Mathematics

Making Sense of Fractions: This Tactic Helped Students Grasp a Key Math Topic

By Sarah Schwartz — September 26, 2023 3 min read
teenager child student thinks over solves example problem with fractions on blackboard in school classroom in math algebra lesson
  • Save to favorites
  • Print

Fractions are an important building block in students’ mathematical foundations. Understanding how they work and why is crucial for success in Algebra and more advanced math courses. But fractions are also notoriously difficult to master.

Studies have shown that a significant portion of students—about one third—don’t make much progress in their understanding of the topic between 4th grade, when operations with fractions are typically introduced, and 6th grade, when students are expected to be fluent in fractional arithmetic.

Fractions are so challenging in part because they don’t operate in the same way that whole numbers do, said Nancy C. Jordan, a professor of learning sciences at the University of Delaware. Numbers of the same magnitude can look very different: Take 2/4 and 8/16, for example. And sometimes, when the numbers in a fraction grow bigger, the magnitude actually gets smaller—1/4 is bigger than 1/8, for instance.

On Tuesday, Jordan presented her work on a fraction sense intervention for struggling 6th graders at an Institute of Education Sciences Math Summit, an online conference hosted by the U.S. Department of Education’s research wing.

Jordan’s work, which is funded by an IES grant, will scale up a program that she and her colleagues found improved students’ understanding of fraction concepts and measurement, as well as their ability to apply that understanding to solve problems.

The intervention “aims to make explicit mathematical connections,” said Jordan, demonstrating how fraction magnitudes are represented across different contexts.

Parts of a whole vs. values on a number line

Traditional fraction instruction emphasizes fractions as part of a whole, said Jordan. Think about an eight-slice pizza with two slices missing to represent 6/8, for example, or a group of four circles with three colored in to represent 3/4.

But teaching fractions this way, rather than representing them as numbers with their own magnitudes, can lead to misunderstandings, Jordan said. She shared examples of student work from pre-tests in her research. In one question, students were asked to shade in 3/4 of eight circles. To get the question correct, students would need to shade in 6 circles.

But when students got the question wrong, many shaded in three circles, because they thought of 3/4 as three parts—rather than a value between the numerals 0 and 1.

In Jordan’s intervention, teachers use a number line to represent fractions. This allows teachers to show fraction equivalence on the number line—to demonstrate, for example, that 3/4 is the same distance between 0 to 1 as 6/8. Teachers also link the number line to other fraction representations: fraction bars, a collection of items, or liquid in a measurement cup.

Teachers then help students connect these representations to numbers and equations, and students get regular practice distinguishing between and performing different operations.

Teaching fractions with a number line isn’t a new practice. It was emphasized in the Common Core State Standards introduced in 2010, which at the time represented a major shift in how fractions were taught in schools. The underlying idea behind this change is that number lines help students put fractions into context—demonstrating their relationship to integers.

But Jordan said that presenting fractions as part of a whole is still a common teaching method—as are procedural shortcuts that can leave students with little conceptual understanding of why operations work the way they do. She gave the example of the “butterfly” method of adding and subtracting fractions, which relies a multiplication trick to find a common denominator.

Jordan said her intervention demonstrates that even if students have misconceptions, it’s possible to help them develop deeper understanding in older elementary grades: “Even students who are struggling mightily with basic fractions after three years of instruction can learn to make sense of fractions.”

Related Tags:

Events

This content is provided by our sponsor. It is not written by and does not necessarily reflect the views of Education Week's editorial staff.
Sponsor
School & District Management Webinar
Leadership in Education: Building Collaborative Teams and Driving Innovation
Learn strategies to build strong teams, foster innovation, & drive student success.
Content provided by Follett Learning
School & District Management K-12 Essentials Forum Principals, Lead Stronger in the New School Year
Join this free virtual event for a deep dive on the skills and motivation you need to put your best foot forward in the new year.
This content is provided by our sponsor. It is not written by and does not necessarily reflect the views of Education Week's editorial staff.
Sponsor
Privacy & Security Webinar
Navigating Modern Data Protection & Privacy in Education
Explore the modern landscape of data loss prevention in education and learn actionable strategies to protect sensitive data.
Content provided by  Symantec & Carahsoft

EdWeek Top School Jobs

Teacher Jobs
Search over ten thousand teaching jobs nationwide — elementary, middle, high school and more.
View Jobs
Principal Jobs
Find hundreds of jobs for principals, assistant principals, and other school leadership roles.
View Jobs
Administrator Jobs
Over a thousand district-level jobs: superintendents, directors, more.
View Jobs
Support Staff Jobs
Search thousands of jobs, from paraprofessionals to counselors and more.
View Jobs

Read Next

Mathematics From Our Research Center Top 10 Challenges to Teaching Math and Science Using Real Problems
Teachers cite lack of time and insufficient professional development as barriers to teaching STEM using a problem-solving approach.
3 min read
African-american schoolgirl pupil student using working with microscope at biology chemistry lesson class at school lab. STEM concept.
iStock/Getty
Mathematics From Our Research Center Teachers Are Evenly Divided on the Best Way to Teach Math
Educators are divided as to whether students learn math best through procedures or from solving real-world problems.
2 min read
 Conceptual photo of of a young boy studying mathematics using fingers in primary school.
Kilukilu/iStock/Getty
Mathematics Young Students Gravitate to Math. How Teachers Can Build on That Curiosity
A focus on rich, real-world problems makes math more interesting, relevant, and enticing to students.
8 min read
Photo illustration of young boy working on math problem.
F. Sheehan for Education Week + iStock / Getty Images Plus
Mathematics What the Research Says 4 Questions to Boost Algebra Gains for Middle Schoolers
More than 1 in 3 public school students now takes Algebra 1 in middle school. Here's how to make sure they succeed in this gatekeeper class.
5 min read
Photo of a Black male teacher giving a math less to Junior-high Black students.
Martine Severin/E+