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The impact of guidance during problem-solving prior to instruction on students’ inventions and learning outcomes

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Abstract

Multiple studies have shown benefits of problem-solving prior to instruction (cf. Productive Failure, Invention) in comparison to direct instruction. However, students’ solutions prior to instruction are usually erroneous or incomplete. In analogy to guided discovery learning, it might therefore be fruitful to lead students towards the discovery of the canonical solution. In two quasi-experimental studies with 104 students and 175 students, respectively, we compared three conditions: problem-solving prior to instruction, guided problem-solving prior to instruction in which students were led towards the discovery of relevant solution components, and direct instruction. We replicated the beneficial effects of problem-solving prior to instruction in comparison to direct instruction on posttest items testing for conceptual knowledge. Our process analysis further revealed that guidance helped students to invent better solutions. However, the solution quality did not correlate with the posttest results in the guided condition, indicating that leading students towards the solution does not additionally promote learning. This interpretation is supported by the finding that the two conditions with problem-solving prior to instruction did not differ significantly at posttest. The second study replicated these findings with a greater sample size. The results indicate that different mechanisms underlie guided discovery learning and problem-solving prior to instruction: In guided discovery learning, the discovery of an underlying model is inherent to the method. In contrast, the effectiveness of problem-solving prior to instruction does not depend on students’ discovery of the canonical solution, but on the cognitive processes related to problem-solving, which prepare students for a deeper understanding during subsequent instruction.

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Notes

  1. In recent, as yet unpublished studies, Kapur implements similar support in his Productive Failure conditions (personal communication, March 2010). However, he does not empirically compare the supported condition to his previous unsupported Productive Failure condition.

References

  • Aberson, C. (2002). Interpreting null results: Improving presentation and conclusions with confidence intervals. Journal of Articles in Support of the Null Hypothesis, 1(3), 36–42.

    Google Scholar 

  • Craik, F. I. M., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. Journal of Verbal Learning and Verbal Behavior, 11(6), 671–684.

    Article  Google Scholar 

  • de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68(2), 179–201.

    Article  Google Scholar 

  • 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 

  • 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). Herleen: Open Universiteit Nederland.

    Google Scholar 

  • diSessa, A. A., Hammer, D., Sherin, B. L., & Kolpakowski, T. (1991). Inventing graphing: meta-representational expertise in children. The Journal of Mathematical Behavior, 10(2), 117–160.

    Google Scholar 

  • Diziol, D., & Rummel, N. (2010). How to design support for collaborative e-learning: A framework of relevant dimensions. In B. Ertl (Ed.), E-Collaborative knowledge construction: Learning from computer-supported and virtual environments (pp. 162–179). Hershey, PA: IGI Global.

    Chapter  Google Scholar 

  • Gibson, J. J., & Gibson, E. J. (1955). Perceptual learning: Differentiation or enrichment. Psychological Review, 62, 32–41.

    Article  Google Scholar 

  • Kapur, M. (2010). A further study of productive failure in mathematical problem solving: Unpacking the design components. Instructional Science, 39(4), 561–579.

    Google Scholar 

  • Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science, 40(4), 651–672.

    Article  Google Scholar 

  • Kapur, M., & Bielaczyc, K. (2011). Classroom-based experiments in productive failure. In L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 2812–2817). Austin, TX: Cognitive Science Society.

    Google Scholar 

  • Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. The Journal of the Learning Sciences, 21(1), 45–83.

    Article  Google Scholar 

  • Kapur, M., & Rummel, N. (2009). The assistance dilemma in CSCL. In A. Dimitracopoulou, C. O’Malley, D. Suthers, & P. Reimann (Eds.), Computer supported collaborative learning practices—CSCL 2009 Conference Proceedings (Vol. 2, pp. 37–42). Berlin: International Society of the Learning Sciences.

    Google Scholar 

  • Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction—effects of direct instruction and discovery learning. Psychological Science, 15(10), 661–667.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Kultusministerkonferenz (2003). Bildungsstandards im Fach Mathematik für den Mittleren Bildungsabschluss [Learning standards for mathematics for intermediate secondary education] (Beschluss vom 4.12.2003). Neuwied, Luchterhand.

  • Norman, D. A. (1988). The psychology of everyday things. New York: Basic Books.

    Google Scholar 

  • OECD (2010). PISA 2012 mathematics framework. Retrieved from http://www.oecd.org/pisa/pisaproducts/46961598.pdf.

  • Renkl, A. (2008). Lehren und Lernen im Kontext der Schule [Teaching and learning in school contexts]. In A. Renkl (Ed.), Lehrbuch Pädagogische Psychologie (pp. 109–153). Bern: Huber.

    Google Scholar 

  • Rittle-Johnson, B., & Star, J. R. (2011). The power of comparison in learning and instruction: Learning outcomes supported by different types of comparisons. In B. Ross & J. Mestre (Eds.), Psychology of learning and motivation: Cognition in education (Vol. 55, pp. 199–226). San Diego: Elsevier.

    Google Scholar 

  • Rittle-Johnson, B., Siegler, R., & Alibali, M. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.

    Article  Google Scholar 

  • Roll, I., Aleven, V., & Koedinger, K. R. (2009). Helping students know ‘further’—increasing the flexibility of students’ knowledge using symbolic invention tasks. In N. A. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st annual conference of the Cognitive Science Society (pp. 1169–1174). Austin, TX: Cognitive Science Society.

    Google Scholar 

  • Roll, I., Aleven, V., & Koedinger, K. R. (2011). Outcomes and mechanisms of transfer in invention activities. In L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Proceedings of the 33rd annual meeting of the Cognitive Science Society (pp. 2824–2829). Boston: Cognitive Science Society.

    Google Scholar 

  • Roll, I., Holmes, N., Day, J., & Bonn, D. (2012). Evaluating metacognitive scaffolding in guided invention activities. Instructional Science, 40(4), 691–710.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: MacMillan.

    Google Scholar 

  • Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475–522.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schwartz, D. L., Chase, C. C., Oppezzo, M. A., & Chin, D. B. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103(4), 759–775.

    Article  Google Scholar 

  • Sears, D. A. (2006). Effects of innovation versus efficiency tasks on collaboration and learning. Doctoral dissertation, Stanford University. Retrieved from http://www.stat.auckland.ac.nz/~iase/publications/dissertations/06.Sears.Dissertation.pdf.

  • Sleeman, D., Kelly, A. E., Martinak, R., Ward, R. D., & Moore, J. L. (1989). Studies of diagnosis and remediation with high school algebra students. Cognitive Science, 13(4), 551–568.

    Article  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1997). Understanding and improving classroom mathematics instruction: An overview of the TIMSS video study. Phi Delta Kappan, 79(1), 14–21.

    Google Scholar 

  • van Joolingen, W. (1999). Cognitive tools for discovery learning. International Journal of Artificial Intelligence in Education, 10, 385–397.

    Google Scholar 

  • van Joolingen, W. R., de Jong, T., Lazonder, A. W., Savelsbergh, E. R., & Manlove, S. (2005). Co-Lab: Research and development of an online learning environment for collaborative scientific discovery learning. Computers in Human Behavior, 21(4), 671–688.

    Article  Google Scholar 

  • VanLehn, K. (1989). Problem solving and cognitive skill acquisition. In M. Posner (Ed.), Foundations of cognitive science (pp. 527–579). Cambridge, MA: MIT Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Westermann, K., & Rummel, N. (2012). Delaying instruction: Evidence from a study in a university relearning setting. Instructional Science, 40(4), 673–689.

    Article  Google Scholar 

  • Wiedmann, M., Leach, R. C., Rummel, N., & Wiley, J. (2012). Does group composition affect learning by invention? Instructional Science, 40(4), 711–730.

    Article  Google Scholar 

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Acknowledgments

We would especially like to thank Manu Kapur for his suggestions on the design of the study and for providing us with his study materials and with a great deal of background information concerning his own studies. We thank the German Academic Exchange Service for funding a research stay in Manu Kapur’s research group at the National Institute of Education in Singapore. The second study was funded by the Center of Educational Studies of our university. We thank Lars Holzäpfel for his feedback from a mathematics education perspective on our study materials and tests. We are very thankful to the participating schools and teachers for their organizational efforts and for offering their lessons. We thank our student research assistants Katja Goepel, Christian Hartmann, and Andreas Vogel for their help in collecting and coding the data.

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  1. Institute of Educational Research, Ruhr-Universität Bochum, Universitätsstr. 150, 44801, Bochum, Germany

    Katharina Loibl & Nikol Rummel

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  1. Katharina Loibl
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  2. Nikol Rummel
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Correspondence to Katharina Loibl.

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Loibl, K., Rummel, N. The impact of guidance during problem-solving prior to instruction on students’ inventions and learning outcomes. Instr Sci 42, 305–326 (2014). https://doi.org/10.1007/s11251-013-9282-5

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