基于真实问题的数学分析课程教学改革

Reform of Teaching in Mathematical Analysis Course Using Problem-Based Learning

摘要: 数学分析作为数学学科的核心基础课程，是连接抽象理论与实际应用的重要纽带。针对传统数学分析课程中存在的教学内容抽象、教学方法单一、理论与实践脱节等问题，本研究从课程内容重构、教学模式创新及评价机制优化三个方面，提出基于真实问题的教学改革方案。通过引入工程、经济、物理等领域的真实案例重构教学内容，采用分层教学与数字化资源支持个性化学习，并建立形成性评价与竞赛成绩相结合的考核体系。改革旨在提升学生的逻辑思维能力、数学建模能力及跨学科应用能力，强化数学分析的实践价值，促进多学科交叉融合。试点实践表明，该方案显著提高了学生的课堂参与度与问题解决效率，为数学分析课程教学提供了可推广的创新范式，助力培养兼具理论素养与实践能力的高层次数学人才。

Abstract: As a core foundational course in mathematics, mathematical analysis serves as a critical bridge connecting abstract theory with practical applications. To address the issues of abstract content, rigid teaching methods, and disconnection between theory and practice in traditional mathematical analysis courses, this study proposes a teaching reform scheme based on real-world problems, focusing on three aspects: curriculum restructuring, pedagogical innovation, and evaluation mechanism optimization. By integrating authentic case studies from fields such as engineering, economics, and physics into the curriculum, adopting hierarchical teaching and digital resources to support personalized learning, and establishing a hybrid assessment system combining formative evaluations and competition performance, the reform aims to enhance students’ logical thinking, mathematical modeling, and interdisciplinary application skills. It also strengthens the practical value of mathematical analysis and promotes cross-disciplinary integration. Pilot implementation demonstrates that this approach significantly improves classroom engagement and problem-solving efficiency, offering a replicable innovative paradigm for mathematical analysis education. It facilitates the cultivation of high-level mathematical talents equipped with both theoretical expertise and practical competence.