Abstract: The teaching quality of the mathematical modeling course is closely linked to students' performance in academic competitions and the cultivation of their innovative abilities. This paper establishes an innovative "trinity" teaching model centered around mathematical modeling competitions. This model integrates theoretical instruction in mathematical modeling, case-based practice, and competition training. By implementing such teaching activities, we aim to cultivate students' innovative abilities and conduct an in-depth exploration and reform of mathematical modeling teaching methods. Under this teaching model, students are encouraged to participate in various academic competitions. The results indicate that students' competition performance and innovative practical abilities have significantly improved.

Key words: mathematical modeling, case practice, teaching model