*By Emily Leclerc, Waisman Science Writer*

For many students, math is a tough subject that can have a lot of anxiety associated with it. Within math, fractions are often considered particularly hard. A new paper published in the Annals of the New York Academy of Sciences found that math anxiety does have a significant impact on a child’s ability to work with fractions. Specifically, the study establishes that increased levels of math anxiety impairs children’s capability to learn symbolic fraction skills.

This finding indicates that if the way symbolic fraction skills are taught could alleviate math anxiety and rely on more foundational skills, symbolic fractions may become an easier subject for children to learn. The study was led by Isabella Starling-Alves, PhD, of the Department of Educational Psychology at the University of Wisconsin-Madison, and Edward Hubbard, PhD, an associate professor of educational psychology and a Waisman Center investigator.

“We have lots of research that shows that people are usually afraid of math. And they show a lot of anxiety when doing math and this impacts their performance. And within math, fractions are known as particularly hard,” Starling-Alves says. Traditionally, fractions are one of the most feared math subjects taught in school. Students of all ages approach fractions with trepidation and are often met with a tough subject worthy of their anxiety.

Fractions can be a particularly tough area for children to learn as they require kids to essentially reinvent their understanding of the value of numbers. Because fractions are traditionally a tough subject, they can be used as a predictor of how well a person will do later in more advanced math like algebra and calculus. The better a child does with fractions, the more likely they are to excel in advanced math. “That idea was part of the inspiration and motivation for this work,” Hubbard says. “We knew from previous work that how well kids understand fractions are these predictors of later outcomes.”

One of the main focuses of this study was to better understand the impact of math anxiety on two different types of fraction skills; symbolic fractions and nonsymbolic ratios. These skills were studied in two age groups, 2^{nd}/3^{rd} graders who are just beginning to learn fractions and 5^{th}/6^{th} graders who have mastered fractions. Symbolic fractions are the type of fractions people typically think of like ½ or ¼ or ⅔. Nonsymbolic ratios are ratios that are seen more often in the external world and are interpreted by comparing relative values. “When we talk about a nonsymbolic ratio or a nonsymbolic fraction, we mean things where people can perceive relative size or relative amount of stuff and recognize that the two are potentially more similar in magnitude or less similar in magnitude,” Hubbard says. “Like the relative lengths of a pair of lines.”

The skills needed to work with symbolic and nonsymbolic fractions are different and those differences play heavily into the impact of math anxiety on their use. Working with symbolic fractions requires the use of arithmetic and skills that can only be acquired in a more formal school setting whereas interpreting nonsymbolic fractions relies on a more fundamental skill that even animals possess – the ability to compare the amount of two different things.

“My kids are slightly more than half my height but not a lot more because they’re still kids,” Hubbard says. “So even without putting numbers, symbols or exact quantities [to what we see], we can perceive the relative size of one thing compared to another. That’s part of what we think is that ability to compare relative magnitudes without doing formal arithmetic.” This skill often develops young and can be seen in children as young as six-months. This perception of ratios is also seen in animals.

Hubbard says in studies where researchers placed speakers in an African savannah that played lion calls, a group of lions would only investigate the calls if they outnumbered the calls by a certain ratio. They were able to perceive their number of lions relative to another group and determine if they were outnumbered. This ability to almost instinctually interpret nonsymbolic ratios and fractions makes this form of fractions much easier for children to learn and understand.

Starling-Alves and Hubbard’s study found that children with higher math anxiety typically did worse with symbolic fractions, but not with nonsymbolic fractions. Starling-Alves and Hubbard attribute this in part to the fact that learning nonsymbolic fractions is based in a fundamental skill all humans have whereas symbolic fractions need the use of arithmetic and other learned math knowledge. Another important factor is that the children’s math anxiety was seen to have more of an impact in the 2^{nd}/3^{rd} grader group as they were new to the skill. Math anxiety still played a role in lower fraction performance in the 5^{th}/6^{th} grader group but not as much. Understanding all of this could help teachers redesign the way fractions are taught to both reduce the anxiety around fractions and make the subject easier to learn and digest.

“Our results show that when kids have negative feelings towards math, they have lower performance in fraction tasks, in particular tasks that involve symbolic fractions,” Starling-Alves says. “But when they looked at these perceptual nonsymbolic rations, it was not affected by their anxiety. It seems that when things are very automatic at a perceptual level, the math anxiety has a less negative impact on performance. We then may be able to use this previous knowledge kids have that is already solid to help them overcome this math anxiety and improve their future math outcomes.”

The findings from this study present the possibility to reinvent how fractions are taught to make them an easier and less daunting subject for students. If that happens, it also has the potential to improve long term math outcomes by improving students’ performances in more advanced math like algebra and calculus.

Moving forward, Starling-Alves wants to design research studies that will look at different intervention methods to alleviate students’ math anxiety. She would also like to flip the study and look at how anxiety around fractions affects teachers and how well they can teach the subject. If a teacher is apprehensive about a subject, that can often be conveyed to the students. For both Starling-Alves and Hubbard, this study presents a solid basis to move the research forward on how to knock fractions off the most feared list.

*This research was supported by a Grant from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (R01 HD088585) to E.M.H. and by a Core Grant (U54 HD090256) to the Waisman Intellectual and Developmental Disabilities Research Center. I.S.A. was supported by CAPES (Doc-Pleno, 88881.128282/2016-01).*

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