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.

Profiles of young students’ understanding of fractions on number lines

“…Thus, students need to become aware of the explicit representational nuances and implicit meanings of number lines. The use of number lines has been regarded as one of the best practices for fraction instructions to facilitate students' sense-making (Siegler et al, 2012), as the number lines can function as a thinking tool about fraction ideas as well as an action tool for embodying those ideas (Bruce et al, 2023). Likewise, it is crucial for teachers to help students grasp the key ideas of fractions before rushing to introduce number lines (Charalambous & Pitta-Pantazi, 2007).…”

“…Using visual representations during instructions and problem-solving activities is an effective way to support students in making sense of fraction concepts (Sidney et al, 2019). Especially, the number line serves as a conceptual tool for developing awareness of units, understanding fraction magnitudes, recognizing various fraction types, and establishing fraction equivalence (Bruce et al, 2023;Cramer et al, 2017;Sidney et al, 2019;Siegler et al, 2011). Engaging in number line activities such as labeling various fractions or units enables students to apply their prior understanding of fundamental fraction ideas and fosters the development of more advanced fraction schemes (Charalambous & Pitta-Pantazi, 2007;Cramer et al, 2019;Hackenberg et al, 2016).…”