Unpacking the Connections Between Fractions and Algebra: The Importance of Fraction Schemes and Units Coordination

Abstract

ABSTRACT Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children’s units coordination structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to magnitude knowledge as a central conceptual structure supporting fractions and algebra knowledge. In an online study with 59 eighth graders, we compared the associations of these two foundational factors with fractions and algebra knowledge by assessing students’ units coordination skills, magnitude knowledge, and several general cognitive skills alongside multiple aspects of fractions and algebra knowledge. In regression models controlling for math anxiety and general cognitive skills, units coordination and fraction schemes were better predictors of students’ algebra knowledge than were fraction magnitude or fraction arithmetic skills. We replicated findings from previous studies that showed units coordination and fraction schemes were closely related and showed for the first time that units coordination was significantly associated with fraction number line estimation and fraction arithmetic scores, even after accounting for general cognitive skills. We emphasize the need for interdisciplinary teams to continue investigating relations among these constructs to further our understanding and ultimately support student learning of fractions and algebra.