马尔可夫链在大学教学评价中的应用——以《高等代数与解析几何》课程为例

Application of Markov Chains in Teaching Evaluation in Universities—A Case Study of the Course “Advanced Algebra and Analytic Geometry”

摘要: 本文选取济南大学金融数学专业同一名教师任教的两个班级，以《高等代数与解析几何》课程的成绩为研究对象，通过收集分析三次考核数据，探讨马尔可夫链理论在大学课程教学评价中的应用。首先，依据实际情况制定统一标准，合理划分学生成绩等级。其次，计算转移概率矩阵，分析状态迁移特征与提升度。最后，进行教学效果评估。本研究发现，马尔可夫链理论能有效评价教学效果，并帮助教师获取针对性的教学反馈。研究结果不仅为大学课程教学评价提供了可操作的数学工具，也为其他类似课程的教学改进提供了重要的参考依据。

Abstract: This paper selects two classes taught by the same instructor in the Financial Mathematics program at the University of Jinan, and takes the grades of the course “Advanced Algebra and Analytic Geometry” as the research object. By collecting and analyzing the results of three assessments, it explores the application of Markov chain theory in university course teaching evaluation. First, a unified standard is formulated according to the actual situation to reasonably classify student grade levels. Second, the transition probability matrix is calculated, and the characteristics of state transition and the degree of improvement are analyzed. Finally, the teaching effectiveness is evaluated. The study finds that Markov chain theory can effectively assess teaching outcomes and help instructors obtain targeted teaching feedback. The results not only provide an operable mathematical tool for university course teaching evaluation, but also offer an important reference for improving instruction in other similar courses.