R. Glaser (Ed.)
    • Chi M.T.H. Self-explaining expository texts: the dual processes of generating inferences and repairing mental models. Advances in instructional psychology 2000, 161-238. Lawrence Erlbaum Associates, Mahwah, NJ. R. Glaser (Ed.).
    • (2000) Advances in instructional psychology , pp. 161-238
    • Chi, M.T.H.1
  • 16
    • 43949150689 scopus 로고
    • Eliciting self-explanations improves understanding
    • Chi M.T.H., De Leeuw N., Chiu M., Lavancher C. Eliciting self-explanations improves understanding. Cognitive Science 1994, 18:439-477. 10.1207/s15516709cog1803_3.
    • (1994) Cognitive Science , vol.18 , pp. 439-477
    • Chi, M.T.H.1    De Leeuw, N.2    Chiu, M.3    Lavancher, C.4
  • 17
    • 58149410841 scopus 로고
    • Categorization and representation of physics problems by experts and novices
    • Chi M.T.H., Feltovich P.J., Glaser R. Categorization and representation of physics problems by experts and novices. Cognitive Science 1981, 5(2):121-152. http://dx.doi.org/10.1207/s15516709cog0502_2.
    • (1981) Cognitive Science , vol.5 , Issue.2 , pp. 121-152
    • Chi, M.T.H.1    Feltovich, P.J.2    Glaser, R.3
  • 18
    • 0035030527 scopus 로고    scopus 로고
    • Locus of feedback control in computer-based tutoring: impact on learning rate, achievement, and attitudes
    • Proceedings of ACM CHI'2001 Conference on Human Factors in Computing Systems
    • Corbett, A. T., & Anderson, J. R. (2001). Locus of feedback control in computer-based tutoring: impact on learning rate, achievement, and attitudes. In Proceedings of ACM CHI'2001 Conference on Human Factors in Computing Systems, 245-252.
    • (2001) , pp. 245-252
    • Corbett, A.T.1    Anderson, J.R.2
  • 19
    • 33644939746 scopus 로고    scopus 로고
    • The effects of self-explanations of correct and incorrect solutions on algebra problem-solving performance
    • Erlbaum, Mahwah, NJ, K. Forbus, D. Gentner, T. Regier (Eds.)
    • Curry L. The effects of self-explanations of correct and incorrect solutions on algebra problem-solving performance. Proceedings of the 26th annual conference of the cognitive science society 2004, 1548. Erlbaum, Mahwah, NJ. K. Forbus, D. Gentner, T. Regier (Eds.).
    • (2004) Proceedings of the 26th annual conference of the cognitive science society , pp. 1548
    • Curry, L.1
  • 20
    • 0038008535 scopus 로고    scopus 로고
    • Reading about energy: the effects of text structure in science learning and conceptual change
    • Diakidoy I.A.N., Kendeou P., Ioannides C. Reading about energy: the effects of text structure in science learning and conceptual change. Contemporary Educational Psychology 2003, 28(3):335-356. 10.1016/S0361-476X(02)00039-5.
    • (2003) Contemporary Educational Psychology , vol.28 , Issue.3 , pp. 335-356
    • Diakidoy, I.A.N.1    Kendeou, P.2    Ioannides, C.3
  • 21
    • 84856573546 scopus 로고    scopus 로고
    • The effectiveness of using incorrect examples to support learning about decimal magnitude
    • Durkin K., Rittle-Johnson B. The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction 2012, 22:206-214. 10.1016/j.learninstruc.2011.11.001.
    • (2012) Learning and Instruction , vol.22 , pp. 206-214
    • Durkin, K.1    Rittle-Johnson, B.2
  • 22
    • 0036930063 scopus 로고    scopus 로고
    • Effects of conceptual assignments and conceptual change discussions on students' misconceptions and achievement regarding force and motion
    • Eryilmaz A. Effects of conceptual assignments and conceptual change discussions on students' misconceptions and achievement regarding force and motion. Journal of Research In Science Teaching 2002, 39(10):1001-1015. 10.1002/tea.10054.
    • (2002) Journal of Research In Science Teaching , vol.39 , Issue.10 , pp. 1001-1015
    • Eryilmaz, A.1
  • 23
    • 36448969715 scopus 로고    scopus 로고
    • Finding and fixing errors in worked examples: can this foster learning outcomes?
    • Große C.S., Renkl A. Finding and fixing errors in worked examples: can this foster learning outcomes?. Learning & Instruction 2007, 17:617-634. 10.1016/j.learninstruc.2007.09.008.
    • (2007) Learning & Instruction , vol.17 , pp. 617-634
    • Große, C.S.1    Renkl, A.2
  • 25
    • 39749167794 scopus 로고    scopus 로고
    • Learning to prove in geometry: learning from heuristic examples and how it can be supported
    • Hilbert T.S., Renkl A., Kessler S., Reiss K. Learning to prove in geometry: learning from heuristic examples and how it can be supported. Learning and Instruction 2008, 18:54-65. 10.1016/j.learninstruc.2006.10.008.
    • (2008) Learning and Instruction , vol.18 , pp. 54-65
    • Hilbert, T.S.1    Renkl, A.2    Kessler, S.3    Reiss, K.4
  • 26
    • 35048826669 scopus 로고    scopus 로고
    • Construction of an online learning system for decimal numbers through the use of cognitive conflict strategy
    • Huang T.-H., Liu Y.-C., Shiu C.-Y. Construction of an online learning system for decimal numbers through the use of cognitive conflict strategy. Computers & Education 2008, 50:61-76. 10.1016/j.compedu.2006.03.007.
    • (2008) Computers & Education , vol.50 , pp. 61-76
    • Huang, T.-H.1    Liu, Y.-C.2    Shiu, C.-Y.3
  • 27
    • 85064779867 scopus 로고    scopus 로고
    • Learner experience and efficiency of instructional guidance
    • Kalyuga S., Chandler P., Sweller J. Learner experience and efficiency of instructional guidance. Educational Psychology 2001, 21(1):5-23. 10.1080/01443410124681.
    • (2001) Educational Psychology , vol.21 , Issue.1 , pp. 5-23
    • Kalyuga, S.1    Chandler, P.2    Sweller, J.3
  • 29
    • 0001071316 scopus 로고
    • Concepts associated with the equality symbol
    • Kieran C. Concepts associated with the equality symbol. Educational Studies in Mathematics 1981, 12:317-326.
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 317-326
    • Kieran, C.1
  • 33
    • 84863442345 scopus 로고    scopus 로고
    • The Knowledge-learning-instruction (kli) framework: bridging the science-practice chasm to enhance robust student learning
    • Koedinger K.R., Corbett A.C., Perfetti C. The Knowledge-learning-instruction (kli) framework: bridging the science-practice chasm to enhance robust student learning. Cognitive Science 2012, 36:757-798. 10.1111/j.1551-6709.2012.01245.x.
    • (2012) Cognitive Science , vol.36 , pp. 757-798
    • Koedinger, K.R.1    Corbett, A.C.2    Perfetti, C.3
  • 34
    • 0008772371 scopus 로고
    • Children's understanding of numerical variables
    • Küchemann D. Children's understanding of numerical variables. Mathematics in School 1978, 7:23-26.
    • (1978) Mathematics in School , vol.7 , pp. 23-26
    • Küchemann, D.1
  • 35
    • 67349276617 scopus 로고    scopus 로고
    • In pursuit of knowledge: comparing self-explanations, concepts, and procedures as pedagogical tools
    • Matthews P.G., Rittle-Johnson B. In pursuit of knowledge: comparing self-explanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology 2009, 104:1-21. 10.1016/j.jecp.2008.08.004.
    • (2009) Journal of Experimental Child Psychology , vol.104 , pp. 1-21
    • Matthews, P.G.1    Rittle-Johnson, B.2
  • 36
    • 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. You'll see what you mean: students encode equations based on their knowledge of arithmetic. Cognitive Science 2004, 28:451-466. 10.1016/j.cogsci.2003.11.002.
    • (2004) Cognitive Science , vol.28 , pp. 451-466
    • McNeil, N.M.1    Alibali, M.W.2
  • 37
    • 0034196467 scopus 로고    scopus 로고
    • Substituting one mystery for another: the role of self-explanations in solving algebra word-problems
    • Neuman Y., Schwarz B. Substituting one mystery for another: the role of self-explanations in solving algebra word-problems. Learning and Instruction 2000, 10:203-220. 10.1016/S0959-4752(99)00027-4.
    • (2000) Learning and Instruction , vol.10 , pp. 203-220
    • Neuman, Y.1    Schwarz, B.2
  • 38
    • 23844467823 scopus 로고    scopus 로고
    • Learning from error and the design of task environments
    • Ohlsson S. Learning from error and the design of task environments. International Journal of Educational Research 1996, 25(5):419-448. 10.1016/S0883-0355(97)81236-0.
    • (1996) International Journal of Educational Research , vol.25 , Issue.5 , pp. 419-448
    • Ohlsson, S.1
  • 39
    • 0002089226 scopus 로고    scopus 로고
    • Learning from worked-out examples: the effects of example variability and elicited self-explanations
    • Renkl A., Stark R., Gruber H., Mandl H. Learning from worked-out examples: the effects of example variability and elicited self-explanations. Contemporary Educational Psychology 1998, 23:90-108. 10.1006/ceps.1997.0959.
    • (1998) Contemporary Educational Psychology , vol.23 , pp. 90-108
    • Renkl, A.1    Stark, R.2    Gruber, H.3    Mandl, H.4
  • 41
    • 33644942863 scopus 로고    scopus 로고
    • Promoting transfer: effects of self-explanation and direct instruction
    • Rittle-Johnson B. Promoting transfer: effects of self-explanation and direct instruction. Child Development 2006, 77:1-29. 10.1111/j.1467-8624.2006.00852.x.
    • (2006) Child Development , vol.77 , pp. 1-29
    • Rittle-Johnson, B.1
  • 42
    • 34548852840 scopus 로고    scopus 로고
    • Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations
    • Rittle-Johnson B., Star J.R. Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology 2007, 99(3):561-574. 10.1037/0022-0663.99.3.561.
    • (2007) Journal of Educational Psychology , vol.99 , Issue.3 , pp. 561-574
    • Rittle-Johnson, B.1    Star, J.R.2
  • 43
    • 30644460273 scopus 로고    scopus 로고
    • Self-explanation in a multi-media context
    • Cambridge Press, R. Mayer (Ed.)
    • Roy M., Chi M.T.H. Self-explanation in a multi-media context. Cambridge handbook of multimedia learning 2005, 271-286. Cambridge Press. R. Mayer (Ed.).
    • (2005) Cambridge handbook of multimedia learning , pp. 271-286
    • Roy, M.1    Chi, M.T.H.2
  • 44
    • 84872445237 scopus 로고    scopus 로고
    • Can tutored problem solving benefit from faded worked-out examples
    • Paper presented at The European Cognitive Science Conference, Delphi, Greece
    • Schwonke, R., Wittwer, J., Aleven, V., Salden, R. J. C. M., Krieg, C., and Renkl, A. (2007). Can tutored problem solving benefit from faded worked-out examples? Paper presented at The European Cognitive Science Conference, Delphi, Greece.
    • (2007)
    • Schwonke, R.1    Wittwer, J.2    Aleven, V.3    Salden, R.J.C.M.4    Krieg, C.5    Renkl, A.6
  • 46
    • 12444255767 scopus 로고    scopus 로고
    • Microgenetic studies of self-explanations
    • Cambridge University, New York, N. Granott, J. Parziale (Eds.)
    • Siegler R.S. Microgenetic studies of self-explanations. Microdevelopment: Transition processes in development and learning 2002, 31-58. Cambridge University, New York. N. Granott, J. Parziale (Eds.).
    • (2002) Microdevelopment: Transition processes in development and learning , pp. 31-58
    • Siegler, R.S.1
  • 47
    • 45349085649 scopus 로고    scopus 로고
    • Differentiation and integration: guiding principles for analyzing cognitive change
    • Siegler R.S., Chen Z. Differentiation and integration: guiding principles for analyzing cognitive change. Developmental Science 2008, 11:433-448. 10.1111/j.1467-7687.2008.00689.x.
    • (2008) Developmental Science , vol.11 , pp. 433-448
    • Siegler, R.S.1    Chen, Z.2
  • 48
    • 33748080809 scopus 로고    scopus 로고
    • The development of flexibility in equation solving
    • Star J.R., Seifert C. The development of flexibility in equation solving. Contemporary Educational Psychology 2006, 31:280-300. 10.1016/j.cedpsych.2005.08.001.
    • (2006) Contemporary Educational Psychology , vol.31 , pp. 280-300
    • Star, J.R.1    Seifert, C.2
  • 50
    • 84963474629 scopus 로고
    • The use of worked examples as a substitute for problem solving in learning algebra
    • Sweller J., Cooper G. The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction 1985, 2(1):59-89. 10.1207/s1532690xci0201_3.
    • (1985) Cognition and Instruction , vol.2 , Issue.1 , pp. 59-89
    • Sweller, J.1    Cooper, G.2
  • 51
    • 13844294137 scopus 로고    scopus 로고
    • Making sense of the minus sign or becoming flexible in 'negativity'
    • Vlassis J. Making sense of the minus sign or becoming flexible in 'negativity'. Learning and Instruction 2004, 14:469-484. 10.1016/j.learninstruc.2004.06.012.
    • (2004) Learning and Instruction , vol.14 , pp. 469-484
    • Vlassis, J.1
  • 52
    • 84963164526 scopus 로고
    • Structuring effective worked examples
    • Ward M., Sweller J. Structuring effective worked examples. Cognition and Instruction 1990, 7(1):1-39. 10.1207/s1532690xci0701_1.
    • (1990) Cognition and Instruction , vol.7 , Issue.1 , pp. 1-39
    • Ward, M.1    Sweller, J.2
  • 53
    • 84872441708 scopus 로고    scopus 로고
    • What Works Clearinghouse Middle School Math: Cognitive Tutor Algebra 1.
    • What Works Clearinghouse (2009). Middle School Math: Cognitive Tutor Algebra 1.
    • (2009)
  • 54
    • 84963179358 scopus 로고
    • Learning mathematics from examples and by doing
    • Zhu X., Simon H.A. Learning mathematics from examples and by doing. Cognition and Instruction 1987, 4:137-166. 10.1207/s1532690xci0403_1.
    • (1987) Cognition and Instruction , vol.4 , pp. 137-166
    • Zhu, X.1    Simon, H.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.