Fractions are common in everyday life and act as a predictor of algebra learning. However, numerous studies reveal that both students and teachers face difficulties in understanding them, so they remain a challenging area of research. This study aims to examine how the level of teacher knowledge about fractions and their teaching impacts on the progress of students' learning. This research was developed from a quantitative methodology, and the study instruments were structured tests with closed questions applied to 634 fourth grade students and 19 teachers from 19 schools. The data were analyzed using a Bayesian predictive model. The main finding of this study was that the effect of teachers' knowledge on average student learning progress manifests itself in three phases. It is in the third phase that this effect becomes noticeable, with the best results observed in both students and teachers. This suggests that teachers who are well informed about fractions and their teaching can positively and substantially affect students' mathematics learning.