Fractions are typically taught as slices of pizza or pieces of pie. These real-world objects offer a simple, visual, and concrete way for students to begin thinking about fraction concepts, like parts of a whole. However, they can also make it harder for students to relate fractions and their properties to the whole numbers they already know.
Overcoming whole number bias in fraction instruction
The fact is that fractions are more than just parts of a whole. Fractions are numbers themselves. They have predictable names and locations on the number line, and they can be compared to each other, just like any other number. However, multiple bodies of research show that many students tend to think of fractions as two separate whole numbers rather than as a single number, known as whole number bias. This leads to fundamental errors in comparing fractions, understanding equivalent fractions, and fraction arithmetic.
Research shows the strongest instruction incorporates visual representations like length models and number lines to foster an understanding of fraction magnitude (size). It is only when students have a firm grasp on fraction magnitude that they can perform advanced work with fractions, like adding and subtracting fractions, placing fractions on a number line, or comparing fractions.
So how do we rethink and revamp fraction instruction to reshape students’ understanding of fractions? Read on for the research behind fraction instruction and tips to teach fractions effectively.
Understanding the challenges of teaching fractions
On a major national assessment, 50% of eighth graders in the United States were unable to order fractions from least to greatest, showing evidence of whole number bias.
Without a firm understanding that fractions are numbers (each with a location on the number line), students will only succeed with advanced fractions problem-solving by memorizing sets of disconnected procedures.
Teachers often face common student misconceptions when teaching fractions. One frequent challenge is students’ misunderstanding that fractions with larger denominators are automatically greater in size. For example, when comparing 1/8 and 1/3, a student might incorrectly assume 1/8 is greater since 8 is more than 3. Without strong fraction number sense, students will not be able to compare fractions or perform fraction arithmetic with accuracy or confidence.
Research-based insights on fraction instruction
Research shows that the strongest fractions instruction incorporates visual representations like length models and number lines to foster an understanding of fraction magnitude. Students who develop a rich understanding of fraction magnitude unlock the ability to perform advanced work with fractions, such as arithmetic, comparison, and estimation.
Number lines are increasingly recognized as the single most powerful and important representation to teach fractions in the elementary years. When students can place and order fractions on a number line, they demonstrate a deeper understanding of that fraction’s size and value in relation to other numbers. To find the denominators, students can count the number of intervals between 0 and 1. They can count the number of intervals between 0 and a particular point and associate that number with the numerator.
3 effective ways to revamp your fractions instruction
Flip the script on traditional fraction instruction with the following teaching tips. And see how ExploreLearning Frax uses the latest research to provide you with simple ways to implement these strategies into your next fractions unit.
Focus on fractions as numbers first
Each fraction has a specific magnitude (size) and position on the number line alongside whole numbers and other fractions. With Frax, students work with length models and number lines to interpret, represent, compare, order, and estimate fractions. In doing so, they overcome whole number bias and develop a strong understanding of fraction magnitude.
Introduce part-whole model second
Once students have built a deeper understanding of fractions as numbers and how they relate to other numbers, you can introduce part-whole and shaded area models. Frax provides targeted learning opportunities through carefully scaffolded missions that strengthen students’ understanding of fractions. Frax’s story-based games and practice activities help learners understand fractions as numbers before diving into part-whole and shaded area activities.
Build on students’ knowledge of fractions
As students learn more about fractions, it’s important to scaffold instruction. Frax uses brief, just-in-time remediation and adaptive questioning to help students learn by doing and master their understanding of fractions as numbers. Frax also provides real-time reporting to monitor student progress. Teachers are also notified when students are struggling so they can easily intervene at a given moment to provide clarification.
Implementing Frax for effective fractions instruction
What if just 13 hours of engaging fractions practice (spread over a month or more) in a game-based environment could save you and your students days and weeks of frustration? Revamp your fractions instruction to support student learning with tips like these and the incorporation of Frax.
Use Frax before your fractions unit to help students develop a baseline understanding of fractions concepts and a mutual belief that fractions make as much sense as other familiar numbers. When students develop shared fractions knowledge before your core instruction, you’re empowered to take your teaching to levels only you can.