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Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles

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Abstract

Promoting self-explanation (i.e., generating explanations for oneself in an attempt to make sense of new information) is a recommended study strategy and instructional practice. A meta-analysis of the literature on prompting self-explanation to improve mathematics learning confirmed that prompted self-explanation leads to a small to moderate improvement in procedural knowledge, conceptual knowledge and procedural transfer when assessed immediately after the intervention. However, evidence that self-explanation reliably promotes learning within a classroom context or retention of knowledge over a delay is much more limited. Moderator analyses indicated that the effect on immediate outcomes was stronger if scaffolding of high-quality explanation was provided but did not vary based on whether time on task was controlled across conditions. Based on the research literature, we propose instructional recommendations for mathematics educators: (a) scaffold high-quality explanations via training on self-explanation or structuring the self-explanation responses, (b) design explanation prompts so they do not sacrifice attention to other important content, (c) prompt learners to explain correct information, and (d) prompt learners to explain why common misconceptions are incorrect. We conclude with issues for future research, such as the need for additional research on effective use of self-explanation in classroom contexts and the merits of self-explanation relative to alternative instructional techniques.

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References

  • Aleven, V. A. W. M. M., & Koedinger, K. R. (2002). An effective metacognitive strategy: Learning by doing and explaining with a computer-based cognitive tutor. Cognitive Science, 26, 147–179.

    Article  Google Scholar 

  • 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, 181–214.

    Article  Google Scholar 

  • 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, 774–783.

    Article  Google Scholar 

  • Berry, D. C. (1983). Metacognitive experience and transfer of logical reasoning. The Quarterly Journal of Experimental Psychology Section A, 35, 39–49.

    Article  Google Scholar 

  • Berthold, K., Eysink, T. H. S., & Renkl, A. (2009). Assisting self-explanation prompts are more effective than open prompts when learning with multiple representations. Instructional Science, 37, 345–363.

    Article  Google Scholar 

  • Berthold, K., & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of Educational Psychology, 101, 70–87.

    Article  Google Scholar 

  • Berthold, K., Röder, H., Knörzer, D., Kessler, W., & Renkl, A. (2011). The double-edged effects of explanation prompts. Computers in Human Behavior, 27, 69–75.

    Article  Google Scholar 

  • Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24–34.

    Article  Google Scholar 

  • Booth, J. L., Oyer, M. H., Pare-Blagoev, E. J., Elliot, A. J., Barbieri, C., Augustine, A., & Koedinger, K. R. (2015). Learning algebra by example in real-world classrooms. Journal of Research on Educational Effectiveness, 8, 530–551.

    Article  Google Scholar 

  • Broers, N. J., & Imbos, T. (2005). Charting and manipulating propositions as methods to promote self-explanation in the study of statistics. Learning and Instruction, 15, 517–538.

    Article  Google Scholar 

  • Calin-Jageman, R. J., & Ratner, H. H. (2005). The role of encoding in the self-explanation effect. Cognition and Instruction, 23, 523–543.

    Article  Google Scholar 

  • Canobi, K. H. (2009). Concept-procedure interactions in children’s addition and subtraction. Journal of Experimental Child Psychology, 102, 131–149.

    Article  Google Scholar 

  • Chi, M. T. H. (2000). Self-explaining: The dual processes of generating inference and repairing mental models advances in instructional psychology: Educational design and cognitive science, Vol. 5 (pp. 161–238). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.

    Google Scholar 

  • Chi, M. T. H. (2009). Active-constructive-interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1, 73–105.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chi, M. T. H., de Leeuw, N., Chiu, M.-H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18, 439–477.

    Google Scholar 

  • Common Core State Standards (2010). Washington D.C.: National Governors Association Center for Best Practices & Council of Chief State School Officers.

  • DeCaro, M. S., & Rittle-Johnson, B. (2012). Exploring Mathematics Problems Prepares Children to Learn from Instruction. Journal of Experimental Child Psychology, 113, 552–568.

    Article  Google Scholar 

  • Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques: Promising directions from cognitive and educational psychology. Psychological Science in the Public Interest, 14, 4–58.

    Article  Google Scholar 

  • Durkin, K., & Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction, 22, 206–214.

    Article  Google Scholar 

  • Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87, 215–251.

    Article  Google Scholar 

  • Ferguson, C. J., & Brannick, M. T. (2012). Publication bias in psychological science: Prevalence, methods for identifying and controlling, and implications for the use of meta-analyses. Psychological Methods, 17, 120–128.

    Article  Google Scholar 

  • Gerjets, P., Scheiter, K., & Catrambone, R. (2006). Can learning from molar and modular worked examples be enhanced by providing instructional explanations and prompting self-explanations? Learning and Instruction, 16, 104–121.

    Article  Google Scholar 

  • Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38.

    Article  Google Scholar 

  • Große, C. S., & Renkl, A. (2006). Effects of multiple solution methods in mathematics learning. Learning and Instruction, 16, 122–138.

    Article  Google Scholar 

  • Große, C. S., & Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning and Instruction, 17, 612–634.

    Article  Google Scholar 

  • Hilbert, T. S., Renkl, A., Kessler, S., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18, 54–65.

    Article  Google Scholar 

  • Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 45, 62–101.

    Article  Google Scholar 

  • Kapur, M. (2010). Productive failure in mathematical problem solving. Instructional Science, 38, 523–550.

    Article  Google Scholar 

  • Kramarski, B., & Dudai, V. (2009). Group-metacognitive support for online inquiry in mathematics with differential self-questioning. Journal of Educational Computing Research, 40, 377–404.

    Article  Google Scholar 

  • Krauss, R. M. (1987). The role of the listener: Addressee influences on message formulation. Journal of Language and Social Psychology, 6, 81–98.

    Article  Google Scholar 

  • Lange, K. E., Booth, J. L., & Newton, K. J. (2014). Learning algebra from worked examples. Mathematics Teacher, 107, 534–540.

    Article  Google Scholar 

  • Legare, C. H., Gelman, S. A., & Wellman, H. M. (2010). Inconsistency with prior knowledge triggers children’s causal explanatory reasoning. Child Development, 81, 929–944.

    Article  Google Scholar 

  • Leppink, J., Broers, N. J., Imbos, T., Vleuten, C. P. M., & Berger, M. P. F. (2012). Self-explanation in the domain of statistics: an expertise reversal effect. Higher Education, 63, 771–785.

    Article  Google Scholar 

  • Loehr, A. M., Rittle-Johnson, B., & Rajendran, A. (2014). Promoting mathematical problem solving and explanation: The effects of extended homework use. Paper presented at the American Education Research Association Conference, Philadelphia, PA.

  • Loewenthal, K. (1967). The development of codes in public and private language. Psychonomic Science, 8, 449–450.

    Article  Google Scholar 

  • Matthews, P., & Rittle-Johnson, B. (2009). In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology, 104, 1–21.

    Article  Google Scholar 

  • McEldoon, K. L., Durkin, K. L., & Rittle-Johnson, B. (2013). Is self-explanation worth the time? A comparison to additional practice. British Journal of Educational Psychology, 83, 615–632.

    Article  Google Scholar 

  • McNeil, N. M., & Alibali, M. W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 883–899.

    Article  Google Scholar 

  • McNeil, N. M., Chesney, D. L., Matthews, P. G., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Wheeler, M. C. (2012). It pays to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence. Journal of Educational Psychology, 104, 1109–1121.

    Article  Google Scholar 

  • Mwangi, W., & Sweller, J. (1998). Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction, 16, 173–199.

    Article  Google Scholar 

  • O’Neil, H. F., Chung, G. K. W. K., Kerr, D., Vendlinski, T. P., Buschang, R. E., & Mayer, R. E. (2014). Adding self-explanation prompts to an educational computer game. Computers in Human Behavior, 30, 23–28.

    Article  Google Scholar 

  • Pashler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing instruction and study to improve student learning. Washington, DC: Institute of Education Sciences.

    Book  Google Scholar 

  • Rau, M. A., Aleven, V., & Rummel, N. (2015). Successful learning with multiple graphical representations and self-explanation prompts. Journal of Educational Psychology, 107, 30–46.

    Article  Google Scholar 

  • Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science, 21, 1–29.

    Article  Google Scholar 

  • Renkl, A. (1999). Learning mathematics from worked-out examples: Analyzing and fostering self-explanations. European Journal of Psychology of Education, 14, 477–488.

    Article  Google Scholar 

  • Renkl, A., Stark, R., Gruber, H., & Mandl, H. (1998). Learning from worked-out examples: The effects of example variability and elicited self-explanations. Contemporary Educational Psychology, 23, 90–108.

    Article  Google Scholar 

  • Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation and direct instruction. Child Development, 77, 1–15.

    Article  Google Scholar 

  • Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31, 101–112.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Loehr, A. M. (2016). Eliciting explanations: Constraints on when self-explanation aids learning. Psychonomic Bulletin and Review. doi:10.3758/s13423-016-1079-5.

    Google Scholar 

  • Rittle-Johnson, B., & Loehr, A. M. (2017). Instruction based on self-explanation. In R. E. Mayer & P. A. Alexander (Eds.), Handbook of research on learning and instruction (2nd ed., pp. 349–364). New York, NY: Routledge.

    Google Scholar 

  • Rittle-Johnson, B., Saylor, M., & Swygert, K. E. (2008). Learning from explaining: Does it matter if mom is listening? Journal of Experimental Child Psychology, 100, 215–224.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1118–1134). Oxford: Oxford University Press.

    Google Scholar 

  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587–597.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Siegler, R. S. (1999). Learning to spell: Variability, choice, and change in children’s strategy use. Child Development, 70, 332–348.

    Article  Google Scholar 

  • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346–362.

    Article  Google Scholar 

  • Roediger, H. L. III, & Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17, 249–255.

    Article  Google Scholar 

  • Schwartz, D. L., Chase, C. C., Chin, D. B., & Oppezzo, M. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103, 759–775.

    Article  Google Scholar 

  • Siegler, R. S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 28, 225–273.

    Article  Google Scholar 

  • Siegler, R. S. (2002). Microgenetic studies of self-explanation. In N. Garnott & J. Parziale (Eds.), Microdevelopment: A process-oriented perspective for studying development and learning (pp. 31–58). Cambridge, MA: Cambridge University Press.

    Chapter  Google Scholar 

  • Siegler, R. S., & Chen, Z. (2008). Differentiation and Integration: Guiding principles for analyzing cognitive change. Developmental Science, 11, 433–448.

    Article  Google Scholar 

  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404–411 (Retrieved from http://www.jstor.org/stable/30034943).

  • Star, J. R. (2007). Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38, 132–135.

    Google Scholar 

  • Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., & Maruno, S. (2007). Effects of self-explanation as a metacognitive strategy for solving mathematical word problems. Japanese Psychological Research, 49, 222–233.

    Article  Google Scholar 

  • Webb, N. M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22, 366–389.

    Article  Google Scholar 

  • Wittwer, J., & Renkl, A. (2010). How effective are instructional explanations in example-based learning? A meta-analytic review. Educational Psychology Review, 22, 393–409.

    Article  Google Scholar 

  • Wong, R. M. F., Lawson, M. J., & Keeves, J. (2002). The effects of self-explanation training on students’ problem solving in high-school mathematics. Learning and Instruction, 12, 233–262.

    Article  Google Scholar 

  • Wylie, R., & Chi, M. T. (2014). The self-explanation principle in mulimedia learning. In R. E. Mayer (Ed.), The cambridge handbook of multimedia learning (Vol. 2, pp. 413–432). New York, NY: Cambridge University Press.

    Chapter  Google Scholar 

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Acknowledgements

Writing of this article was supported in part by National Science Foundation grant DRL-0746565 to Rittle-Johnson.

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Authors and Affiliations

  1. Department of Psychology and Human Development, Peabody College, Vanderbilt University, 230 Appleton Place, Peabody #0552, Nashville, TN, 37203, USA

    Bethany Rittle-Johnson & Abbey M. Loehr

  2. Peabody Research Institute, Vanderbilt University, Nashville, USA

    Kelley Durkin

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  1. Bethany Rittle-Johnson
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  2. Abbey M. Loehr
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  3. Kelley Durkin
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Correspondence to Bethany Rittle-Johnson.

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Rittle-Johnson, B., Loehr, A.M. & Durkin, K. Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM Mathematics Education 49, 599–611 (2017). https://doi.org/10.1007/s11858-017-0834-z

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