Predicting fraction and algebra achievements online: A large-scale longitudinal study using data from an online learning environment

Background: Mastering fractions seems among the most critical academic skill for students to acquire in school as fraction understanding significantly predicts later academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and operations) is highly relevant. However, almost all existing studies identifying more basic numerical skills as predictors of fraction understanding rest on data acquired in face-to-face testing - mostly in classrooms. Objectives: In this article, we evaluated whether obtained results generalize to data from the curriculum-based online learning environment Bettermarks for mathematics used in schools in the Netherlands. In particular, we i) evaluated whether fraction understanding can be predicted by prior skills on different more basic mathematical topics before we ii) examined whether fraction understanding predicted achievements in algebra over and beyond the influence of basic mathematical skills. Methods: We considered data from more than 5,000 students who solved over 1 million mathematical problem sets. Results and Conclusions: In line with previous findings, we found that fraction understanding was predicted significantly by prior skills on basic mathematical topics. Our analyzes also revealed that algebra achievements were predicted significantly by fraction understanding beyond influences of basic mathematical skills. Implications: Together, these findings substantiated previous results based on face-to-face testing and, thus, indicate that data from large-scale online learning environments may well qualify to provide significant insights into the development of mathematical skills.