Abstract

Many children have a limited view of the equal sign and do not understand that the left and right sides of an equation need to represent the same amount, even after instruction. In the present study, I investigated domain-general and domain-specific factors that account for differences in children’s performance on noncanonical equivalence problems. Fifty-six third- and fourth-grade students were asked to solve a series of noncanonical equivalence problems before and after receiving explicit instruction on the equal sign. As a group, students showed significantly higher scores after instruction, but close to a third of them were unsuccessful on more than half of the items on the posttest. Individual interviews were conducted to determine the source of the variability; and interview tasks assessed conceptual understanding of the equal sign in a nonsymbolic context and in a symbolic context (as measured by students’ ability to rate and generate equal sign definitions and to justify their answers to noncanonical equations). Regression analyses indicated that of all the variables, only general ability and mathematical fluency were significant predictors of performance on the posttest. Qualitative analyses of the interview data revealed that students generated three different types of definitions of the equal sign (i.e., operational, relational, combined), and that there was a significant effect of definition type on posttest performance. No significant difference was found in the performance of students who offered combined and relational definitions, but as a group, they outperformed students who held entirely operational definitions. The study’s limitations, implications of the research findings, and avenues for future research are discussed.