Abstract: Mathematical skills are an important predictor of academic and life prospects. In this presentation, I will discuss three examples of how advanced statistical methods applied to rich data sets can help understand the development of mathematical skills better. In a first study, we used a robust nested cross-validation approach to identify the most suitable model reflecting estimation patters of 487 students in a series of number line estimation tasks with fractions. Results replicated strong reliance on reference points for fraction number line estimation for the first time and suggested that stable application of number line estimation strategies was associated with better performance. In a second study, we developed a theory-informed model stack utilizing regularised regression as meta-learner to combine random forests representing different mathematical skills (e.g., symbolic vs. non-symbolic, etc.) and structural aspects of their measurement (e.g., production vs. recognition items). Leveraging educational monitoring data of N=4994 students, the final model stack significantly outperformed earlier theoretical as well as purely data-driven approaches highlighting production items as particularly influential predictors. In a final study, we applied psychological network analysis to evaluate contributions of basic mathematical skills to understanding percentages. Considering data of N=2798 students working on approximately 4.1 million mathematical problems using the intelligent tutoring system bettermarks, we observed that understanding percentages was best predicted by instantiations of basic mathematical skills sharing similar features, such as fraction word problems and fraction/natural number multiplication/division problems. Taken together, these findings suggest that advanced statistical methods may help exploit the full potential of available data to better understand the development of mathematical skills.