证明过程关乎成败--切比雪夫不等式教学技巧浅析  

The Proof Process is about Success or Failure--A Study of Teaching Skills on Chebyshev's Inequality

作　　者：李俊海[1] LI Junhai(College of Science,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]河南工业大学理学院,河南郑州450001

出　　处：《高等数学研究》2024年第4期32-34,47,共4页Studies in College Mathematics

基　　金：河南工业大学教育教学研究项目(lxyjy202213).

摘　　要：切比雪夫不等式是证明大数定律的引理,也是估计概率取值范围的重要工具.由于课时限制,课堂上往往略讲或删除它的证明过程,且只讲理论用途而忽视其应用价值.针对删除证明过程这一不良现象,剖析了证明过程的重要性和必要性,并给出合理的授课思路、讲解用语和注意事项.在讲授应用技巧时,建议采用案例对比方法,因为它能突出应用价值并衬托后继教学内容的重要性.最后,通过多年教学效果调查数据,证明了这些教学技巧的合理性.Due to limited class hours,the proof process for Chebyshev's inequality is often omitted or skipped in class,and its practical applications are overlooked in favor of emphasizing its theoretical aspects.To address this issue,the importance and necessity of including the proof process are analyzed,along with providing teaching strategies,explanation techniques,and precautions.When teaching application skills,it is recommended to use the case comparison method,as it highlights the practical value and underscores the significance of subsequent content.Finally,the effectiveness of these teaching techniques is demonstrated through survey data collected over several years.

关 键 词：切比雪夫不等式 教学技巧 理论证明 案例对比方法 

分 类 号：G642[文化科学—高等教育学]