Instructional Science

, Volume 39, Issue 4, pp 561–579 | Cite as

A further study of productive failure in mathematical problem solving: unpacking the design components

  • Manu KapurEmail author


This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi: 10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b) productive failure (PF), where they solved complex problems in small groups without any instructional facilitation up until a teacher-led consolidation, or (c) facilitated complex problem solving (FCPS), which was the same as the PF condition except that students received instructional facilitation throughout their lessons. Despite seemingly failing in their collective and individual problem-solving efforts, PF students significantly outperformed their counterparts in the other two conditions on both the well-structured and higher-order application problems on the post-test, and demonstrated greater representation flexibility in working with graphical representations. The differences between the FCPS and LP conditions did not reach significance. Findings and implications of productive failure for theory, design of learning, and future research are discussed.


Failure Complex problems Mathematical problem solving Persistence Multiple representations 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Curriculum Teaching and Learning, Learning Sciences Laboratory, National Institute of EducationNanyang Technological UniversitySingaporeSingapore

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