Abstract
In the context of the globalization of the 21st century and the growing demands for critical thinking and interdisciplinary training, the integration of Problem Based Learning (PBL) methods into STEAM educational programs is becoming a pressing issue. The article analyzes the influence of PBL principles on the development of mathematical competencies and the integration of STEAM in high school. Modern concepts, empirical data and mechanisms for the formation of internal motivation, beliefs in abilities and sustainable interest in STEM careers are considered. The article provides an analysis of studies, a comparative analysis of methodological approaches, and discusses the results of multivariate regression analysis and mediation models. The final conclusions allow us to recommend areas for improving PBL practices to improve the quality of STEAM education.