Designing for Productive Failure

Abstract

In this article, we describe the design principles undergirding productive failure (PF; M. Kapur, 2008 Kapur, M. 2008. Productive failure. Cognition and Instruction, 26: 379–424. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). We then report findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability. In the 1st study, 7th-grade mathematics students from intact classes experienced 1 of 2 conditions: (a) PF, in which students collaboratively solved complex problems on average speed without any instructional support or scaffolds up until a teacher-led consolidation; or (b) direct instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings suggested that although PF students generated a diversity of linked representations and methods for solving the complex problems, they were ultimately unsuccessful in their problem-solving efforts. Yet despite seemingly failing in their problem-solving efforts, PF students significantly outperformed DI students on the well-structured and complex problems on the posttest. They also demonstrated greater representation flexibility in solving average speed problems involving graphical representations, a representation that was not targeted during instruction. The 2nd and 3rd studies, conducted in schools with students of significantly lower mathematical ability, largely replicated the findings of the 1st study. Findings and implications of PF for theory, design of learning, and future research are discussed.