Why Are Fractions So Hard to Understand?

Fractions have consistently been identified as a source of frustration and confusion among students, teachers and parents alike. Recent data from the 2022 National Assessment of Educational Progress (NAEP) supports this statement reporting that in 2022, only 26% of 4th grade students nationally were able to determine the validity of statements (mark true or false) comparing fractions (NAEP 2022). This is a skill typically taught in 3rd grade and one of the easier fraction skills students will learn!

Fractions are formally introduced to students beginning in the third grade. Here they begin laying the foundation of developing an understanding of fractions to support them as they progress through learning to perform different operations with fractions in the 4th and 5th grades as well as the beginning of 6th grade. 

Mastering fractions in these earlier grade levels is critical for students' future success in middle school math and beyond. Throughout middle school and high school almost every new math skill they will be confronted with will contain a fractional element. Unfortunately, fractions present as a difficult hurdle for students to grasp leaving so many parents and teachers asking the question, Why are fractions so hard to understand?

1. Lack of Fraction Sense

One of the main reasons fractions are a problem area for many students is that they did not develop a core foundational knowledge of fractions when they were first introduced. They lack a sense of understanding what a fraction represents and tend to only associate fractions with counting shaded and unshaded parts of shapes. This can be caused by not spending enough time exploring all of the things fractions can represent and the different ways to model them.

2. Confusing Number Sense and Fraction Sense

When learning about whole numbers, students concretely learn to associate numbers with quantities. However, while fractions are numbers, and also represent a quantity, the quantity a fraction represents can only be determined by understanding the part to whole relationship of the numbers that make up a fraction. Additionally, when working with fractions, students continue to rely on their knowledge of rules that apply to whole numbers. These rules sometimes, but not always apply to fractions, which can be very confusing.

3. Not All Wholes are Created Equal 

In the beginning students mainly solve problems involving fractional quantities that do not provide context and they can always assume that the size of the corresponding wholes are the same. However, students will progress to solving problems that do include context in which each fraction's whole may be different. For example, if Holly and Natalie read 1/2 of the same book, then they both read an equal amount. On the other hand, if Holly read 1/2 of a book with 200 pages and Natalie read 1/2 of a book with 400 pages, then they definitely didn't read equal amounts. It is important for this concept to be established early to make sure to consider the size of the wholes when they are given in a problem. 

In the end, if students are only given the opportunity to think of fractions as counting how many pieces are shaded and unshaded, then that is the understanding of fractions they will have. They will struggle to solve problems with fractional quantities involving distance, time, measurement and more. In Fractions Unlocked, we help students solidify a knowledge of fractions by exploring the part-whole relationship fractions represent across many different contexts & models and practicing multiple ways of representing fractions to help them accurately work through and solve problems involving fractions.