反例等在实变函数教学中的应用  

Application of Counterexamples and Other Aspects to the Teaching of Real Variable Function

作　　者：苏先锋[1] 李晓萌[1] SU Xianfeng;LI Xiaomeng(School of Mathemetical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2023年第2期83-87,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省教育厅教学研究项目(2020jyxm1697);安徽省高校自然科学基金项目(KJ2020A1198)。

摘　　要：实变函数是数学类专业最重要的专业课程之一。为提高该课程教学效果,充分发挥其育人功能,针对实变函数教学中普遍存在学生对基础知识理解不透彻、课程内涵建设不深入、学习途径单一等问题开展教学应用探索。首先,对实变函数中的反例进行分类,帮助学生更加深刻地理解基础知识。其次,增强实变函数课程的内涵建设,发挥其在提升学生数学素养和综合素养中的积极作用。最后,探索移动学习在实变函数教学中的应用,使其成为课程学习的新途径之一。教学实践表明,反例、内涵建设和移动学习在实变函数教学中发挥重要作用,取得良好的教育教学效果。Real variable function is one of the most important courses in mathematical major.In order to im⁃prove the teaching effect of this course and give full play to its educational function,this paper studies the teaching application of the problems commonly existing in the teaching of real variable function,such as stu⁃dents′incomplete understanding of basic knowledge,insufficient construction of curriculum connotation and single learning path.Firstly,the counterexamples of real functions are classified to help students understand the basic knowledge more deeply.Secondly,the connotation construction of the course is strengthened to play its positive role in improving students′mathematical literacy and comprehensive literacy.Finally the ap⁃plication of mobile learning in the teaching of real variable function is studied and it becomes one of the new path of course learning.The teaching practice shows that the counterexamples,connotation construction and mobile learning play an important role in the teaching of real variable function and achieve good teaching ef⁃fect.

关 键 词：实变函数 反例 LEBESGUE积分 移动学习 

分 类 号：O174[理学—数学]