Early algebra knowledge predicts later fraction understanding and improves with fraction instruction

Recent studies show that students' fraction knowledge predicts their later algebra knowledge. This longitudinal study investigated whether this relationship is bidirectional-that is, whether early algebra knowledge predicts later fraction knowledge-and whether early algebra knowledge improves during fraction instruction. We followed 379 German fifth- and sixth-graders, assessing their early algebra and fraction knowledge before and after a period of six to nine months of fraction instruction. Pretest early algebra knowledge proved a stronger predictor of post-instruction fraction knowledge than either pretest fraction knowledge or end-of-year math grades reported at the study's outset (small-to-medium effect size). Additionally, students' early algebra knowledge improved during fraction instruction (small effect size). While prior research typically frames fractions as foundational for algebra, our findings complement this view by providing evidence that the reverse direction also holds true: early algebra knowledge predicts later fraction knowledge. Although the results do not establish causality, they point to the possibility that strengthening early algebraic thinking could benefit fraction learning, and that instruction on fractions may, in turn, improve algebra knowledge. Future experimental studies should explore how to leverage these findings instructionally to support mathematical development.