Cognitive change in insight problem solving: Initial model errors and counterexamples

Abstract

We report the results of four experiments that examined the cognitive changes that occur in problem solvers' mental models of insight problems. The experiments showed that participants produced more correct solutions to insight problems that required single steps than multiple steps. Experiment 1 showed that their diagrams and explanations corresponded to initial model errors. Experiment 2 found more correct solutions for problems reworded to enable the retrieval of counterexamples to common assumptions. Experiment 3 found more correct solutions when physical props enabled the construction of a counterexample to the initial erroneous model and also to subsequent erroneous models. Experiment 4 showed more correct solutions when physical props limited the subsequent possibilities. The implications of the results for alternative theories of insight problem solving are discussed.

Keywords:

• Cognitive change
• Insight
• Mental models
• Problem solving

Acknowledgments

The research was funded by the Irish Research Council for the Humanities and Social Sciences through a Government of Ireland PhD Scholarship and by Enterprise Ireland through a PhD award, both to MAM. We thank Marco Ragni for helpful comments on an earlier draft of the paper.

Notes

¹Each problem was presented for a period of time (range 30–70 s) determined in a pilot study where eight volunteers read each problem aloud slowly and carefully and their average reading time was doubled. Previous studies have shown that 97% of correct solutions occur within 2 minutes, including time to read the problem (Lockhart, Lamon, & Gick, 1988).

²All statistical tests in the experiments are one-tailed unless otherwise indicated.

³We analysed only the 160 problems that participants indicated had not been seen before (of a potential set of 208 problems: 26 participants×8 problems). An independent rater scored over one-third of the responses, and interrater reliability was 99%.

⁴We analysed the 139 problems that participants indicated had not been seen before (of a potential set of 152 problems: 38 participants×4 problems). An independent rater classified the hints for over one-third of the responses and agreement was more than 90%.

⁵One hundred and forty-two unseen problems (of a potential set of 160 problems) were analysed.