Achievements in arithmetic and measurement units predict fraction understanding in an additive and linear manner

Learning fractions is one of the most difficult but nevertheless critical mathematical topics in school as understanding fractions significantly predicts later mathematics achievement and vocational prospects. Importantly, mastery of basic mathematical topics (e.g., arithmetic skills) was repeatedly observed to serve as a stepping stone for learning fractions. However, it has not yet been investigated in detail whether achievements on such basic mathematical topics predict fraction understanding uniquely and linearly or whether there are also multiplicative and non-linear dependencies. Such multiplicative and/or non-linear dependencies would suggest that closing knowledge gaps on key topics is of paramount importance, as knowledge gaps on these topics could have negative consequences for the understanding of fractions. Therefore, we predicted students’ fraction understanding by their performance on four prior topics (i.e., Geometry, Basic Arithmetic, Measurement Units, and Advanced Arithmetic) and compared the fits of different regression models (including topics as main effects only vs. also including interaction and quadratic terms). Our analyses considered three cohorts of students (approximate age range: 12–13 years) attending different school tracks that vary in difficulty (i.e., 6468 students of academic track schools; as well as 4598 students, and 1743 students of two vocational track schools) who used an intelligent tutor system. Results were similar across all three cohorts substantiating the robustness of our results: students’ fraction understanding was linearly predicted by achievements in basic mathematical skills (i.e., arithmetic and measurement units). We found no substantial support favoring more complex models across all three cohorts. As such, the results suggested that achievements in arithmetic and measurement units serve as unique and linear stepping stones for later fraction understanding. These findings suggest that those students with knowledge gaps in arithmetic and measurement units should be encouraged to revise these topics before moving on to more advanced topics—such as fractions—as these more advanced topics build on them.