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Why Won't You Change Your Mind? Knowledge of Operational Patterns Hinders Learning and Performance on Equations


  • This research was supported by a Marian Schwartz Fellowship in Experimental Psychology and an APA Dissertation Award to N. M. McNeil and by National Science Foundation Grant BCS-0096129 to M. W. Alibali. The research would not have been possible without the support of the administrators, parents, and students in the Madison Metropolitan School District, Edgewood School, and Our Redeemer Schools in Madison, Wisconsin, and Sacred Hearts School in Sun Prairie, Wisconsin. We thank Jenny Saffran, Colleen Moore, Julia Evans, and the members of the Cognitive Development Research Group at the University of Wisconsin for helpful discussions about the study. We also thank Jerry Haeffel for comments on previous versions of the paper.

concerning this article should be addressed to Nicole McNeil, who is now at Yale University PACE Center, P.O. Box 208358, New Haven, CT 06520-8358. Electronic mail may be sent to


This study examined whether knowledge of arithmetic contributes to difficulties with equations. In Experiment 1, children (ages 7–11) completed tasks to assess their adherence to 3 operational patterns prevalent in arithmetic: (a) the strategy of performing all given operations on all given numbers, (b) the “operations=answer” problem structure, and (c) the concept that the equal sign means “the total.” Next, children received a lesson on equations; then, they solved a set of equations. There was a negative relationship between adherence to the operational patterns and learning. In Experiment 2, undergraduates' knowledge of the operational patterns was activated or not. Students whose knowledge was activated did not perform as well on equations. Results suggest that early-learned patterns constrain future learning and performance.