In the context of the new era of education, advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking, scientific spirit, and value orientation. However, traditional teaching has overemphasized knowledge instillation while neglecting value guidance, making it difficult to meet the demands of cultivating interdisciplinary talents. This study introduces the OBE concept and constructs a “knowledge–ability–value” teaching framework, integrating outcome orientation, backward design, and diversified evaluation to promote the systematic incorporation of ideological and political education into the curriculum. Taking limits, definite integrals, and series as representative knowledge points, the paper designs case-based pathways to foster dialectical thinking, patriotism, and scientific spirit. Practice has shown that this model effectively unifies knowledge education and value education, enhancing students’ logical reasoning, sense of responsibility, and scientific literacy. The study provides an operational pathway for the reform of ideological and political education in advanced mathematics courses and carries practical significance for implementing the goal of “all-round education.”