“问题链–思政链”双螺旋模型驱动下高等数学分层分类教学模式的创新实践

Innovative Practice of Hierarchical Teaching Mode of Advanced Mathematics Driven by “Problem Chain - Ideological and Political Chain” Double Helix Model

摘要: 在高等教育深化改革背景下，面对如今高等数学教学过程中知识传授与思政育人融合不足、分层分类教学实施效果不佳等问题，提出“问题链–思政链”双螺旋模型驱动下教学模式创新实践。以数学问题链为知识载体，设计由浅入深、环环相扣的数学问题，引导学生逐步掌握高等数学核心概念与解题方法，将思政元素有机融入问题情境，形成思政链，实现知识传授与价值引领的螺旋式上升。在分层分类教学中，针对不同层次学生的认知特点与专业需求，设计差异化问题链与思政链，增强教学的针对性与实效性。实践表明，问题驱动激发学生主动思考，思政元素的无痕融入提升课程亲和力，分层分类设计满足个性化学习需求，解决传统教学中知识碎片化、思政教育形式化等问题。结合高等数学学科特性，研究结果表明，该教学模式有助于促进学生在知识、能力和思政素养方面的全面发展，但研究也存在一定的局限性，后续优化教学模型，以期为高等数学教学改革提供更具参考价值的实践方案。

Abstract: In the context of deepening reform in higher education, facing the problems of insufficient integration of knowledge imparting and ideological and political education in the current higher mathematics teaching process, and poor implementation of hierarchical and classified teaching, an innovative teaching mode driven by the “problem chain - ideological and political chain” double helix model is proposed for practice. Using the mathematical problem chain as a knowledge carrier, design interconnected mathematical problems from shallow to deep, guiding students to gradually master the core concepts and problem-solving methods of advanced mathematics, organically integrating ideological and political elements into problem contexts, forming an ideological and political chain, and achieving a spiral upward trend of knowledge transmission and value guidance. In hierarchical classification teaching, differentiated problem chains and ideological and political chains are designed based on the cognitive characteristics and professional needs of students at different levels to enhance the pertinence and effectiveness of teaching. Practice has shown that problem driven approaches stimulate students’ active thinking, seamless integration of ideological and political elements enhances course affinity, layered and classified design meets personalized learning needs, and effectively solves problems such as fragmented knowledge and formalized ideological and political education in traditional teaching. Based on the characteristics of higher mathematics discipline, a teaching reform model of “designing mathematical problem chain - integrating ideological and political elements - implementing hierarchical classification” has been constructed, which is an important reference value for promoting ideological and hierarchical classification teaching in higher mathematics and improving the quality and educational effect of higher mathematics teaching.