Productive Failure as strategy against the double curse of incompetence

Abstract

Learners who lack knowledge often also lack the ability to assess their limited competence correctly. Due to the incorrect self-assessment, they are unlikely to apply strategies that would help them to acquire relevant knowledge. This effect is known as the double curse of incompetence. When students solve problems prior to being taught the canonical solution in a so-called Productive Failure setting (PF), they usually come up with solution ideas that are erroneous or incomplete. Due to this struggle with the problem at hand, they may become aware of the limitations of their knowledge. Demonstrating how typical student solutions fail to solve the problem during subsequent instruction may further help students to assess their competence correctly. Improved awareness of limited competence, in turn, may foster fruitful learning strategies when learning the canonical solution. Indeed, our empirical study showed that students in PF conditions have a more realistic perception of their own knowledge than students in so-called direct instruction conditions (DI), and that they also ultimately learn more. The same pattern was true for students who were confronted with limitations of typical student solutions during instruction.

Keywords:

• knowledge gap
• perceived competence
• Productive Failure
• self-assessment
• student solution

Acknowledgements

We would like to thank Manu Kapur for providing us with his study materials and with a great deal of background information concerning his own studies. We thank Lars Holzäpfel for his feedback from a mathematics education perspective on our study materials and tests. We are thankful to the participating schools for the organizational efforts. We thank our student research assistants, Katja Goepel, Christian Hartmann, and Andreas Vogel for their help in collecting and coding the data.

Additional information

Funding

This research was funded by the Center of Educational Studies of the Ruhr-Universität Bochum, Germany.