浅谈大学数学基础课的三个易错知识点  

A Brief Discussion on Three Fallible Knowledge Points in Basic University Mathematics Curriculum

作　　者：沈莞蔷[1] 陈晶[1] SHENWanqiang;CHEN Jing

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《科教文汇》2021年第23期63-66,共4页Journal of Science and Education

基　　金：国家自然科学基金(61772013、61973137);江南大学金课建设研究专项基金(JG2019059)资助。

摘　　要：该文浅谈了大学数学基础课的三个易错知识点——"特征向量不为零""二重积分换元要乘以雅克比行列式"和"多个概率公式的记忆"。它们易出错的现象表明,学生对其本质理解不深刻。对特征向量,从其定义、性质和应用三个方面,阐述了它表示方向的本质,因此不能为零;对乘以雅克比行列式,从例子入手,结合生活中的实际应用,阐述其统一规范的本质;对概率公式,从直观表示的文氏图入手,结合不同的公式以及例题,阐述了概率的度量本质。对这些本质的探讨,与客观的数学概念、定理、公式中的主观因素紧密联系,为加深学生对这些知识点的理解、降低他们的错误率提供帮助。This paper briefly discusses the three fallible knowledge points in university mathematics basic curriculum:“eigenvector is not zero”,“multiplying a Jacobian’s determinant is needed in substitution for double integrals”and“memorizing several probability formulas”.Their error-prone phenomenon means that students’understanding for them is not deep enough.For eigenvector,its essence of presenting a direction is expounded from its definition,property and application,so it cannot be zero;for multiplying a Jacobian’s determinant,its essence of unifying regulations is expounded from an instance combined with some practical applications in life;for probability formulas,probability’s essence of measurement is expounded from the intuitive Venn’s diagram combined with different formulas and an example.The discussions for the essences closely connected with the subjective factors in the objective mathematical concepts,theorems and formulas will help to deepen students’understanding and reduce their error rate of the two knowledge points.

关 键 词：大学数学 特征向量 雅克比行列式 概率 

分 类 号：G642[文化科学—高等教育学]