Fraction Ball: A Playful Learning Intervention That Improves Children's Rational Number Knowledge

• In Event: Translating Findings From Cognitive Science to Improve Fraction Learning in the Classroom and the Playground.

Abstract

This study evaluated “Fraction Ball” a novel intervention that provides an embodied, playful learning experience by reimagining the lines on a basketball court to emphasize fraction and decimal number learning. Fraction Ball was designed based on evidence that the number line is foundational for rational number knowledge (Siegler et al., 2011). To promote magnitude understanding (Hansen et al., 2015) and reduce “whole number bias” (Ni & Zhou, 2005), the point system is in fraction/decimal units. In Fraction Ball, the distance from below the basket to the 3-point arc is converted into a “0 to 1” area with arcs that act as number line markers and divide one end of the court into fourths, and the other end into thirds (Figure 2). To promote fraction to decimal conversions, the court is split in half with fraction and decimal symbols side by side (e.g. 1/4 (0.25), 2/3 (0.66)). On the side of the court children tally their score on a number line with fraction and decimal representations (Figure 3). Teacher led games were designed to promote rational number arithmetic and reinforce conceptual understanding through play. Children in their team take on three different roles during the games—shooter, rebounder, and counter (Figure 4) and compete, for instance, to make as many points as possible in 2-minutes, race to an exact number (e.g., 3.25). Further, the competition provides motivation for children to engage in rational number arithmetic quickly and accurately.
Method
We examined the learning value of 300 minutes of Fraction Ball as a supplement to in-class fraction learning during Physical Education (PE) class in a K-8 school that serves a high majority of Latinx children from low-income families. Hypotheses and analysis plan were pre-registered and can be found here.
Ten classrooms (four 4th, four 5th, and two 6th grade) were enrolled (N=160 students). Within each classroom we randomly assigned half the students to play Fraction Ball for six 50-minute sessions (twice per-week for three-weeks) and the other half to remain in PE. Participants took two sets of identical pretests and posttests (timed and untimed) composed of 5 subscales, arithmetic, conversion (fraction to decimal and vice-versa), number line placement (0-to-1 and 0-to-5). Subscales were used to create three additional measures for overall accuracy, near transfer, and far transfer.
Results
The impact of Fraction Ball on the posttest overall accuracy composite score of fraction and decimal knowledge was .44 standard deviations controlling for pretest scores and grade level (β = 0.44, p < .001). See Table 1 for complete results of regression analyses.
Significance
Playing six 50-min sessions of Fraction Ball had significant impacts on children’s rational number understanding as reflected by higher scores in overall accuracy, near transfer, and conversions of fractions to decimals and visa-versa. Fraction Ball represents a low-cost, highly scalable intervention that promotes math learning in a fun and engaging approach. Further interpretation of the results and next steps in this line of research will be discussed in the presentation of this project.

Authors

• Andres Sebastian Bustamante, University of California - Irvine

• Kreshnik Begolli, University of California - Irvine

• Daniela Alvarez-Vargas, University of California, Irvine

• Drew Bailey, University of California - Irvine

• Lindsey E. Richland, University of California - Irvine

• Lourdes Farag, El Sol Academy

• Ivet Gonzalez, El Sol Academy