Abstract

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 canonical formulation. On the posttest however, PF students significantly outperformed DI students on conceptual understanding and transfer without compromising procedural fluency. These results challenge the claim that there is little efficacy in having learners solve problems targeting concepts that are novel to them, and that DI needs to happen before learners should solve problems on their own.

Citation

Kapur, M. (2012). Productive Failure in Learning the Concept of Variance. Instructional Science: An International Journal of the Learning Sciences, 40(4), 651-672. Retrieved February 27, 2021 from https://www.learntechlib.org/p/167483/.

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Keywords

• Direct Instruction
• Grade 9
• High Schools
• Junior High Schools
• mathematical models
• mathematics
• mathematics education
• Mathematics Instruction
• Middle Schools
• multivariate analysis
• Pretests Posttests
• secondary education
• Secondary School Mathematics