科研反哺教学视角下的《复变函数》课程教学改革探究

Exploring Teaching Reform of the Complex Functions Course from the Perspective of Research Feeding Back into Eaching

摘要: 复变函数作为数学类专业的一门核心基础课程，理论体系完整但内容抽象，传统教学面临学生参与度低、知识应用能力薄弱等困境。本文以成果导向教育理念为理论框架，系统阐释科研反哺复变函数教学的内在逻辑，并从教学内容改革、教学方法改革、改造知识内容呈现方式、完善评价体系四个维度提出改革路径。研究认为，科研反哺的本质是将科研的思维方法、前沿成果与问题意识转化为教学资源，实现从“知识传授”向“能力建构”的范式转换。实践表明，这一改革路径有助于激发学生学习动机、培养创新思维与科研素养，为数学基础课程的教学改革提供可资借鉴的思路。

Abstract: Complex analysis, as a core foundational course for math majors, has a complete theoretical system but is abstract in content. Traditional teaching faces challenges like low student engagement and weak ability to apply knowledge. This paper uses the concept of outcome-based education as its theoretical framework, systematically explaining the internal logic of using research to inform complex analysis teaching, and proposes reform paths in four areas: content reform, teaching method reform, transforming the way knowledge is presented, and improving the evaluation system. The study suggests that the essence of research-informed teaching is turning research thinking methods, cutting-edge findings, and problem awareness into teaching resources, achieving a shift from knowledge delivery to ability building. Practice shows that this reform path helps motivate students, cultivate innovative thinking and research literacy, providing useful ideas for teaching reform in foundational math courses.