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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. Lay Description: What is already known about this topic: Understanding fractions is one of the most difficult mathematical skill for students to learn in school.Longitudinal studies using face‐to‐face testing indicated that fraction understanding as well as achievements in algebra can robustly be predicted by prior mathematics skills. What this paper adds: We evaluated data from more than 5,000 Dutch students who performed over 1 million curriculum‐based mathematical problem sets in an online learning environment.Our analyses showed that fraction understanding as well as achievements in algebra and can be predicted by prior mathematics skills. Implications for practitioners: These results indicated that previous results from face‐to‐face testing generalize to data obtained from large‐scale online learning environments.Thus, these results open up a new avenue for research using online learning environments on the development of mathematical skills. [ABSTRACT FROM AUTHOR]

Task solving processes and changes in these processes have long been expected to provide valuable information about children's performance in school. This article used electronic tangibles (concrete materials that can be physically manipulated) and a dynamic testing format (pretest, training, and posttest) to investigate children's task solving processes and changes in these processes as a result of training. We also evaluated the value of process information for the prediction of school results. Participants were N = 253 children with a mean age of 7.8 years. Half of them received a graduated prompts training; the other half received repeated practice only. Three process measures were used: grouping behaviour, verbalized strategies, and completion time. Different measures showed different effects of training, with verbalized strategies showing the largest difference on the posttest between trained and untrained children. Although process measures were related to performance on our dynamic task and to math and reading performance in school, the amount of help provided during training provided the most predictive value to school results. We concluded that children's task solving processes provide valuable information, but the interpretation requires more research. Lay Description: What is already known about this topic: Dynamic testing provides information on a child's ability to learn.Solving process information provides indications for intervention.Computerized testing can be of great help in recording process information. What this paper adds: Process‐oriented dynamic testing provides explanatory information beyond traditional tests.The use of a tangible user interface (TUI) console uncovers valuable information on solving processes.Process measures are related to series completion performance, math, and reading.Need for instruction is the best predictor of math and reading ability.Implications for practice and/or policy: A framework for interpreting process information is necessary in dynamic testing.Process‐oriented dynamic testing may be more suitable to inform education.TUIs provide a more natural testing environment. [ABSTRACT FROM AUTHOR]