Exploring the Promotion of Tiered Mathematics Instruction Through Discipline-Based Competitions to Enhance Students’ Innovative Capabilities

This study proposes a novel model that integrates mathematics discipline competitions with tiered instruction, aiming to enhance students’ mathematical creativity and innovation. Leveraging collegiate mathematics contests as a driving force, the approach promotes teaching, learning, and pedagogical reform through competition. A comprehensive, multi-dimensional tiered instructional system for university-level mathematics courses has been developed. The practical implementation emphasizes adjustment and optimization of the teaching process, the formulation of diversified course objectives, and the incorporation of mathematical modeling cases. This dual focus on foundational knowledge and competency development contributes to the cultivation of applied talents. Prioritizing individualized student development, the study establishes a dynamic interaction mechanism linking mathematics competitions, daily tiered instruction, and pedagogical reform. This mechanism fosters a new talent development model characterized by the integration of instruction and competition as well as learning and innovation. Furthermore, the study effectively integrates mathematical modeling with experimental mathematics to advance high-level instruction and practice in university mathematics education.