Improving Children’s Understanding of Mathematical Equivalence: An Efficacy Study

Abstract A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children’s Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) nontraditional arithmetic practice, (3) concreteness fading exercises, and (4) comparison and explanation. In a large-scale randomized control trial in California public schools, 132 second grade teachers were randomly assigned to either use the ICUE intervention or an active control consisting of nontraditional arithmetic practice alone. Using data from 121 teachers in the analytic sample, the study found that students in the intervention group outperformed students in the active control on proximal and transfer measures of equivalence with no observable tradeoffs in computational fluency. The findings suggest that the ICUE intervention helps students construct a robust understanding of mathematical equivalence, a critical precursor to success in algebra.