Productive failure in mathematical problem solving
 Manu Kapur
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This paper reports on a quasiexperimental study comparing a “productive failure” instructional design (Kapur in Cognition and Instruction 26(3):379–424, 2008) with a traditional “lecture and practice” instructional design for a 2week curricular unit on rate and speed. Seventyfive, 7thgrade mathematics students from a mainstream secondary school in Singapore participated in the study. Students experienced either a traditional lecture and practice teaching cycle or a productive failure cycle, where they solved complex problems in small groups without the provision of any support or scaffolds up until a consolidation lecture by their teacher during the last lesson for the unit. Findings suggest that students from the productive failure condition produced a diversity of linked problem representations and methods for solving the problems but were ultimately unsuccessful in their efforts, be it in groups or individually. Expectedly, they reported low confidence in their solutions. Despite seemingly failing in their collective and individual problemsolving efforts, students from the productive failure condition significantly outperformed their counterparts from the lecture and practice condition on both wellstructured and higherorder application problems on the posttests. After the posttest, they also demonstrated significantly better performance in using structuredresponse scaffolds to solve problems on relative speed—a higherlevel concept not even covered during instruction. Findings and implications of productive failure for instructional design and future research are discussed.
 Title
 Productive failure in mathematical problem solving
 Journal

Instructional Science
Volume 38, Issue 6 , pp 523550
 Cover Date
 201011
 DOI
 10.1007/s112510099093x
 Print ISSN
 00204277
 Online ISSN
 15731952
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Illstructured problems
 Failure in problem solving
 Persistence
 Classroombased research
 Mathematical problem solving
 Authors

 Manu Kapur ^{(1)}
 Author Affiliations

 1. National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore, 637616, Singapore