Understanding fractions is a cornerstone of mathematical learning, essential for personal and career
Understanding fractions has a significant impact on both individuals and society. Fractions are an integral part of everyday life, from performing various job tasks to making healthy-living choices and managing personal finances. Unfortunately, many adults struggle with basic fraction concepts and procedures. These challenges often begin in primary school and can persist through secondary school. However, there is a growing body of research that offers valuable insights into how to effectively teach and learn fractions. The purpose of this guide is to describe the importance of learning fractions and present four research-informed instructional strategies to enhance fraction teaching and learning.
Importance of learning fractions
What are fractions?
Mathematically speaking, fractions are rational numbers that represent a part of a whole that is partitioned into equal parts. The whole can be defined as a single object (e.g., a pizza), a set of objects (e.g., a box of biscuits), a specific length (e.g., a kilometre), a specific volume (e.g., a litre), or other representations. Fractions are symbolically expressed by a numerator to denote the number of equal parts being counted and a denominator to denote the total number of equal parts in the whole. For example, 2/5 represents the quantity of two equal parts of a whole that is partitioned into five equal parts.
Why are fractions important?
Understanding fractions lays the groundwork for success in advanced mathematics and science. Fraction knowledge uniquely predicts students’ performance in algebra, even more than their knowledge of whole numbers (Bailey et al., 2012; Booth & Newton, 2012; Cirino et al., 2022; Viegut, Stephens, & Matthews, 2024). Booth and Newton (2012) found that students’ ability to place unit fractions on a number line is a key algebra readiness skill, as it is linked to understanding features of algebraic equations (like the equal sign, negative sign, variables), solving equations, and working with word problems. Similarly, the ability to place non-unit fractions on a number line connects to solving algebraic equations, likely because it builds on students’ proportional reasoning skills. Since fraction knowledge is a unique predictor of success in Algebra 1, which is considered a gateway to advanced mathematics in secondary school (e.g., advanced secondary algebra), building strong fraction skills is crucial (Siegler et al., 2012). Tyson and Roksa (2017) found that success in Algebra 1, particularly in rigorous courses, increases students’ likelihood of succeeding in higher-level maths (e.g., Algebra 2). This, in turn, has a positive impact on higher education and career outcomes (Gaertner, Kim, DesJardins, & McClarty, 2014). Overall, these findings highlight the pivotal role of fractions in advancing students’ maths proficiency and underscore the importance of developing a strong understanding of fractions in upper primary and early secondary school.
What are important fraction concepts?
When students begin to study fractions, it is often their first exposure to number systems beyond whole numbers (see Figure 1). As such, students begin to learn that some properties and concepts that they learned in relation to whole numbers do not apply to all real numbers — which include rational and irrational numbers (see section 2.4 for examples). There are three important concepts students learn as they deepen their understanding of fractions: magnitude, equivalence, and density. Applying these concepts to fractions is often students’ first exposure to how concepts and operations differ across number systems. Understanding fraction magnitude means that students understand that fractions represent a unique quantity, and that quantity can be ordered, compared, and represented on a number line. When applied to fractions, equivalence means knowing that a fraction can be symbolically represented in a variety of equivalent ways but still represents the same quantity. Fraction density refers to the fact that a quantity can be partitioned into infinitely smaller parts.
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To support teachers in implementing key fraction concepts and skills in the classroom, this guide begins with Practice 1, which outlines the learning progression that supports students’ development of fraction proficiency. Practice 2 focuses on designing fraction instruction that is coherent across grades and aligned with other mathematics concepts, like whole numbers. Practice 3 explores the relationship between conceptual understanding and procedural fluency, emphasising the importance of making explicit connections for students. Lastly, Practice 4 addresses common errors and misconceptions that can arise if students’ understanding of fractions is not systematically developed over time.
Each practice includes a description of the approach, the research that supports it, and practical guidance for implementation in the classroom. Throughout the guide, several themes emerge. First, we emphasise the power of using the number line to teach fractions. Second, we reinforce the recommendation by Powell, King, and Benz (2023) to implement systematic and explicit instruction while judiciously incorporating multiple representations — concrete, semi-concrete, and abstract — during instruction. Finally, we stress the importance of carefully planning instruction within and across grades. Effective planning includes:
Leanne Ketterlin Geller, Ph.D., is a professor in the department of Education Policy and Leadership at Southern Methodist University (SMU), Dallas, Texas. She holds the Texas Instruments Endowed Chair in Education and directs the Research in Mathematics Education unit
Allison McClure is a PhD student at SMU and a member of the Research in Mathematics Education unit. She received a prestigious pre-doctoral scholarship funded by the US Department of Education Office of Special Education Programs focused on developing leaders investigating mathematics evidence.
Cassandra Hatfield brings more than two decades of experience as a mathematics educator and researcher. As a research project manager at SMU, she works alongside lead researchers to design learning progressions, instructional plans, and formative assessments to support primary and secondary school students