By Charlene N. Rivera-Bonet, Waisman Science Writer
At a Glance:
- Kids’ brains are wired to understand fractions earlier than we think
Even before formal schooling, children’s brains can grasp ratios as holistic magnitudes — suggesting they’re naturally wired to understand foundational fraction concepts like comparing amounts. - The brain recycles old skills for new math challenges
When children start learning numerical fractions, they reuse the same brain circuits they used to process visual ratios presented by a set of dot clusters or a set of line lengths. This phenomenon, called “neuronal recycling,” could help educators design more intuitive lessons. - Rethinking how we teach fractions could unlock higher math
Traditional fraction instruction focuses on steps, not meaning. By tapping into kids’ existing ability to see fractions as magnitudes rather than parts of whole numbers, educators could lower math anxiety and open doors to advanced math and STEM success.
Long before children start using slices of pizzas to learn about fractions, their brains are already wired to understand ratios. Yet, fractions tend to be hard and cause anxiety for math learners. A new study from the Waisman Center at the University of Wisconsin–Madison reveals that children as young as seven use specialized brain circuits to process ratios — like groups of dots or lines — well before they receive any formal instruction in fractions. Those same neural pathways are later “recycled” to handle numerical fractions in school, offering an opportunity to inform the way fractions are taught by leveraging the pre-existing brain mechanisms to enhance student’s understanding of fractions.
“We’re interested broadly in why fractions are so hard for so many people, and better understanding what we can do to help people learn and understand fractions,” says Edward Hubbard, associate professor of educational psychology and director of the Educational Neuroscience Lab at the University of Wisconsin–Madison, which published the study. The research stems from the idea that perhaps children come equipped with a perceptual ability to understand and compare ratios such as the relative length of one line versus another. “And if they come equipped with that sort of perceptual foundation, then maybe we can reorient fractions instruction so that we can capitalize on that perceptual ability, instead of the traditional way that we teach fractions, which mostly involves lots and lots of pizzas,” Hubbard adds.
For the study, they recruited a group of second graders before they formally learned about fractions. They used behavioral tests and performed magnetic resonance imaging (MRI) to look at the second grader’s brains while they processed different types of fractions: symbolic, which involves numbers like two-thirds or one-quarter, and non-symbolic, which involves ratios presented by different lengths of lines or numbers of dots.
They then did similar testing in children that were in fifth grade, who have already received formal instruction in symbolic fractions.
Results showed that when processing non-symbolic fractions before any formal instruction, second graders recruit the right-parietal frontal network, a part of the brain involved in helping understand numbers and quantities. This suggests that the brain is sensitive to fractions even before learning about them.
Fifth graders, after receiving formal instruction on fractions, used the same brain network and showed the same patterns of brain activity when processing both non-symbolic and symbolic fractions. Critically, they also used this network, and even showed similar patterns of brain activity, when processing symbolic fractions. This points to a theory called neuronal recycling, or the brain’s version of repurposing old tools (brain regions) for new jobs.
The researchers hope that, by understanding how the brain processes these fractions, they will be able to help educators tailor fraction instruction in a way that leverages the children’s pre-existing brain sensitivity to ratios.
“Understanding fractions is key for progressing to higher-level mathematics,” says Yunji Park, former graduate student in Hubbard’s lab and first author of the study. “Several studies have shown that fraction abilities predict higher mathematical abilities, such as algebra.” Hubbard describes it as a gateway skill. “So, if we can help more kids get over that hurdle with the introduction of fractions, maybe we open up all of higher mathematics to a much larger group of people,” Hubbard explains. “And that, of course, then translates into a more STEM-educated workforce and more career opportunities.”
Most times, Hubbard points out, children are taught the steps of the operation when dealing with fractions, but not necessarily what fractions actually mean and represent. “One key to overcoming fraction difficulty is thinking about fractions as a magnitude,” Park says. “And our brain is already equipped with the ability to process ratios as magnitudes.” Their study suggests that children’s brains can perceive fractions as magnitudes or quantities, but people tend to think about them in whole numbers. Taking advantage of the brain’s ability to perceive fractions as a magnitude could facilitate learning. “I think our paper can be meaningful for instructors and educators who try to teach the fraction magnitudes to the kids,” Park says.
Hubbard says a clear example of the common failure to understand fractions is a recent unsuccessful attempt by a fast food chain to compete with McDonald’s quarter-pound hamburger. They launched a burger that was one third of a pound. That is, 1/3 (0.33 lbs) versus 1/4 (0.25 lbs) of a quarter-pounder. After failing to sell the burger, they asked a focus group why they wouldn’t buy the third-pounder, to which they responded “Well, you’re ripping us off. You’re charging us the same amount for a third-pound hamburger as we could spend for a quarter-pounder, because three is less than four” Hubbard narrates.
People weren’t buying it because they weren’t thinking about the relationship between the numerator and the denominator (or ratio), but they were looking at the fraction as a whole number. “Kids, even adults, will make mistakes with fractions because they focus only on the components, the five and the eight, the two and the three, as opposed to the relative size of these,” Hubbard explains. What may help, he adds, is for them to focus on the relative magnitude of the pieces rather than on each component.
The Hubbard lab continues to work to find ways to make fraction learning a bit easier and less stressful for children. Data from the present study, which was almost a decade in the making, will serve to look into individual differences of how children learn and process fractions, and expand into looking at how the entire brain orchestrates to process mathematical information.