Exploration and Implementation of the "Problem-Oriented + Progressive Case" Teaching Model Reform: A Case Study of Probability Theory and Mathematical Statistics

Mathematics is the most brilliant pearl of human wisdom. As a critical branch of modern mathematics, probability theory and mathematical statistics serve as foundational courses for engineering, economics, and management disciplines. Presently, the inherently mathematical nature of these courses often leads students to focus excessively on calculations while neglecting conceptual understanding, resulting in weak knowledge transfer abilities. Bridging "concrete phenomena" with "the principles of probability and statistics" in modeling requires high levels of various student competencies, and the disconnect between traditional teaching content and the current environment has led to outdated teaching cases. Additionally, a singular assessment method discourages student enthusiasm and results in low learning efficiency. To address these issues, our team adopted a "problem-oriented + hierarchical planning" teaching model. We restructured the teaching content, reshaped the teaching process, rebuilt online teaching resources, re-established multiple assessment methods, and integrated ideological and political elements. This reform achieved initial success and received high recognition from students. Furthermore, our team mentors guide students to participate in competitions such as the National College Students Mathematical Modeling Competition, the "Internet +" College Students Innovation and Entrepreneurship Competition, and the National College Students Mathematics Competition, thereby fostering the development of application-oriented talents.