ABSTRACT
This study investigated whether children’s schema for typical addition interferes with their ability to learn about mathematical equivalence. In a pretest, elementary school children (1) solved a set of math equivalence problems (e.g., 3 + 4 + 5 = 3 + _), (2) reconstructed equivalence problems after viewing them briefly, and (3) provided definitions of the equal sign. Children were categorized according to the number of measures (out of 3) on which they exhibited the typical addition schema. Children then received one of four interventions that presented new information about equivalence problems. Finally, children completed a posttest similar to the pretest. From pretest to posttest, children who exhibited the addition schema on all three measures were the least likely to change their strategy for solving the problems, followed by children who exhibited the schema on two or one of the measures. All of the children who did not exhibit the schema on any of the three measures changed. It is important to note that all children used incorrect strategies at pretest, so it was the addition schema in particular that was associated with change resistance. Thus, a strong schema can interfere with learning. Furthermore, children’s addition schema may put them at risk for difficulties in learning higher-level mathematics.
