HPM视角下的数学教学设计:以椭圆为例  

Teaching Mathematics from the Viewpoint of HPM: the Case of the Ellipse

作　　者：汪晓勤[1] 王苗[1] 邹佳晨[1] 

机构地区：[1]华东师范大学数学系

出　　处：《数学教育学报》2011年第5期20-23,共4页Journal of Mathematics Education

基　　金：上海市2008年度教育科学研究项目——数学史与数学教育关系研究(B08014)

摘　　要：发生教学原理是HPM视角下数学教学设计的主要理论依据,要求根据重构的历史进行教学.以椭圆为例考察椭圆的历史,并对其进行重构,据此进行教学设计.教学实践表明：HPM视角下的椭圆概念教学创造了学生的学习动机,激发了学生的学习兴趣,对于椭圆焦半径性质的旦德林球推导法,学生在理解上并没有困难;进一步的问卷调查发现：较之教材上的椭圆引入方法,大多数学生更愿意接受HPM视角下的引入方法.因此,有必要进一步深入开展HPM视角下的数学教学研究,开发更多的HPM教学案例,让数学史融入数学教学不再成为一句空话.The teaching design from the viewpoint of HPM is mainly based on the genetic principle,which asks for a topic to be taught according to its reconstructed history.In this paper,the history of the concept of the ellipse is examined and reconstructed.Based on the reconstructed history,the genetic approach to its teaching is designed and practiced in a senior middle school in Shanghai.Senior middle school students＇ opinions on this approach is investigated through a questionnaire survey.It is found that students have no difficulty in understanding the derivation of the focal-radii property of the ellipse by means of the Dandelin sphere and the teaching design based on the history of mathematics is more preferable than that based on the textbook.

关 键 词：椭圆 椭圆的定义 椭圆的方程 发生教学法 旦德林球 

分 类 号：G420[文化科学—课程与教学论]