This paper aims to investigate an instructional approach that integrates mathematical thinking with ideological and political education, and applies it to courses in computational mathematics/information and computer science majors. This approach serves as a bridge between mathematical thinking and pedagogical ideologies, incorporating relevant mathematical anecdotes and employing an inquiry-based teaching methodology. It provides an innovative approach to teaching undergraduate and graduate-level mathematical courses, promoting students' understanding of mathematical concepts and the grasp of mathematical thinking. Additionally, it nurtures students' comprehensive abilities, ethical qualities, and a sense of social responsibility.