Basic mathematical skills and fraction understanding predict percentage understanding: Evidence from an intelligent tutoring system

Longitudinal studies indicated that basic mathematical skills (e.g., basic arithmetic operations) are a significant predictor of understanding fractions, which itself is critical for later academic and life prospects. However, it is still unclear whether the understanding of other forms of rational numbers, such as percentages, is also predicted by basic mathematical skills and it is particularly unclear whether such predictions are reflected in data from intelligent tutoring systems (ITSs). Therefore, we leveraged a large-scale dataset (2,798 students; working on 4.1 million mathematical problems) from an ITS to predict percentage understanding based on basic mathematical skills (i.e., arithmetic, measurement units, and geometry) and fraction understanding. In a first step, we observed that skills in advanced arithmetic, measurement units, and geometry, as well as fraction understanding significantly predicted percentage understanding. Closer inspection in a second step indicated that percentage understanding was best predicted by problems with similar features (e.g., fraction word problems, fraction/natural number multiplication/division problems). Together, our results point practitioners and software developers to consider the revision of specific subtopics which share similar features of percentage problems for students who face difficulties with percentages.