Fraction Ball: Iterative Design and Classroom Expansion of a Play-Based Rational Number Intervention

• In Event: Experimental Mathematics Interventions in Classrooms and Schoolyards to Promote Early Numeracy and Rational Number Learning

Abstract

Rational numbers represent a challenging topic for children and become gatekeepers for advanced mathematics and science. Studies conducted in laboratory settings have provided valuable insights into rational number understanding, but most interventions developed from the science of learning have not been successful in school contexts. Co-design methodology facilitates the integration of the science of learning principles with local knowledge to create feasible, usable, and scalable interventions in school contexts. In this study, we present an intervention merging science of learning theory with teacher knowledge to build children’s rational number knowledge through playful learning. We redesigned a basketball court to consist of number arcs from 0 to 1 in increments of thirds or fourths and a walkable number line (Figure 1) and in a previous study we demonstrated the impacts of this game on students' rational number knowledge (Authors, 2022). Here, we collaborated with 20 elementary school teachers to iterate on the six outdoor basketball games and co-design six new classroom lessons to reinforce rational number learning. We conducted an RCT with 16 teachers and 360 students enrolled in fourth (n = 218) and fifth grade (n = 142). Classrooms were blocked into eight pairs based on students’ pre-test scores (e.g., the first block consisted of the two classrooms with the highest scores) and then randomly assigned within each block to the intervention (8 teachers, 198 students) or control group (8 teachers, 162 students). Students primarily identified as Latine (97%), most received free or reduced lunch (83%), and many were English Language Learners (47%). Students completed an assessment at pre and post-test with timed and untimed sections measuring conversions between fractions and decimals, fraction addition, and rational number magnitude knowledge. The study was pre-registered at https://osf.io/kjqmz before post-test data collection. Figure 2 shows impact estimates of the intervention on all the standardized outcomes, clustering standard errors by teacher and controlling for students’ pre-test scores and grade level. The impact estimate on the overall composite score was .37 SD (p < .01), indicating an overall positive impact of Fraction Ball on student rational number learning. A similar impact was seen on near transfer items (b = .44, p < .001), but not far transfer (b = .13, p = .19). Across subtests, impact estimates were between .26 SD and .80 SD and statistically significant (ps < .05), except for the timed fraction addition subtest (b = .05, p = .74). Impact estimates were robust to models with random intercepts by teacher or FIML to account for missing data. In summary, the intervention had small to large statistically significant impacts on various rational number skills. Nonetheless, we identified transfer and timed fraction addition items as areas for improvement in future iterations of the intervention. These findings demonstrate the value of adopting a co-design methodology with teachers and connecting learning experiences across the classroom and school yard contexts. Fraction Ball represents a powerful example of effective approaches to implementing interventions based on learning principles in complex school contexts and making connections across children’s learning experiences.

Authors

• Andres Sebastian Bustamante, University of California - Irvine
  Presenting Author

• Kreshnik Begolli, University of California, Irvine

• Vanessa Noemy Bermudez, University of California - Irvine

• LuEttaMae Lawrence, Utah State University

• Daniela Alvarez-Vargas, University of California - Irvine

• Sabrina Valdez, University of California Irvine

• Evelyn Santana, University of California-Irvine

• Lourdes Michelle Acevedo-Farag, University of California - Irvine

• Lindsey Engle Richland, University of California - Irvine

• Katherine Rhodes, University of California - Irvine

• June Ahn, University of California Irvine

• Drew Bailey, University of California - Irvine