Using the Number Line to Promote Understanding of Fractions for Struggling Fifth Graders: A Formative Pilot Study

Abstract

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth‐grade struggling students’ knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative pilot study and present preliminary data that demonstrate the potential of the intervention. Intervention lessons—adapted from a commercially available program—emphasize consistent use of the number line in conjunction with concrete representations to scaffold learning and facilitate understanding of grade‐level and foundational fractions content. We explain how intervention revisions were guided by the formative evaluation. In the second section, we present key concepts that distinguish understanding fractions principles from understanding whole number principles. These concepts relate to understanding foundations of fractions (e.g., magnitude, equivalence, part‐whole, and measurement) and the four operations. We present these key concepts and show how the fractions intervention addressed them as a guide to practitioners for teaching new and difficult fractions content, as students integrate fractions understanding with their understanding of whole numbers.

Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures

“…Also, material that did not focus on fractions (e.g., geometry) was eliminated from the lessons. These adapted lessons were piloted and revised prior to implementation in this study (Schumacher et al 2018). Details on how lessons were adapted are described in the pilot study.…”

Fraction ball: Playful and physically active fraction and decimal learning.

“…For example, Fazio and colleagues (2016) observed transfer from computerized fraction number line training to other measures of children's fraction magnitude knowledge. Intensive intervention focused on fraction magnitude knowledge can influence both fraction magnitude and fraction arithmetic knowledge (Barbieri et al, 2020;Fuchs et al, 2013;Malone et al, 2019;Schumacher et al, 2018). These interventions have been beneficial…”

Fifth graders’ understanding of fractions on the number line

“…Although the number line is more abstract than other continuous models, it is considered one of the most important representations for fractions (Cramer & Wyberg, ). Representing fractions on a number line is essential for students to understand fractions as a number while minimizing the misconception of fractions representing two numbers (Schumacher et al, ). Cramer, Ahrendt, Monson, Wyberg, and Colum () as well as Schumacher et al () found the number line to be a great tool to help children interpret a measurable distance from zero to a fraction.…”

“…Representing fractions on a number line is essential for students to understand fractions as a number while minimizing the misconception of fractions representing two numbers (Schumacher et al, ). Cramer, Ahrendt, Monson, Wyberg, and Colum () as well as Schumacher et al () found the number line to be a great tool to help children interpret a measurable distance from zero to a fraction. Keijzer and Terwel () found that when that the number line model was central to support the development of fractional strategies, students outperformed a control group who mainly worked individually with the circle as the major fraction model.…”

“…Over the past 35 years, numerous researchers have explored students’ understanding of fractions on the number line (Baturo & Cooper, ; Bright et al, ; Hannula, ; Larson, ; Merenluoto, ; Mitchell & Horne, ; Ni & Zhou, ; Pearn & Stephens, ; Pititto, ; Schumacher et al, ; Wong & Evans, ; Yanik et al, ). However, no research was found that focused solely on fifth graders’ understanding of fractions on a number line.…”