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Productive failure in learning the concept of variance
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Paper presented at the American Educational Research Association (AERA) Annual Meeting, Denver, Colorado, 30 April to 4 May 2010
We report on a quasi-experimental study comparing a “productive failure (PF)” design with a “direct instruction (DI)” design for a curricular unit on variance. N = 140, 9th-grade mathematics students from an all-boys secondary school in Singapore experienced either DI or a PF design, where they solved a complex problem in small groups without the provision of any support up until a teacher-led consolidation. PF students produced a diversity of progressively sophisticated problem representations and methods for solving the problem but
were ultimately unsuccessful in developing the canonical solution. Despite seemingly failing in their problem-solving efforts, PF students performed on par with DI students on well-structured problems on variance, and significantly outperformed them on complex, data analysis problems.
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