# Research-Based Teaching Practices for Improving Students' Understanding of Mathematical Equivalence Have Not Made it into Elementary Classrooms

- Elena Silla, Department of Psychology, University of Wisconsin-Madison, Madison, Wisconsin, United States
- Caroline Hornburg, Department of Human Development and Family Science, Virginia Tech, Blacksburg, Virginia, United States
- Matthew Kloser, Center for STEM Education, University of Notre Dame, Notre Dame, Indiana, United States
- Nicole McNeil, Department of Psychology, University of Notre Dame, Notre Dame, Indiana, United States

**Abstract**Elementary math instruction traditionally has emphasized procedures rather than concepts. Thus, students tend to lack a strong understanding of foundational concepts like mathematical equivalence. Cognitive scientists and mathematics educators have found small yet effective ways to modify traditional arithmetic instruction to promote students’ conceptual understanding of math equivalence. Educational standards also now reflect this academic research. However, it is unclear whether classroom practices have caught up with research and policy. In the current study, we observed teachers’ practices during arithmetic instruction. The goal was to determine if teachers are using research-based practices that promote understanding of math equivalence and if variation in use of research-based practices is associated with students’ growth in understanding of math equivalence across the school year. Eight second and third grade classrooms (M students per classroom = 23) were observed twice during math instruction. Students completed a math test both before and after the observation period. Research-based practices were rarely observed in any classrooms, so there was not much variation in classroom use of research-based practices to predict student growth. Students improved their performance on all problem types tested, but performance on math equivalence problems was significantly lower than on other problem types. Results suggest that policies and practices designed to improve students’ understanding of math equivalence may not have filtered down to affect instructional practices in classrooms.