Educational Psychology Review

, Volume 27, Issue 1, pp 181–218 | Cite as

Comparing Four Instructional Techniques for Promoting Robust Knowledge

  • J. Elizabeth Richey
  • Timothy J. Nokes-Malach
Review Article


Robust knowledge serves as a common instructional target in academic settings. Past research identifying characteristics of experts’ knowledge across many domains can help clarify the features of robust knowledge as well as ways of assessing it. We review the expertise literature and identify three key features of robust knowledge (deep, connected, and coherent) and four means of assessing these features (perception, memory, problem solving, and transfer). Focusing on the domains of math and science learning, we examine how four instructional techniques—practice, worked examples, analogical comparison, and self-explanation—can promote key features of robust knowledge and how those features can be assessed. We conclude by discussing the implications of this framework for theory and practice.


Analogical comparison Worked examples Self-explanation Practice Expertise 



This work was supported by Grant SBE0836012 from the National Science Foundation to the Pittsburgh Science of Learning Center ( We gratefully acknowledge Christian Schunn, Joel Chan, and Jooyoung Jang for their feedback on this work, Jose Mestre and Brian Ross for insights into the ideas discussed, and Daniel Robinson and three anonymous reviewers for their very helpful suggestions and comments on the article.


  1. Adelson, B. (1981). Problem solving and the development of abstract categories in programming languages. Memory & Cognition, 9(4), 422–433. doi: 10.3758/BF03197568.CrossRefGoogle Scholar
  2. Ainsworth, S., & Burcham, S. (2007). The impact of text coherence on learning by self-explanation. Learning and Instruction, 17(3), 286–303. doi: 10.1016/j.learninstruc.2007.02.004.CrossRefGoogle Scholar
  3. Aleven, V. A. W. M. M., Koedinger, K. R., & Popescu, O. (2003). A tutorial dialog system to support self-explanation: Evaluation and open questions. In Proceedings of the 11th International Conference on Artificial Intelligence in Education (pp. 39–46).Google Scholar
  4. Alfieri, L., Nokes-Malach, T. J., & Schunn, C. D. (2013). Learning through case comparisons: a meta-analytic review. Educational Psychologist, 48(2), 87–113. doi: 10.1080/00461520.2013.775712.CrossRefGoogle Scholar
  5. Allard, F., & Starkes, J. L. (1991). Motor-skill experts in sports, dance, and other domains. In K. A. Ericsson & J. Smith (Eds.), Toward a general theory of expertise: Prospects and limits (pp. 126–152). Cambridge: Cambridge University Press.Google Scholar
  6. Anderson, J. R. (1987). Skill acquisition: compilation of weak-method problem situations. Psychological Review, 94(2), 192–210. doi: 10.1037/0033-295X.94.2.192.CrossRefGoogle Scholar
  7. Anderson, J. R. (1993). Problem solving and learning. American Psychologist, 48, 35–44. doi: 10.1037/0003-066X.48.1.35.CrossRefGoogle Scholar
  8. Anderson, J. R., Fincham, J. M., & Douglass, S. (1997). The role of examples and rules in the acquisition of a cognitive skill. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23(4), 932–945. doi: 10.1037/0278-7393.23.4.932.Google Scholar
  9. Anzai, Y., & Simon, H. A. (1979). The theory of learning by doing. Psychological Review, 86(2), 124–140. doi: 10.1037/0033-295X.86.2.124.CrossRefGoogle Scholar
  10. Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214. doi: 10.3102/00346543070002181.CrossRefGoogle Scholar
  11. Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783. doi: 10.1037/0022-0663.95.4.774.CrossRefGoogle Scholar
  12. Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn?: a taxonomy for far transfer. Psychological Bulletin, 128(4), 612–637. doi: 10.1037//0033-2909.128.4.612.CrossRefGoogle Scholar
  13. Barron, B. J. S., Schwartz, D. L., Vye, N. J., Moore, A., Petrosino, A., Zech, L., & Bransford, J. D. (1998). Doing with understanding: lessons from research on problem- and project-based learning. Journal of the Learning Sciences, 7(3–4), 271–311. doi: 10.1080/10508406.1998.9672056.Google Scholar
  14. Berthold, K., & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of Educational Psychology. doi: 10.1037/a0013247.Google Scholar
  15. Blanchette, I., & Dunbar, K. N. (2000). How analogies are generated: the roles of structural and superficial similarity. Memory & Cognition, 28(1), 108–124. doi: 10.3758/BF03211580.CrossRefGoogle Scholar
  16. Booth, J. L., & Koedinger, K. R. (2008). Key misconceptions in algebraic problem solving. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society (pp. 571–576). Austin: Cognitive Science Society.Google Scholar
  17. Bransford, J. D., & Schwartz, D. L. (1999). Rethinking transfer: A simple proposal with multiple implications. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research in education (Vol. 24, pp. 61–100). Washington, D.C: American Educational Research Association.Google Scholar
  18. Bransford, J. D., Sherwood, R., Vye, N. J., & Rieser, J. (1986). Teaching thinking and problem solving: research foundations. American Psychologist, 41(10), 1078–1089. doi: 10.1037/0003-066X.41.10.1078.CrossRefGoogle Scholar
  19. Brown, D. E., & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: abstract transfer versus explanatory model construction. Instructional Science, 18(4), 237–261. doi: 10.1007/BF00118013.CrossRefGoogle Scholar
  20. Brown, D. E., & Hammer, D. (2008). Conceptual change in physics. In S. Vosniadou (Ed.), International handbook on research in conceptual change (pp. 127–154).Google Scholar
  21. Brown, A. L., & Kane, M. J. (1988). Preschool children can learn to transfer: learning to learn and learning from example. Cognitive Psychology, 20(4), 493–523. doi: 10.1016/0010-0285(88)90014-X.CrossRefGoogle Scholar
  22. Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42. doi: 10.2307/1176008.CrossRefGoogle Scholar
  23. Burns, B. D., & Vollmeyer, R. (2002). Goal specificity effects on hypothesis testing in problem solving. The Quarterly Journal of Experimental Psychology, 55A(1), 241–261. doi: 10.1080/02724980143000262.CrossRefGoogle Scholar
  24. Capon, N., & Kuhn, D. (2004). What’s so good about problem-based learning? Cognition and Instruction, 22(1), 61–79. doi: 10.1207/s1532690Xci2201_3.CrossRefGoogle Scholar
  25. Catrambone, R. (1996). Generalizing solution procedures learned from examples. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(4), 1020–1031. doi: 10.1037/0278-7393.22.4.1020.Google Scholar
  26. Catrambone, R. (1998). The subgoal learning model: creating better examples so that students can solve novel problems. Journal of Experimental Psychology: General, 127(4), 355–376. doi: 10.1037/0096-3445.127.4.355.CrossRefGoogle Scholar
  27. Catrambone, R., & Holyoak, K. J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(6), 1147–1156. doi: 10.1037//0278-7393.15.6.1147.Google Scholar
  28. Catrambone, R., & Holyoak, K. J. (1990). Learning subgoals and methods for solving probability problems. Memory & Cognition, 18(6), 593–603. doi: 10.3758/BF03197102.CrossRefGoogle Scholar
  29. Chandler, P., & Sweller, J. (1991). Cognitive load theory and the format of instruction. Cognition and Instruction, 8(4), 293–332. doi: 10.1207/s1532690xci0804.CrossRefGoogle Scholar
  30. Chase, W. G., & Simon, H. A. (1973). The mind’s eye in chess. In W. G. Chase (Ed.), Visual information processing (pp. 215–281). New York: Academic Press.CrossRefGoogle Scholar
  31. Chen, Z. (1999). Schema induction in children’s analogical problem solving. Journal of Educational Psychology, 91(4), 703–715. doi: 10.1037/0022-0663.91.4.703.CrossRefGoogle Scholar
  32. Chi, M. T. H. (2000). Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in instructional psychology, Vol. 5 (pp. 161–238). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  33. Chi, M. T. H. (2006). Laboratory methods for assessing experts’ and novices’ knowledge. In K. A. Ericsson, N. Charness, P. J. Feltovich, & R. Hoffman (Eds.), The Cambridge handbook of expertise and expert performance (pp. 167–184). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In S. Vosniadou (Ed.), International handbook on research in conceptual change (pp. 61–82). Hillsdale: Erlbaum.Google Scholar
  35. Chi, M. T. H., & Koeske, R. D. (1983). Network representation of a child’s dinosaur knowledge. Developmental Psychology, 19(1), 29–39. doi: 10.1037/0012-1649.19.1.29.CrossRefGoogle Scholar
  36. Chi, M. T. H., & Ohlsson, S. (2005). Complex declarative learning. In K. J. Holyoak & R. G. Morrison (Eds.), Cambridge handbook of thinking and reasoning (pp. 371–399). New York: Cambridge University Press. doi: 10.1207/s15327809jls0101_4.Google Scholar
  37. Chi, M. T. H., & VanLehn, K. A. (1991). The content of physics self-explanations. Journal of the Learning Sciences, 1(1), 69–105. doi: 10.1207/s15327809jls0101_4.CrossRefGoogle Scholar
  38. Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5(2), 121–152. doi: 10.1207/s15516709cog0502_2.CrossRefGoogle Scholar
  39. Chi, M. T. H., Glaser, R., & Farr, M. J. (Eds.). (1988). The nature of expertise. Hillsdale: Lawrence Erlbaum Associates, Inc.Google Scholar
  40. Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: how students study and use examples in learning to solve problems. Cognitive Science, 13, 145–182. doi: 10.1207/s15516709cog1302_1.CrossRefGoogle Scholar
  41. Chi, M. T. H., de Leeuw, N., Chiu, M.-H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439–477. doi: 10.1207/s15516709cog1803_3.Google Scholar
  42. Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: a theoretical framework and implications for science instruction. Review of Educational Research, 63(1), 1–49. doi: 10.3102/00346543063001001.CrossRefGoogle Scholar
  43. Clement, C. A., & Gentner, D. (1991). Systematicity as a selection constraint in analogical mapping. Cognitive Science, 15(1), 89–132. doi: 10.1016/0364-0213(91)80014-V.CrossRefGoogle Scholar
  44. Compton, B. J., & Logan, G. D. (1991). The transition from algorithm to retrieval in memory-based theories of automaticity. Memory & Cognition, 19(2), 151–158. doi: 10.3758/BF03197111.CrossRefGoogle Scholar
  45. Conati, C., & VanLehn, K. A. (2000). Toward computer-based support of meta-cognitive skills: a computational framework to coach self-explanation. International Journal of Artificial Intelligence in Education, 11, 389–415.Google Scholar
  46. Cooper, G. A., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362. doi: 10.1037//0022-0663.79.4.347.CrossRefGoogle Scholar
  47. Crowley, K., & Siegler, R. S. (1999). Explanation and generalization in young children’s strategy learning. Child Development, 70(2), 304–316. doi: 10.1111/1467-8624.00023.CrossRefGoogle Scholar
  48. Cummins, D. D. (1992). Role of analogical reasoning in the induction of problem categories. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18(5), 1103–1124. doi: 10.1037/0278-7393.18.5.1103.Google Scholar
  49. Day, S. B., & Goldstone, R. L. (2012). The import of knowledge export: connecting findings and theories of transfer of learning. Educational Psychologist, 47, 153–176. doi: 10.1080/00461520.2012.696438.CrossRefGoogle Scholar
  50. Delaney, P. F., Reder, L. M., Staszewski, J. J., & Ritter, F. E. (1998). The strategy-specific nature of improvement: the power law applies by strategy within task. Psychological Science, 9(1), 1–7. doi: 10.1111/1467-9280.00001.CrossRefGoogle Scholar
  51. Dellarosa, D. (1985). Abstraction of problem-type schemata through problem comparison (Tech. Rep. No. 146). Boulder.Google Scholar
  52. Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike problem analyses: effects on schema acquisition. Journal of the Learning Sciences, 2(3), 307–331. doi: 10.1207/s15327809jls0203_3.CrossRefGoogle Scholar
  53. Dunbar, K. N., Fugelsang, J. A., & Stein, C. (2007). Do naive theories ever go away? Using brain and behavior to understand changes in concepts. In P. Shah & M. Lovett (Eds.), Thinking with data (pp. 193–206). New York: Erlbaum.Google Scholar
  54. Ericsson, K. A., & Charness, N. (1994). Expert performance: its structure and acquisition. American Psychologist, 49(8), 725–747. doi: 10.1037/0003-066X.50.9.803.CrossRefGoogle Scholar
  55. Ericsson, K. A., & Charness, N. (1997). Cognitive and developmental factors in expert performance. In P. J. Feltovich, K. M. Ford, & R. R. Hoffman (Eds.), Expertise in contex: Human and machine (pp. 3–41). Cambridge: MIT Press.Google Scholar
  56. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102(2), 211–245. doi: 10.1037/0033-295X.102.2.211.CrossRefGoogle Scholar
  57. Ericsson, K. A., & Smith, J. (1991). Toward a general theory of expertise: Prospects and limits (p. 344). New York: Cambridge University Press.Google Scholar
  58. Ericsson, K. A., Chase, W. G., & Faloon, S. (1980). Acquisition of a memory skill. Science, 208(4448), 1181–1182. doi: 10.1126/science.7375930.CrossRefGoogle Scholar
  59. Ericsson, K. A., Krampe, R. T., & Tesch-Römer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363–406. doi: 10.1037//0033-295X.100.3.363.CrossRefGoogle Scholar
  60. Fitts, P. M. (1964). Perceptual-motor skill learning. In A. W. Melton (Ed.), Categories of human learning (pp. 243–285). New York: Academic Press.CrossRefGoogle Scholar
  61. Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. Journal of Experimental Psychology: General, 120(1), 34–45. doi: 10.1037/0096-3445.120.1.34.CrossRefGoogle Scholar
  62. Gadgil, S., Nokes-Malach, T. J., & Chi, M. T. H. (2012). Effectiveness of holistic mental model confrontation in driving conceptual change. Learning and Instruction, 22(1), 47–61. doi: 10.1016/j.learninstruc.2011.06.002.CrossRefGoogle Scholar
  63. Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7(2), 155–170. doi: 10.1016/S0364-0213(83)80009-3.CrossRefGoogle Scholar
  64. Gentner, D. (2002). Analogical reasoning, psychology of. In Encyclopedia of Cognitive Science. London: Nature Publishing Group.Google Scholar
  65. Gentner, D., & Medina, J. (1998). Similarity and the development of rules. Cognition, 65(2–3), 263–297. doi: 10.1207/s15516709cog1003_2.CrossRefGoogle Scholar
  66. Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: a general role for analogical encoding. Journal of Educational Psychology, 95(2), 393–405. doi: 10.1037/0022-0663.95.2.393.CrossRefGoogle Scholar
  67. Gentner, D., Loewenstein, J., Thompson, L., & Forbus, K. D. (2009). Reviving inert knowledge: analogical abstraction supports relational retrieval of past events. Cognitive Science, 33(8), 1343–1382. doi: 10.1111/j.1551-6709.2009.01070.x.CrossRefGoogle Scholar
  68. Gick, M. L. (1986). Problem-solving strategies. Educational Psychologist, 21(1), 99–120. doi: 10.1207/s15326985ep2101&2_6.CrossRefGoogle Scholar
  69. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15(1), 1–38. doi: 10.1016/0010-0285(83)90002-6.CrossRefGoogle Scholar
  70. Gick, M. L., & Paterson, K. (1992). Do contrasting examples facilitate schema acquisition and analogical transfer? Canadian Journal of Psychology, 46(4), 539–550. doi: 10.1037/h0084333.CrossRefGoogle Scholar
  71. Guo, J.-P., Pang, M. F., Yang, L.-Y., & Ding, Y. (2012). Learning from comparing multiple examples: on the dilemma of “similar” or “different”. Educational Psychology Review, 24(2), 251–269. doi: 10.1007/s10648-012-9192-0.CrossRefGoogle Scholar
  72. Hardiman, P. T., Dufresne, R. J., & Mestre, J. P. (1989). The relation between problem categorization and problem solving among experts and novices. Memory & Cognition, 17(5), 627–638. doi: 10.3758/BF03197085.CrossRefGoogle Scholar
  73. Hatano, G., & Inagaki, K. (1986). Two courses of expertise. In Child development and education in Japan (pp. 262–272). New York: Freeman. doi: 10.1002/ccd.10470.Google Scholar
  74. Hausmann, R. G. M., & Chi, M. T. H. (2002). Can a computer interface support self-explaining? Cognitive Technology, 7(1), 4–14.Google Scholar
  75. Hausmann, R. G. M., & VanLehn, K. A. (2007). Explaining self-explaining: A contrast between content and generation. In R. Luckin, K. R. Koedinger, & J. Greer (Eds.), 13th international conference on artificial intelligence in education (pp. 417–424). Amsterdam: IOS Press.Google Scholar
  76. Hickey, D. T., & Pellegrino, J. W. (2005). Theory, level, and function: Three dimensions for understanding transfer and student assessment. In J. P. Mestre (Ed.), Transfer of learning from a modern multidisciplinary perspective (pp. 251–294). Greenwich: Information Age Publishing.Google Scholar
  77. Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics. Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  78. Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14(3), 251–283. doi: 10.1207/s1532690xci1403_1.CrossRefGoogle Scholar
  79. Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical transfer. Memory & Cognition, 15(4), 332–340. doi: 10.3758/BF03197035.CrossRefGoogle Scholar
  80. Judd, C. H. (1908). The relation of special training to general intelligence. Educational Review, 36, 28–42.Google Scholar
  81. Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples. Journal of Educational Psychology, 93(3), 579–588. doi: 10.1037/0022-0663.93.3.579.CrossRefGoogle Scholar
  82. Kellman, P. J., & Garrigan, P. (2009). Perceptual learning and human expertise. Physics of Life Reviews, 6(2), 53–84. doi: 10.1016/j.plrev.2008.12.001.CrossRefGoogle Scholar
  83. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. doi: 10.1207/s15326985ep4102_1.CrossRefGoogle Scholar
  84. Koedinger, K. R., & Aleven, V. A. W. M. M. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19(3), 239–264. doi: 10.1007/s10648-007-9049-0.CrossRefGoogle Scholar
  85. Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: elements of expertise in geometry. Cognitive Science, 14(4), 511–550. doi: 10.1207/s15516709cog1404_2.CrossRefGoogle Scholar
  86. Koedinger, K. R., Corbett, A. T., & Perfetti, C. (2012). The knowledge-learning-instruction framework: bridging the science-practice chasm to enhance robust student learning. Cognitive Science, 36(5), 757–798. doi: 10.1111/j.1551-6709.2012.01245.x.CrossRefGoogle Scholar
  87. Koedinger, K. R., Booth, J. L., & Klahr, D. (2013). Instructional complexity and the science to constrain it. Science, 342(22), 935–937. doi: 10.1126/science.1238056.CrossRefGoogle Scholar
  88. Kolodner, J. L. (1997). Educational implications of analogy: a view from case-based reasoning. American Psychologist, 52(1), 57–66. doi: 10.1037/0003-066X.52.1.57.CrossRefGoogle Scholar
  89. Kurtz, K. J., Miao, C.-H., & Gentner, D. (2001). Learning by analogical bootstrapping. Journal of the Learning Sciences, 10(4), 417–446. doi: 10.1207/S15327809JLS1004new_2.CrossRefGoogle Scholar
  90. Larkin, J., McDermott, J., Simon, D. P., & Simon, H. A. (1980). Expert and novice performance in solving physics problems. Science, 208(4450), 1335–1342. doi: 10.1126/science.208.4450.1335.CrossRefGoogle Scholar
  91. Loewenstein, J., Thompson, L., & Gentner, D. (1999). Analogical encoding facilitates knowledge transfer in negotiation. Psychonomic Bulletin Review, 6(4), 586–597. doi: 10.3758/BF03212967.CrossRefGoogle Scholar
  92. Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95(4), 492–527. doi: 10.1037/0033-295X.95.4.492.CrossRefGoogle Scholar
  93. Luchins, A. S. (1942). Mechanization in problem solving: the effect of Einstellung. Psychological Monographs, 54(6), 1–95. doi: 10.1037/h0093502.CrossRefGoogle Scholar
  94. Lynch, E. B., Coley, J. D., & Medin, D. L. (2000). Tall is typical: central tendency, ideal dimensions, and graded category structure among tree experts and novices. Memory & Cognition, 28(1), 41–50. doi: 10.3758/BF03211575.CrossRefGoogle Scholar
  95. Markman, A. B., & Gentner, D. (1993). Structural alignment during similarity comparisons. Cognitive Psychology, 25(4), 431–467. doi: 10.1006/cogp.1993.1011.CrossRefGoogle Scholar
  96. McKeithen, K. B., Reitman, J. S., Rueter, H. H., & Hirtle, S. C. (1981). Knowledge organization and skill differences in computer programmers. Cognitive Psychology, 13(3), 307–325. doi: 10.1016/0010-0285(81)90012-8.CrossRefGoogle Scholar
  97. McLaren, B. M., Lim, S.-J., & Koedinger, K. R. (2008). When and how often should worked examples be given to students? New results and a summary of the current state of research. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society (pp. 2176–2181). Austin: Cognitive Science Society.Google Scholar
  98. Neves, D. M., & Anderson, J. R. (1981). Knowledge compilation: Mechanisms for the automatization of cognitive skills. In Cognitive skills and their acquisition (pp. 57–84). Hillsdale: Erlbaum.Google Scholar
  99. Newell, A., & Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 1–55). Hillsdale: Erlbaum.Google Scholar
  100. Nokes, T. J., & Ohlsson, S. (2005). Comparing multiple paths to mastery: what is learned? Cognitive Science, 29(5), 769–796. doi: 10.1207/s15516709cog0000_32.CrossRefGoogle Scholar
  101. Nokes-Malach, T. J., & Mestre, J. (2013). Toward a model of transfer as sense-making. Educational Psychologist, 48(3), 184–207. doi: 10.1080/00461520.2013.807556.
  102. Nokes, T. J., Schunn, C. D., & Chi, M. T. H. (2010). Problem solving and human expertise. In E. Peterson, E. Baker, & B. McGraw (Eds.), International encyclopedia of education, Volume 5 (Vol. 5, pp. 265–272). Oxford: Elsevier.CrossRefGoogle Scholar
  103. Nokes, T. J., Hausmann, R. G. M., VanLehn, K. A., & Gershman, S. (2011). Testing the instructional fit hypothesis: the case of self-explanation prompts. Instructional Science, 39(5), 645–666. doi: 10.1007/s11251-010-9151-4.CrossRefGoogle Scholar
  104. Nokes-Malach, T. J., VanLehn, K. A., Belenky, D. M., Lichtenstein, M., & Cox, G. (2013). Coordinating principles and examples through analogy and self-explanation. European Journal of Psychology of Education, 28(4), 1237–1263. doi: 10.1007/s10212-012-0164-z.CrossRefGoogle Scholar
  105. Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14(3), 510–520. doi: 10.1037/0278-7393.14.3.510.Google Scholar
  106. Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17(3), 398–415. doi: 10.1037/0278-7393.17.3.398.Google Scholar
  107. Ohlsson, S. (1993). Abstract schemas. Educational Psychologist, 28(1), 51–66. doi: 10.1207/s15326985ep2801.CrossRefGoogle Scholar
  108. Ohlsson, S., & Rees, E. (1991). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8(2), 103–179. doi: 10.1207/s1532690xci0802_1.CrossRefGoogle Scholar
  109. Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77(3), 272–284. doi: 10.1037/0022-0663.77.3.272.CrossRefGoogle Scholar
  110. Paas, F. G. W. C. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: a cognitive-load approach. Journal of Educational Psychology, 84(4), 429–434. doi: 10.1037/0022-0663.84.4.429.CrossRefGoogle Scholar
  111. Paas, F. G. W. C., & Van Merriënboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: a cognitive-load approach. Journal of Educational Psychology, 86(1), 122–133. doi: 10.1037/0022-0663.86.1.122.CrossRefGoogle Scholar
  112. Phye, G. D. (1990). Inductive problem solving: schema inducement and memory-based transfer. Journal of Educational Psychology, 82(4), 826–831. doi: 10.1037/0022-0663.82.4.826.CrossRefGoogle Scholar
  113. Phye, G. D. (2001). Problem-solving instruction and problem-solving transfer: the correspondence issue. Journal of Educational Psychology, 93(3), 571–578. doi: 10.1037//0022-0663.93.3.571.CrossRefGoogle Scholar
  114. Pirolli, P. L., & Anderson, J. R. (1985). The role of learning from examples in the acquisition of recursive programming skills. Canadian Journal of Psychology, 39(2), 240–272. doi: 10.1037/h0080061.CrossRefGoogle Scholar
  115. Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: toward a theory of conceptual change. Science Education, 66(2), 211–227. doi: 10.1002/sce.3730660207.CrossRefGoogle Scholar
  116. Proffitt, J. B., Coley, J. D., & Medin, D. L. (2000). Expertise and category-based induction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26(4), 811–828. doi: 10.1037/0278-7393.26.4.811.Google Scholar
  117. Quilici, J. L., & Mayer, R. E. (2002). Teaching students to recognize structural similarities between statistics word problems. Applied Cognitive Psychology, 16(3), 325–342. doi: 10.1002/acp.796.CrossRefGoogle Scholar
  118. Reed, S. K. (1989). Constraints on the abstraction of solutions. Journal of Educational Psychology, 81(4), 532–540. doi: 10.1037/0022-0663.81.4.532.CrossRefGoogle Scholar
  119. Reed, S. K., Ackinclose, C. C., & Voss, A. A. (1990). Selecting analogous problems: similarity versus inclusiveness. Memory & Cognition, 18(1), 83–98. doi: 10.3758/BF03202649.CrossRefGoogle Scholar
  120. Reeves, L. M., & Weisberg, R. W. (1994). The role of content and abstract information in analogical transfer. Psychological Bulletin, 115(3), 381–400. doi: 10.1037/0033-2909.115.3.381.CrossRefGoogle Scholar
  121. Renkl, A. (1997). Learning from worked-out examples: a study on individual differences. Cognitive Science, 21(1), 1–29. doi: 10.1207/s15516709cog2101_1.CrossRefGoogle Scholar
  122. Renkl, A. (2002). Worked-out examples: instructional explanations support learning by self-explanations. Learning and Instruction, 12(5), 529–556. doi: 10.1016/S0959-4752(01)00030-5.CrossRefGoogle Scholar
  123. Renkl, A. (2005). The worked-out-example principle in multimedia learning. In R. Mayer (Ed.), Cambridge handbook of multimedia learning (pp. 229–246). New York: Cambridge University Press.CrossRefGoogle Scholar
  124. Renkl, A. (2014). Toward an instructionally oriented theory of example-based learning. Cognitive Science, 38(1), 1–37. doi: 10.1111/cogs.12086.CrossRefGoogle Scholar
  125. Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: a cognitive load perspective. Educational Psychologist, 38(1), 15–22. doi: 10.1207/S15326985EP3801_3.CrossRefGoogle Scholar
  126. Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: smooth transitions help learning. The Journal of Experimental Education, 70(4), 293–315. doi: 10.1080/00220970209599510.CrossRefGoogle Scholar
  127. Richey, J. E., & Nokes-Malach, T. J. (2013). How much is too much? Learning and motivation effects of adding instructional explanations to worked examples. Learning and Instruction, 25, 104–124. doi: 10.1016/j.learninstruc.2012.11.006.CrossRefGoogle Scholar
  128. Richland, L. E., Zur, O., & Holyoak, K. J. (2007). Cognitive supports for analogies in the mathematics classroom. Science, 316, 1128–1129. doi: 10.1126/science.1142103.CrossRefGoogle Scholar
  129. Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189–203. doi: 10.1080/00461520.2012.667065.CrossRefGoogle Scholar
  130. Ringenberg, M., & VanLehn, K. A. (2006). Scaffolding problem solving with annotated, worked-out examples to promote deep learning. In M. Ikeda, K. D. Ashley, & T.-W. Chan (Eds.), Proceedings of the 8th international conference on intelligent tutoring systems (Vol. 4053, pp. 624–634). Berlin: Springer. doi: 10.1007/11774303.Google Scholar
  131. Rittle-Johnson, B. (2006). Promoting transfer: effects of self-explanation and direct instruction. Child Development, 77(1), 1–15. doi: 10.1111/j.1467-8624.2006.00852.x.CrossRefGoogle Scholar
  132. Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561–574. doi: 10.1037/0022-0663.99.3.561.CrossRefGoogle Scholar
  133. 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(2), 346–362. doi: 10.1037/0022-0663.93.2.346.CrossRefGoogle Scholar
  134. Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852. doi: 10.1037/a0016026.CrossRefGoogle Scholar
  135. Robins, S., & Mayer, R. E. (1993). Schema training in analogical reasoning. Journal of Educational Psychology, 85(3), 529–538. doi: 10.1037/0022-0663.85.3.529.CrossRefGoogle Scholar
  136. Ross, B. H., & Kilbane, M. C. (1997). Effects of principle explanation and superficial similarity on analogical mapping in problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23(2), 427–440. doi: 10.1037//0278-7393.23.2.427.Google Scholar
  137. Roy, M., & Chi, M. T. H. (2005). The self-explanation principle in multimedia learning. In R. E. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 271–286). New York: Cambridge University Press.CrossRefGoogle Scholar
  138. Salomon, G., & Perkins, D. N. (1989). Rocky roads to transfer: rethinking mechanism of a neglected phenomenon. Educational Psychologist, 24(2), 113–142. doi: 10.1207/s15326985ep2402_1.CrossRefGoogle Scholar
  139. Scheiter, K., & Gerjets, P. (2006). When less is sometimes more: Optimal learning conditions are required for schema acquisition from multiple examples. In Proceedings of the 27th annual conference of the cognitive science society (pp. 1943–1948). Mahwah: Erlbaum.Google Scholar
  140. Schmidt, H. G., & Boshuizen, H. P. A. (1993). On acquiring expertise in medicine. Educational Psychology Review, 5(3), 205–221. doi: 10.1007/BF01323044.CrossRefGoogle Scholar
  141. Schoenfeld, A. H., & Herrmann, D. J. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning Memory and Cognition, 8(5), 484–494. doi: 10.1037/0278-7393.8.5.484.Google Scholar
  142. Schunn, C. D., & Anderson, J. R. (1999). The generality/specificity of expertise in scientific reasoning. Cognitive Science, 23(3), 337–370. doi: 10.1207/s15516709cog2303_3.CrossRefGoogle Scholar
  143. Schwartz, D. L., Bransford, J. D., & Sears, D. (2005). Efficiency and innovation in transfer. In J. Mestre (Ed.), Transfer of learning from a modern multidisciplinary perspective (pp. 1–51). Greenwich: Information Age Publishing.Google Scholar
  144. Schworm, S., & Renkl, A. (2006). Computer-supported example-based learning: when instructional explanations reduce self-explanations. Computers & Education, 46(4), 426–445. doi: 10.1016/j.compedu.2004.08.011.CrossRefGoogle Scholar
  145. Schworm, S., & Renkl, A. (2007). Learning argumentation skills through the use of prompts for self-explaining examples. Journal of Educational Psychology, 99(2), 285–296. doi: 10.1037/0022-0663.99.2.285.CrossRefGoogle Scholar
  146. Sherman, J., & Bisanz, J. (2009). Equivalence in symbolic and nonsymbolic contexts: benefits of solving problems with manipulatives. Journal of Educational Psychology, 101(1), 88–100. doi: 10.1037/a0013156.CrossRefGoogle Scholar
  147. Simon, D. P., & Simon, H. A. (1978). Individual differences in solving physics problems. In R. Siegler (Ed.), Children’s thinking: What develops? (pp. 325–348). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  148. Singley, M. K., & Anderson, J. R. (1985). The transfer of text-editing skill. International Journal of Man-Machine Studies, 22(4), 403–423. doi: 10.1016/S0020-7373(85)80047-X.CrossRefGoogle Scholar
  149. Singley, M. K., & Anderson, J. R. (1989). The transfer of a cognitive skill. Cambridge: Harvard University Press.Google Scholar
  150. Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: an experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408–426. doi: 10.1016/j.jecp.2008.11.004.CrossRefGoogle Scholar
  151. Sternberg, R. J. (1998). Metacognition, abilities, and developing expertise: what makes an expert student ? Instructional Science, 26, 127–140. doi: 10.1023/A:1003096215103.CrossRefGoogle Scholar
  152. Sweller, J. (1983). Control mechanisms in problem solving. Memory & Cognition, 11(1), 32–40. doi: 10.3758/BF03197659.CrossRefGoogle Scholar
  153. Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognitive Science, 12(2), 257–285. doi: 10.1207/s15516709cog1202_4.CrossRefGoogle Scholar
  154. Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. doi: 10.1207/s1532690xci0201_3.CrossRefGoogle Scholar
  155. Sweller, J., & Levine, M. (1982). Effects of goal specificity on means-ends analysis and learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8(5), 463–474. doi: 10.1037/0278-7393.8.5.463.Google Scholar
  156. Sweller, J., Mawer, R. F., & Howe, W. (1982). Consequences of history-cued and means-end strategies in problem solving. The American Journal of Psychology, 95(3), 455. doi: 10.2307/1422136.CrossRefGoogle Scholar
  157. Sweller, J., Mawer, R. F., & Ward, M. R. (1983). Development of expertise in mathematical problem solving. Journal of Experimental Psychology: General, 112(4), 639–661. doi: 10.1037//0096-3445.112.4.639.CrossRefGoogle Scholar
  158. Sweller, J., van Merriënboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296. doi: 10.1023/A:1022193728205.CrossRefGoogle Scholar
  159. Taatgen, N. A., & Anderson, J. R. (2002). Why do children learn to say “broke”? A model of learning the past tense without feedback. Cognition, 86(2), 123–155.CrossRefGoogle Scholar
  160. Taatgen, N. A., & Lee, F. J. (2003). Production compilation: a simple mechanism to model complex skill acquisition. Human Factors, 45(1), 61–76. doi: 10.1518/hfes. Scholar
  161. Thorndyke, P. W. (1984). Applications to schema theory in cognitive research. In J. A. Anderson & S. M. Kosslyn (Eds.), Tutorials in learning and memory (pp. 167–191). San Francisco: Freeman.Google Scholar
  162. VanLehn, K. A. (1996). Cognitive skill acquisition. Annual Review of Psychology, 47(1), 513–539. doi: 10.1146/annurev.psych.47.1.513.CrossRefGoogle Scholar
  163. VanLehn, K. A. (1999). Rule-learning events in the acquisition of a complex skill: an evaluation of Cascade. Journal of the Learning Sciences. doi: 10.1207/s15327809jls0801_3.Google Scholar
  164. VanLehn, K. A., & Jones, R. M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas or analogies? In M. Polson (Ed.), Proceedings of the fifteenth annual conference of the cognitive science society (pp. 1034–1039). Hillsdale: Erlbaum.Google Scholar
  165. VanLehn, K. A., & van de Sande, B. (2009). Acquiring conceptual expertise from modeling: The case of elementary physics. In K. A. Ericsson (Ed.), Development of professional performance: Toward measurement of expert performance and design of optimal learning environments (pp. 356–378). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  166. Voss, J. F., Tyler, S. W., & Yengo, L. A. (1983). Individual differences in the solving of social science problems. In R. F. Dilion & R. R. Schmeck (Eds.), Individual differences in cognition, Vol. 1. New York: Academic P.Google Scholar
  167. Ward, M. R., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7(1), 1–39. doi: 10.1207/s1532690xci0701_1.CrossRefGoogle Scholar
  168. Wittwer, J., & Renkl, A. (2010). How effective are instructional explanations in example-based learning? A meta-analytic review. Educational Psychology Review, 22(4), 393–409. doi: 10.1007/s10648-010-9136-5.CrossRefGoogle Scholar
  169. Zeitz, C. M. (1994). Expert-novice differences in memory, abstraction, and reasoning in the domain of literature. Cognition and Instruction, 12(4), 277–312. doi: 10.1207/s1532690xci1204_1.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • J. Elizabeth Richey
    • 1
  • Timothy J. Nokes-Malach
    • 1
  1. 1.Department of Psychology and Learning Research and Development CenterUniversity of PittsburghPittsburghUSA

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