基于数学工具性认知的《计算方法》教学创新探索

Exploration on Teaching Innovation of “Computational Methods” Based on the Instrumental Cognition of Mathematics

摘要: 针对传统大学数学教学模式存在定义生硬、学生难以内化认知的局限，本文基于“数学工具性认知”理念，以《计算方法》课程中的拉格朗日插值算法为研究载体，探索大学数学教学创新路径。研究以“手机图片放缩”这一贴近生活的问题为贯穿式案例，通过任务分解、启发式教学引导，将抽象的插值思想与实际应用场景深度结合，逐步引导学生掌握插值构造逻辑与核心方法。教学实践表明，该设计能提升学生对数学知识的理解深度与应用能力，为大学数学教学中突出数学工具性、回归数学本质提供了可借鉴的实践方案，对推动大学数学教学改革具有积极启示意义。

Abstract: Aiming at the limitations of the traditional university mathematics teaching model, such as rigid presentation of definitions and difficulties for students in internalizing knowledge, this paper explores the innovative paths of university mathematics teaching based on the concept of “instrumental cognition of mathematics”, with the Lagrange interpolation algorithm in the course “Computational Methods” as the research carrier. Taking the life-close problem of “mobile phone image scaling” as a throughout case, the study deeply combines abstract interpolation ideas with practical application scenarios through task decomposition and heuristic teaching guidance, and gradually guides students to master the interpolation construction logic and core methods. Teaching practice shows that this design can improve students’ depth of understanding of mathematical knowledge and application ability, provide a practical scheme for highlighting the instrumentality of mathematics and returning to the essence of mathematics in university mathematics teaching, and has positive enlightenment significance for promoting the reform of university mathematics teaching.