Research News

Hubbard, Matthews exploring the neuroscience behind learning about fractions

January 06, 2017
by Adityarup "Rup" Chakravorty, Waisman Communications

Waisman Center researcher Edward Hubbard likes to tell a story about burgers.

In the early 1980s, A&W Restaurants introduced a new burger that had a third of a pound of beef. This burger was supposed to compete with MacDonald’s quarter-pound burger and because both burgers were priced the same, A&W executives expected their bigger burger to win over customers.

It failed spectacularly, and it was all to do with fractions.

When A&W held focus groups to try and understand why their burger failed, they found that “people thought a third of a pound was less than a quarter of a pound. After all, three is less than four!” writes Alfred Taubman, who owned A&W in the 1980s, in his book, “Threshold Resistance.”

As this culinary anecdote indicates, fractions can be a difficult concept to grasp. For children, not understanding fractions can have long-term consequences; several studies have shown that children who struggle to understand fractions in fifth grade, also struggle with algebra when they get to eighth grade.

Edward Hubbard
“Even when we account for other cognitive skills, how well children work with fractions is able to uniquely predict future educational outcomes,” says Hubbard, an assistant professor with the UW-Madison School of Education’s No. 1-ranked Department of Educational Psychology. “So we know that fractions are important, but we also know that fractions are difficult.”

What is it about fractions that makes them so challenging for people, and how can we most effectively teach children about fractions?

Hubbard is trying to answer these questions by finding out which areas of the brain are involved in learning fractions and how current classroom teaching techniques engage these brain regions.

“We are trying to build bridges between what neuroscience tells us about brain systems that deal with processing fractions and what teachers are seeing and doing in classrooms,” says Hubbard.

Through a research project newly funded by the Eunice Kennedy Shriver National Institute of Child Health and Development (NICHD), Hubbard and his colleague Percival Matthews –- also a faculty member with the Department of Educational Psychology –- are following children who are now in second grade for four years as they move to fifth grade, and also following current fifth graders as they progress to the eighth grade.

Hubbard hopes that tracking these children will yield insights into what's happening in their brains from before they encounter fractions (second grade) to their introduction to fractions (in third grade) and all the way to pre-algebra/algebra (in eight grade).

To track these children, Hubbard is using several different research tools, from standardized pencil-and-paper tests to psychological assays and brain imaging.

For example, the researchers may ask children to deal with fractions while they scan their brains to see which regions are most active.

Children may be asked to compare fractions and tell the researchers which of two fractions is larger. By choosing two fractions that are close together – e.g. 4/5 and 7/8 -– the researchers can make this difficult. And by choosing two fractions that are further apart –- e.g. 1/8 and 4/5 -– they can make it easy.

“This type of study with fractions has only been done in adults and never with children,” says Hubbard. “We think it will really help us understand how the ability to process fractions develops.”

Hubbard points out that as society — and the subjects being taught in schools and colleges — changes, teaching tactics that might have worked a hundred or even 50 years ago may not work as well today.

“Hundreds of years ago, some of the brightest people on the planet were just figuring out how to do calculus, and today we ask 18-year old college-bound seniors to routinely do the same thing,” says Hubbard. “We need to understand why some teaching techniques are not working as well if we are to efficiently find new and effective ways to teach.”

Percival Matthews
Combining brain scans with behavioral experiments might provide the best way to develop new ways to teach children fractions, and other subjects, but Hubbard knows it will take time and perseverance.

“It’s not that you do one study and you are immediately out there telling teachers what to do,” says Hubbard.

In fact, what Hubbard, Matthews and their colleagues also hope to do is explain to teachers, and to the public, how and why the strategies and systems that teachers have developed through trial and error over the years work at the biological level.

By getting a better handle on how the brain does math and why some kids might struggle to learn basic concepts like fractions, which then impacts their higher order skills, Hubbard ultimately is hoping to improve educational outcomes for everyone.

“With two young kids of my own, I have both an intellectual investment and also a personal stake in working on these issues,” he says.

To learn more about this research, including other projects focusing on number representation and synesthesia, visit Hubbard's website.

This report originally appeared on the Waisman Center website.

Edward Hubbard at the Waisman Center
Waisman Center researcher Edward Hubbard (right) and graduate student John Binzak. (Photo
by Clark Kellogg, Waisman Communications