Strengthening grade 3-5 students’ foundational knowledge of rational numbers

Document Type


Journal/Book Title/Conference

Teachers College Record






Columbia University, Teachers College

Publication Date



Background: American students have done poorly in algebra and that has generated policy concerns about preparing students for STEM careers. There has been growing recognition that the algebra problem may begin in earlier grades when students do not adequately master rational numbers. Purpose: The study provided a series of workshops organized around problematic issues that students have in learning rational numbers. The research was designed to help all grade 3-5 teachers in a single school district help students gain in their knowledge of rational numbers. Population: The population was drawn from one large school district (13 schools) and included 140 teachers and 2,845 students matched pre to post. Research Design: The study used a quasi-experimental design. As all teachers in the district were involved, there was no control group. Findings: On the basis of pre-post testing, girl and boy students, as well as students from diverse SES schools demonstrated large gains in their knowledge of rational numbers. There were no significant differences in gains for girls and boys at any of the three grade levels, but SES remained a main effect for gains in achievement for grades 3 and 4 even after entering prior achievement as a covariate and the interaction between SES and gender was significant for grade 5. Recommendations: The findings provide clear evidence that students can make notable gains in learning rational numbers if they are given the opportunity to do so. The authors provide their intentions to further analyze the quantitative data (presented in this paper) with qualitative data that were collected in the study (e.g., providing open-ended response opportunities for students to respond to rational number questions like, "What is a fraction? What is a decimal? What is a percent?"