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.

Keywords:

• Efficacy study
• elementary math
• mathematics
• randomized controlled trial

Open Research Statements

Study and Analysis Plan Registration

There is no study and analysis plan registration associated with this manuscript.

Data, Code, and Materials Transparency

The data that support the findings of this study are publicly available on openICPSR (https://doi.org/10.3886/E182542V1). The code and materials that support the findings of this study are not publicly available.

Design and Analysis Reporting Guidelines

This manuscript was not required to disclose use of reporting guidelines, as it was initially submitted prior to JREE mandating open research statements in April 2022.

Transparency Declaration

The lead author (the manuscript’s guarantor) affirms that the manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned (and, if relevant, registered) have been explained.

Replication Statement

This manuscript reports an original study.

Open Scholarship

This article has earned the Center for Open Science badges for Open Data through Open Practices Disclosure. The data are openly accessible at https://doi.org/10.3886/E182542V1.

Additional information

Funding

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150088 to WestEd. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.