Software-Based Intervention with Digital Manipulatives to Support Student Conceptual Understandings of Fractions

Rational number and fractions concepts are inherently difficult; and lack of mastery often holds students back from success in subsequent mathematics courses. This paper describes design characteristics of a software based, adaptive, rational number tutor with virtual manipulatives, realistic contexts, and procedural feedback. Then, the paper presents findings from a randomized crossover trial designed to evaluate the impact of the described intervention on student fraction achievement. The trial was conducted in two districts in two states with 17 elementary school teachers and 297 4th and 5th grade students. Half of the participating classrooms replaced worksheet practice time (over 10 instructional hours) with Woot Math Adaptive Learning (WMAL), a digital tutor that incorporates dynamic digital manipulatives, video tutorials and automatic feedback to students and teachers. After 10 instructional hours the groups switched conditions for another 10 instructional hours so each student would have exposure to the treatment and control conditions. Analysis shows that regardless of treatment order, student performance gains on assessment items (mostly from NAEP and TIMMS) were statistically higher, (d = 0.39, F(1,589) = 5.73, p < 0.05), after 10 days of instruction with WMAL than they were after 10 days of business-as-usual instruction. This difference of 0.39 standard units corresponds to an improvement index of 10.9 (percentile point gain compared to non-treatment). The results demonstrate how the described approach to software and instructional design can work together to support significant increases in student achievement in rational number domains by combining best practices in feedback, curricular design, and adaptive instructional sequences.