正态分布的教学设计:从历史中寻找学生认知生长点  

The Instructional Design of Normal Distribution: Looking for the Growing Point of Students’ Cognition from History

作　　者：李玲 徐章韬[2] LI Ling;XU Zhang-tao(Tong’an No.1 High School of Fujian,Fujian Xiamen 361100,China;School of Mathematics and Statistics,Central China Normal University,Hubei Wuhan 430079,China)

机构地区：[1]福建省同安第一中学,福建厦门361100 [2]华中师范大学数学与统计学学院,湖北武汉430079

出　　处：《数学教育学报》2023年第2期12-17,共6页Journal of Mathematics Education

基　　金：华中师范大学中央高校基本科研业务费项目——对标师范类专业认证标准的持续改进监测体系的研制与实践研究(CCNUTEI 64/10/202311:52:19 AM122021-05)。

摘　　要：文献研究的结果支持“HPM与PME的协调有助于解决概率统计教学难题”的观点.正态分布的发现源于棣莫弗的二项概率逼近工作,但直到高斯提出正态误差的理论后,正态分布才被赋予概率分布的身份,并由测量误差的分布推广到其它数据的分布而引起人们的重视.正态分布课例体现了真善美,体现了HPM、PME与技术的融合,PME与技术对数学史的加工使数学史更好地服务于教学.The results of literature research support the view that the coordination of HPM and PME is helpful to solve the problem of probability and statistics teaching.The discovery of normal distribution originated from de Moivre’s binomial probability approximation work,but it was not until Gauss proposed the theory of normal error that the normal distribution was given the identity of probability distribution,and attracted people’s attention from the distribution of measurement error to the distribution of other data.The normal distribution lesson reflects the truth,goodness and beauty,and reflects the integration of HPM,PME and technology.The processing of history of mathematics by PME and technology enables history of mathematics to serve teaching better.

关 键 词：正态分布 数学史与数学教育 数学教育心理 误差曲线 高尔顿板 

分 类 号：G632[文化科学—教育学]