对高三学生无限、极限理解的调查研究

【作者】 魏琴；

【导师】 陈月兰；

【作者基本信息】 华东师范大学 ， 课程与教学论， 2004， 硕士

【摘要】 “无限”是人们日常语言中一个常用的词汇，同时“无限”也是数学中一个重要的概念，但“无限”在日常语言中的含义与数学中的含义却是不一致的，这就可能导致学生在学习涉及“无限”的一些数学概念时产生一些错误的理解。本文就是在这个背景下进行的一项调查研究，选取的数学概念是极限概念，调查主要分为以下两部分内容： 一是通过对学生的书面回答和访谈获得的信息来分析学生对“∞”的理解，主要分两方面来进行：一方面是调查学生赋予“∞”的含义；另一方面是调查学生解决?这一类极限的方法，并考察这两者之间的联系。 二是通过学生对函数极限概念与对和的极限的理解来分析他们对动态极限概念的理解模式。通过学生的书面回答，发现学生理解函数极限概念的模式是：极限接近但不可能到达、极限是可到达的、极限是近似值和极限是精确值：通过访谈，发现学生理解和的极限的模式是：极限是非常接近、极限是近似值、极限是精确值和极限小于精确值。其中极限是非常接近但不可能达到是学生理解动态极限概念的普遍模式。 接下来本文分析了影响学生理解动态极限概念的两个因素。一是语言，即动态极限概念中出现的“无限接近”；二是无限，即学生难以区别数学中无限大和有限之间的含义、只接受潜无限而否认真无限。 在论文的最后部分，向教师提出了在极限教学时的一些建议，并指出了论文的不足之处和进一步研究的课题。更多还原

【Abstract】 The meaning of infinity as a common vocabulary in our everyday life and an important notion in mathematical fields are quite different, which suggest it’s difficult for students to understand some mathematical concepts involving infinity. This study focuses on informal notion of limit and infinity hold by 401 senior school students:1. By investigation and interview, it was found that students understand mainly "" in the lim f(x) as a large number and potential infinity, and the role those understandingsplay in their solutions of limit problems s as lim f(x).2. By investigation and interview students’ informal models that invoked in giving meaning to the function limit and sum limit, it was found that the former informal models involves limit an unreachable-. limit as reachable limit as precise value and limit as approximation ,and the latter involves limit as closeness limit as precise value limit as approximation and limit precise value, of these models, limit as closeness and unreachable is most common misunderstanding . These informal models arose and developed depend on informal meanings of technical language and conceptual difficulty of the notion of infinity.On the basis of findings mentioned above, some advice are given on limit teaching, it is advisable for teachers to pay attention to appropriate expression of infinity. Finally the limitations of this paper and further study about this topic are pointed out.更多还原