Leveraging Number Lines and Unit Fractions to Build Student Understanding: Insights from a Mixed Methods Study

Abstract

Fractions remain a challenging area of school mathematics at every stage of education, with impacts that extend far beyond the school years. For this study, researchers engaged in classroom-based design research over a 6-year period to investigate effective strategies for teaching fractions with Canadian students. Participants included 86 teachers (representing 12 collaborative research teams spread across 8 school boards) and over 2000 students from Grades 3–10. Quantitative analyses revealed significant pre-post gains in students’ fraction knowledge. Qualitative findings revealed some best practices in fractions instruction, including the importance of focusing on unit fractions and number lines to facilitate student sense-making. These findings lead to a detailed discussion of the benefits of (1) focusing on unit fractions as a central construct that allows students to meaningfully work with fractions and make connections across ideas of increasing complexity; (2) leveraging powerful representations as objects-to-think-with that combine concrete and abstract thinking about fractions; and (3) using a design research methodology in the context of collaborative work with teachers.