Enhancing Flexible Transfer of Fractions: The Role of Sequential and Simultaneous Games With Multiple Representations

We codesigned and evaluated a brief intervention combining two fraction games: Fraction Ball (played on a basketball court) and Bottle Caps Bonanza (played on a tabletop shuffleboard). Using participatory design principles, we engaged teachers and students in codesigning playful learning experiences aimed at improving knowledge transfer and adding fractions with unlike denominators. Students were randomly assigned within seven treatment classrooms to practice fractions with different denominators on one board simultaneously (N = 87) versus practicing on separate boards sequentially (N = 79). Three comparison classrooms (N = 75) only took the pretest and posttest. Our preregistered models suggested significant impacts on multiple aspects of fraction knowledge, including far transfer and overall fraction knowledge, when comparing both treatment groups to the comparison group. The simultaneous condition performed higher on untimed fraction addition with unequal denominators, though this difference was not statistically significant (b = 0.21, p = .05). Furthermore, students with higher prior knowledge benefited more from the simultaneous condition. We conclude that this playful and accessible intervention can effectively improve students' fraction knowledge.