Abstract
Situating our work within the constructivist debate about effective ways of designing for learning, we describe our program of research on productive failure (PF). The PF learning design affords students opportunities to engage in authentic mathematical practice where they start by generating and exploring solutions to a novel design problem followed by consolidation and knowledge assembly. In doing so, PF affords students opportunities to activate and differentiate their prior knowledge, so that they are better prepared to attend to and learn the critical conceptual features of the targeted concepts during the subsequent instruction. Our findings show that the PF learning design is more effective in developing conceptual understanding and transfer than a direct instruction design. Follow-up studies are described in brief wherein key aspects of the productive failure design were tested over multiple classroom-based studies in Singapore public schools and how these studies helped us interrogate and understand the criticality of key mechanisms embodied in the PF design.
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Acknowledgments
The work reported in this chapter was funded by grants from the Ministry of Education of Singapore. This chapter has been reproduced with some adaptation and update, and in accordance with the publishing agreement, from a chapter (Kapur and Toh 2013) that was contributed to a handbook of educational design cases.
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Appendix A: The Complex Problem Scenario
Appendix A: The Complex Problem Scenario
Mr. Ferguson, Mr. Merino, and Mr. Eriksson are the managers of the Supreme Football Club. They are on the lookout for a new striker, and after a long search, they short-listed three potential players: Mike Arwen, Dave Backhand, and Ivan Right. All strikers asked for the same salary, so the managers agreed that they should base their decisions on the players’ performance in the Premier League for the last 20 years. Table 12.1 shows the number of goals that each striker had scored between 1988 and 2007.
The managers agreed that the player they hire should be a consistent performer. They decided that they should approach this decision mathematically and would want a formula for calculating the consistency of performance for each player. This formula should apply to all players and help provide a fair comparison. The managers decided to get your help.
Please come up with a formula for consistency and show which player is the most consistent striker. Show all working and calculations on the paper provided.
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Kapur, M., Toh, L. (2015). Learning from Productive Failure. In: Cho, Y., Caleon, I., Kapur, M. (eds) Authentic Problem Solving and Learning in the 21st Century. Education Innovation Series. Springer, Singapore. https://doi.org/10.1007/978-981-287-521-1_12
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