问题驱动的协方差与相关系数的概念构建  

Concept Construction of Problem-Driven Covariance and Correlation

作　　者：陶红 徐耀坤 侯臣平[1] TAO Hong;XU Yao-kun;HOU Chen-ping(College of Sciences,National University of Defense Technology,Changsha,Hunan 410073,China;College of Electronic Science and Technology,National University of Defense Technology,Changsha,Hunan 410073,China)

机构地区：[1]国防科技大学理学院,湖南长沙410073 [2]国防科技大学电子科学学院,湖南长沙410073

出　　处：《教育教学论坛》2022年第36期52-55,共4页Education And Teaching Forum

基　　金：2020年度国家自然科学委青年基金项目“视图动态变化时的多视图学习方法与应用研究”(62006238);2020年度国家自然科学委青年基金项目“计算时间域鬼成像目标信息获取能力研究”(62001484)。

摘　　要：数学概念对于课程知识体系理解具有重要作用。数学概念教学重在让学生学会构建新概念,而不是单纯学习新概念。以概率论与数理统计中协方差与相关系数两个概念为例,遵循“以问题结构推进教学”的原理,通过国内生产总值与军费支出的关系分析实际案例,提出随机变量关系描述的问题,采用逆向推理得到协方差的定义。在此基础上,进一步深化研究如何描述随机变量关系的强弱及所研究的关系是何种关系,通过一系列层层递进、步步深入、具有内在逻辑联系的问题结构,逐步构建相关系数的定义与内涵。Mathematical concepts play an important role in the understanding of curriculum knowledge system.The teaching of mathematical concepts should focus on making students learn to “constructing new concepts”rather than “learning new concepts”. Based on the principle of problem-driven teaching, this paper presents the concept construction process of covariance and correlation. Concretely, via the case of analyzing the relationship between GDP and military spending, the question of describing the relationship between random variables is raised.Then the concept of covariance is obtained by inverse inference. On this basis, the problems of how to describe the relationship strength degree and what the relationship is are further explored. These problems form a progressive and logically connected problem structure, which can help to build the definition and connotation of covariance and correlation.

关 键 词：协方差 相关系数 问题驱动 概念教学 

分 类 号：O175.14[理学—数学] G642.0[理学—基础数学]