A further study of productive failure in mathematical problem solving: unpacking the design components |
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| Authors: | Manu Kapur |
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| Institution: | (1) Curriculum Teaching and Learning, Learning Sciences Laboratory, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore, 637616, Singapore |
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| Abstract: | This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:, 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. |
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