高中生学习导数及其应用时的困难点研究

发布时间：2018-05-14 08:53

本文选题：导数 + 困难点　；参考：《东北师范大学》2015年硕士论文

【摘要】：“导数及其应用”这一章是高中数学的重要组成部分,同时又是数学分析中微积分的核心内容之一。在许多数学之外的其他自然科学领域中,导数都扮演着重要的角色,起着至关重要的作用。在学习导数知识的过程中,学生可以逐渐体会到“导数及其应用”中所包含的很多重要的数学思想与方法,认识到导数在研究函数性质时的工具作用。在新一轮的课程改革中,加大了对“导数及其应用”的考察力度和要求。我在实际教学中发现：一部分高中生在学习“导数及其应用”时产生了不同程度的理解和运用方面的困难。本文的主要研究目的是调查并研究高中生在学习“导数及其应用”时所产生的困难点有哪些,分析产生这些困难点的具体原因,探究合理的学习“导数及其应用”的教学模式,总结出克服这些困难点的方法和策略以及怎样克服这些困难点,效果怎样。本文研究的类别是“导数及其应用”,面对的群体是高中阶段在学习“微积分”时存在不同程度困难的学生。这部分群体是指智力在正常范围内,在高中学段接受学科教育的,由多种学习因素而引起的在学习“导数及其应用”较为长久的接受不良的学生。表现为课堂上不能跟住教师的思路,无法掌握课堂上所学的知识,在应用导数的知识解决数学中的相关问题时,表现为不灵活或是无法顺利解决问题。本文重点采用调查问卷法,通过分析学生在测试(一)中出现的问题和错误,分析研究学生在学习“导数及其应用”时遇到的困难。困难类型主要有：一是数学概念理解不透彻；二是公式和定理记忆有偏差、运用不得当；三是解题步骤不规范；四是解题方法和步骤不明确；五是知识迁移能力差欠缺必要的数学思想与解题能力。本文结合调查问卷总结出高中生学习“导数及其应用”产生困难的原因,总结出困难类型,并提出相应的教学建议和策略,对比改进前和改进后的效果并作出分析。
[Abstract]:Derivative and its Application is an important part of high school mathematics, and also one of the core contents of calculus in mathematical analysis. Derivative plays an important role in many fields of science other than mathematics. In the process of learning derivative knowledge, students can gradually realize many important mathematical ideas and methods contained in "derivative and its application", and realize the instrumental role of derivative in studying the nature of function. In the new round of curriculum reform, the investigation of derivative and its application has been strengthened. In practical teaching, I find that some senior high school students have some difficulties in understanding and applying "derivative and its application". The main purpose of this paper is to investigate and study the difficulties in learning "derivative and its application" in senior high school students, to analyze the specific causes of these difficulties, and to explore the teaching mode of "derivative and its application". The methods and strategies of overcoming these difficulties are summarized. The category of this paper is "derivative and its application", and the group is the students who are difficult to learn "calculus" in senior middle school. This part of the group refers to students whose intelligence is in the normal range and who receive subject education in the senior middle school, which is caused by a variety of learning factors, and the students who have accepted the derivative and its application in learning for a long time. It can not follow the teacher's thinking in class, can not master the knowledge learned in the classroom. When applying derivative knowledge to solve the related problems in mathematics, it is shown as inflexible or unable to solve problems smoothly. By analyzing the problems and errors of students in the test (1), this paper focuses on the questionnaire method, and analyzes the difficulties encountered by students in learning "derivative and its application". The main types of difficulties are: first, the mathematical concept is not fully understood; second, the formula and theorem memory is biased, the application is not appropriate; third, the steps of solving the problem are not standardized; the fourth, the methods and steps of solving the problem are not clear; Fifth, the poor ability of knowledge transfer lacks the necessary mathematical thought and ability to solve problems. Based on the questionnaire, this paper summarizes the causes of difficulties in learning "derivative and its application", summarizes the types of difficulties, and puts forward corresponding teaching suggestions and strategies, and compares the effects before and after the improvement and makes an analysis.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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