Arithmetic Practice Can Be Modified to Promote Understanding of Mathematical Equivalence created by Nicole M. McNeil, Emily R. Fyfe, April E. Dunwiddie

This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer" format (e.g., 4 + 3 = __) and were organized pseudorandomly throughout the workbook. In the modified workbook, problems were presented with operations on the right side (e.g., __ = 4 + 3), the equal sign was sometimes replaced by relational words (e.g., "is equal to"), and problems were organized by equivalent sums such that several problems in a row would all have the same sum. Children who used the modified workbook constructed a better understanding of math equivalence than did children who used the control workbook. This advantage persisted approximately 5-6 months after the practice had ended, and there were no observed "trade-offs" with computational fluency. A mediation analysis showed that the modified practice improved understanding as intended by decreasing children's reliance on operational patterns. Results suggest that small differences in the organization and format of arithmetic practice can yield substantial differences in children's understanding of fundamental mathematics concepts.