Abstract
Invention and Productive Failure activities ask students to generate methods that capture the important properties of some given data (e.g., uncertainty) before being taught the expert solution. Invention and Productive Failure activities are a class of scientific inquiry activities in that students create, implement, and evaluate mathematical models based on data. Yet, lacking sufficient inquiry skills, students often do not actualize the full potential of these activities. We identified key invention strategies in which students often fail to engage: exploratory analysis, peer interaction, self-explanation, and evaluation. A classroom study with 134 students evaluated the effect of supporting these skills on the quality and outcomes of the invention process. Students in the Unguided Invention condition received conventional Invention Activities; students in the Guided Invention condition received complementary metacognitive scaffolding. Students were asked to invent methods for calculating uncertainties in best-fitting lines. Guided Invention students invented methods that included more conceptual features and ranked the given datasets more accurately, although the quality of their mathematical expressions was not improved. At the process level, Guided Invention students revised their methods more frequently and had more and better instances of unprompted self-explanations even on components of the activity that were not supported by the metacognitive scaffolding. Classroom observations are used to demonstrate the effect of the scaffolding on students’ learning behaviours. These results suggest that process guidance in the form of metacognitive scaffolding augments the inherent benefits of Invention Activities and can lead to gains at both domain and inquiry levels.
Similar content being viewed by others
References
Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1–18.
Azevedo, R., Cromley, J. G., & Seibert, D. (2004). Does adaptive scaffolding facilitate students’ ability to regulate their learning with hypermedia? Contemporary Educational Psychology, 29, 344–370.
Azevedo, R., & Jacobson, M. J. (2008). Advances in scaffolding learning with hypertext and hypermedia: A summary and critical analysis. Educational Technology Research and Development, 56, 93–100.
Bulu, S., & Pedersen, S. (2010). Scaffolding middle school students’ content knowledge and ill-structured problem solving in a problem-based hypermedia learning environment. Educational Technology Research and Development, 58(5), 507–529.
Chase, C. C., Shemwell, J. T., & Schwartz, D. L. (2010). Explaining across contrasting cases for deep understanding in science: An example using interactive simulations. In S. Goldman & J. Pellegrino (Eds.), Proceedings of the 9th international conference of the learning sciences (pp. 153–160). Chicago, IL.
Chi, M. T. H., De Leeuw, N., Chiu, M., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439–477.
Day, J., & Bonn, D. (2011). Development of the concise data processing assessment. Physical Review Special Topics Physics Education Research, 7(1), 010114.
Day, J., Nakahara, H., & Bonn, D. (2010). Teaching standard deviation by building from student invention. The Physics Teacher, 48, 546–548.
de Jong, T. (2006). Scaffolds for scientific discovery learning. In J. Elen, R. E. Clark, & J. Lowyck (Eds.), Handling complexity in learning environments: Theory and research (pp. 107–128). Howard House: Emerald Group Publishing.
de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68, 179–201.
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.
Godfrey-Smith, P. (2003). Theory and reality: An introduction to the philosophy of science. Chicago: University of Chicago Press.
Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424.
Kapur, M. (2009). Productive failure in mathematical problem solving. Instructional Science, 38(6), 523–550.
Kapur, M. (2010). A further study of productive failure in mathematical problem solving: Unpacking the design components. Instructional Science, 39(4), 561–579. doi:10.1007/s11251-010-9144-3.
Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science (this issue).
Kapur, M., & Bielaczyc, K. (2011). Classroom-based experiments in productive failure. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 2812–2817). Austin: Cognitive Science Society.
Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. The Journal of the Learning Sciences, 21(1), 45–83.
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.
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.
Koedinger, K. R., Aleven, V., Roll, I., & Baker, R. S. J.d. (2009). In vivo experiments on whether supporting metacognition in intelligent tutoring systems yields robust learning. In D. J. Hacker, J. Dunlosky, & A. C. Graesser (Eds.), Handbook of metacognition in education (pp. 383–412). New York: Routledge.
Lovett, M. (1998). Cognitive task analysis in service of intelligent tutoring system design: A case study in statistics. In B. P. Goettl, et al. (Eds.), Intelligent Tutoring Systems Lecture Notes in Computer Science (pp. 234–243). Berlin: Springer.
Manlove, S., Lazonder, A. W., & de Jong, T. (2007). Software scaffolds to promote regulation during scientific inquiry learning. Metacognition and Learning, 2, 141–155.
Mathan, S. A., & Koedinger, K. R. (2005). Fostering the intelligent novice: Learning from errors with metacognitive tutoring. Educational Psychologist, 40(4), 257–265.
McDaniel, M. A., & Schlager, M. S. (1990). Discovery learning and transfer of problem-solving skills. Cognition and Instruction, 7(2), 129–159.
Mulder, Y. G., Lazonder, A. W., & de Jong, T. (2009). Finding out how they find it out: An empirical analysis of inquiry learners’ need for support. International Journal of Science Education, 1–21.
Nathan, M. J. (1998). Knowledge and situational feedback in a learning environment for algebra story problem solving. Interactive Learning Environments, 5(1), 135–159.
Needham, D. R., & Begg, I. M. (1991). Problem-oriented training promotes spontaneous analogical transfer: Memory-oriented training promotes memory for training. Memory and Cognition, 19(6), 543–557.
Osman, M. E., & Hannafin, M. J. (1994). Effects of advance questioning and prior knowledge on science learning. The Journal of Educational Research, 88(1), 5–13.
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: Cognitive Science Society.
Roll, I., Aleven, V., & Koedinger, K. R. (2011a). Outcomes and mechanisms of transfer. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 2824–2829). Austin: Cognitive Science Society.
Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2007). Designing for metacognition—applying cognitive tutor principles to the tutoring of help seeking. Metacognition and Learning, 2(2), 125–140.
Roll, I., Aleven, V., McLaren, B. M., & Koedinger, K. R. (2011b). Improving students’ help-seeking skills using metacognitive feedback in an intelligent tutoring system. Learning and Instruction, 21, 267–280.
Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? Cognitive Science and Mathematics Education (pp. 189–215). Hillsdale: Erlbaum.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 334–370). New York: MacMillan.
Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475–522.
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.
Schwartz, D. L., Martin, T., & Pfaffman, J. (2005). How mathematics propels the development of physical knowledge. Journal of Cognition and Development, 6(1), 65–88.
Schwartz, D. L., Sears, D., & Chang, J. (2007). Reconsidering prior knowledge. In M. C. Lovett & P. Shah (Eds.), Thinking With Data (pp. 319–344). New York: Routledge.
Siegler, R. S. (2002). Microgenetic studies of self-explanation. In N. Granott & J. Parziale (Eds.), Microdevelopment—Transition Processes In Development And Learning (pp. 30–58). Cambridge: Cambridge University Press.
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.
Taylor, J. L., Smith, K. M., van Stolk, A. P., & Spiegelman, G. B. (2010). Using invention to change how students tackle problems. CBE Life Sciences Education, 9(4), 504–512.
Terwel, J., van Oers, B., van Dijk, I., & van den Eeden, P. (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational Research and Evaluation, 15(1), 25–44.
Tobias, S., & Duffy, T. M. (2009). Constructivist Instruction: Success or Failure? New York: Taylor and Francis.
Westermann, K., & Rummel, N. (2012). Delaying instruction—evidence from a study in a university relearning setting. Instructional Science. doi:10.1007/s11251-012-9207-8.
White, B. Y., & Frederiksen, J. R. (1998). Inquiry, modeling, and metacognition: Making science accessible to all students. Cognition and Instruction, 16(1), 3–118.
Wiedmann, M., Leach, R. C., Rummel, N., & Wiley, J. (2012). Does group composition affect learning by invention? Instructional Science. doi:10.1007/s11251-012-9204-y.
Acknowledgments
This work was supported by the Pittsburgh Science of Learning Center, which is supported by the National Science Foundation (#SBE-0836012), and by the University of British Columbia through the Carl Wieman Science Education Initiative.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Roll, I., Holmes, N.G., Day, J. et al. Evaluating metacognitive scaffolding in Guided Invention Activities. Instr Sci 40, 691–710 (2012). https://doi.org/10.1007/s11251-012-9208-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11251-012-9208-7