新工科背景下以学习为中心的《数学物理方程》教学范式改革研究

Research on the Reform of the Learning-Centered Teaching Paradigm for “Mathematical Physics Equations” in the Context of New Engineering Education

摘要: 《数学物理方程》是石油、地质、勘探等工科专业的核心基础课程，课程内容兼具理论抽象性与工程应用性，对学生数学功底与逻辑思维要求较高。在长期一线教学中发现，课程普遍存在教学设计固化、教学内容与专业需求贴合度不足、学生学习分层差异大、自主学习过程缺少有效监管等实际问题。为切实提升课堂教学质量，真正落实“以学习为中心”的教学理念，本文立足本校工科专业办学特色，从课堂教学设计优化、分专业差异化教学、分层自主学习引导、全过程多元考核四个维度开展教学范式改革。结合分离变量法、积分变换等核心知识点的课堂实践，融入任务驱动、软件辅助教学与小组探究模式，探索适合新工科培养目标的课堂教学新路径。教学实践表明，改革能够有效化解课程难点、缩小学情差距、强化知识应用能力，切实推动课堂从“教师讲授”向“学生深度学习”转变，可为同类工科数理课程教学优化提供实践参考。

Abstract: “Mathematical Physical Equations” is a core foundational course for engineering majors such as petroleum, geology, and exploration. The course content combines theoretical abstraction with engineering application, and requires students to have a high level of mathematical foundation and logical thinking. In long-term frontline teaching, it has been found that courses generally have practical problems such as rigid teaching design, insufficient alignment between teaching content and professional needs, significant differences in student learning stratification, and lack of effective supervision in the process of self-directed learning. In order to effectively improve the quality of classroom teaching and truly implement the teaching philosophy of “learning-centered”, this article is based on the characteristics of our university’s engineering majors, and carries out teaching paradigm reform from four dimensions: optimizing classroom teaching design, differentiated teaching by major, guiding self-directed learning at different levels, and conducting diversified assessments throughout the entire process. Combining core knowledge points such as variable separation method and integral transformation with classroom practice, integrating task-driven, software-assisted teaching, and group exploration mode, it explores new classroom teaching paths that are suitable for the training objectives of new engineering education. Teaching practice has shown that reform can effectively resolve curriculum difficulties, narrow the gap in learning situations, strengthen knowledge application abilities, and effectively promote the transformation of the classroom from “teacher lectures” to “student deep learning”. It can provide practical references for optimizing the teaching of similar engineering mathematics and physics courses.