Students in two southern California school districts are jumping to understand rational numbers on the basketball court, and the engaging series of games — known as Fraction Ball — are already showing significant results.
Fraction Ball uses movement-based activities to help students working at 3rd, 4th and 5th grade math levels make meaningful connections between math lessons in the classroom and in the schoolyard through play. It also aims to strengthen students' use of their executive functioning skills in math problem-solving with fractions and decimals.
The 16-lesson unit includes eight activities for the math classroom and eight games that can be played during a 50-minute physical education class or at recess on a basketball court. The games have different objectives, such as scoring as many points as possible in 2 minutes or using the smallest number of shots to get to an exact number without overshooting the goal. Teams compete against each other by converting fractions and decimals as quickly and accurately as possible.
On the basketball court, the traditional 3-point arc in front of the basketball hoop is converted to a 1-point line with a colorful graphic. Smaller arcs closer to the basket are labeled with rational numbers. One half of the court uses fourths: 1/4-point, 1/2-point and 3/4-point, with one side of the basket using fraction notation and the other side showing the corresponding decimal values of 0.25, 0.5 and 0.75.
The other half of the court is in thirds, with smaller arcs for 1/3 and 2/3, and also using decimal representations.
The numbers and the game aim to help students visualize the relationships between rational numbers, like seeing that 1/4 and 0.25 are the same value. They practice converting between fractions and decimals while shooting a ball into a hoop. A number line on the side of the court helps them keep score.
Evidence of the positive impact Fraction Ball has had on students' understanding of fractions and decimals have helped Fraction Ball’s creators acquire a $1.9 million research award in 2023 from the Advanced Education Research and Development Fund’s EF+Math Program to adapt and expand the innovative approach throughout Santa Ana schools. A $1.25 million award was received in 2020.
Honing math, executive function skills
Lourdes Acevedo-Farag helped create Fraction Ball in 2018, when, through lucky timing, the charter school where she taught middle school math — El Sol Science and Arts Academy of Santa Ana — had not yet painted lines on the school's outdoor basketball court.
Working with researchers at University of California, Irvine's School of Education, as well as other teachers at the school, Acevedo-Farag began developing Fraction Ball as a way to help her students better understand fractions and decimals in relation to whole numbers.
"We know that rational numbers are really like the gatekeeper to algebra," said Acevedo-Farag, who has since left the classroom to pursue a Ph.D in education at UC Irvine.
Students can find learning to add and subtract fractions and decimals challenging, researchers and educators say. Traditionally, rational number calculations are taught through the memorization of procedural steps to get correct answers. It's the kind of rote work that can be difficult for students, especially those with attention or behavioral issues, according to researchers and educators.
Currently, 15 schools in the Santa Ana Unified School District and three from the Lynwood Unified School district are using Fraction Ball lessons.
Fraction Ball’s design has been tweaked several times since it began at El Sol six years ago, and UC Irvine researchers have tracked students' learning. One analysis of 160 students in grades 4-6 found that students who played six different games for six PE periods had significantly improved rational number understanding, as documented by higher scores in overall accuracy, according to the study published in 2022 in the Journal of Educational Psychology.
Megan Brunner, associate director of research and learning at Advanced Education Research and Development Fund’s EF+Math Program, said there is research showing that when students have stronger executive functioning skills, achievement gaps decrease for historically underserved students.
The work to understand equity-centered educational experiences through math instruction and executive functioning skill-building is "really about helping students be agents over their own learning… and moving away from some of the historically kind of deficit thinking around executive functions," Brunner said.
Acevedo-Farag added that for Fraction Ball specifically, participating students can strengthen their cognitive, physical, executive functioning, listening and collaboration skills — all while playing a fun game.
"As a teacher of 12 years, I saw we either are teaching executive functioning skills, or we're teaching math, and Fraction Ball is the first time I saw that we're doing it together. And it's working," she said.
