# Productive failure in learning the concept of variance

@article{Kapur2010ProductiveFI, title={Productive failure in learning the concept of variance}, author={Manu Kapur}, journal={Instructional Science}, year={2010}, volume={40}, pages={651-672} }

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical formulation of variance taught to them, PF students generated a diversity of formulations for variance but were unsuccessful in developing the…

## 163 Citations

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A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students generated solutions to a complex problem…

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### Classroom-based Experiments in Productive Failure

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- 2011

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### Preparatory effects of problem solving versus studying examples prior to instruction

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The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to instruction – at which point they typically fail. Yet, research on PF shows that students who are involved…

### Preparatory effects of problem solving versus studying examples prior to instruction

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

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- 2011

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…

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Posttest results indicate that including erroneous solution attempts in the instruction phase can be beneficial for learning units in which most students fail to come up with a correct solution themselves, but only if students are prompted to compare the erroneous solution Attempts with correct solutions.

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This paper reports on a quasi-experimental study comparing a “productive failure” instructional design (Kapur in Cognition and Instruction 26(3):379–424, 2008) with a traditional “lecture and…

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