实变函数问题导向教学设计探索与实践——以《勒贝格测度》为例
Exploration and Practice of Problem-Oriented Teaching Design for Real Variable Function—Taking “Lebesgue Measure” as an Example

数学专业课实变函数由于其概念抽象，学习难度大，所以传统教学法存在教学效果差，学生学不懂的问题。近些年随着教育研究不断深入，问题导向教学法逐渐成为教学改革重要途径之一。本文将基于问题导向教学法的教学理念，以实变函数中勒贝格测度作为教学例子，通过合理设计教学过程，探索实变函数课程的问题导向教学的可能路径，推动实变函数课程的教学改革。
The abstract nature and challenging aspects of real variable functions often lead to inadequate teaching outcomes and difficulties in student comprehension when using traditional teaching methodologies in mathematics courses. Recently, as educational research persists in its advancements, the problem-oriented teaching method has emerged as a significant strategy in teaching reform. This article discusses the application of the problem-oriented teaching philosophy, using Lebesgue measure in real variable functions as a case study. It aims to explore viable pathways for implementing problem-oriented teaching in real variable function courses through carefully designing teaching processes and to advance the reform of teaching these courses.