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 mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader 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 results obtained in these previous studies generalized to data from the curriculum-based online learning environment Bettermarks for mathematics used in schools in the Netherlands. 

Methods: We considered data from more than 5000 students who solved over 1 million mathematical problem sets on basic mathematical skills, fractions, but also algebra. 

Results and Conclusions: In line with previous findings, we found that fraction understanding was predicted significantly by more basic mathematical skills. Our analyses also indicated that algebra achievement was predicted significantly by fraction understanding beyond influences of more basic mathematical skills. 

Implications: Together, these findings generalized previous results based on face-to-face testing to the context of data from online learning environments and thus, indicate that data from such large-scale online learning environments may well qualify to provide significant insights into the hierarchical development of mathematical skills.