立体几何解题能力培养的研究

发布时间：2018-04-28 13:53

本文选题：立体几何 + 高中数学　；参考：《广西师范大学》2016年硕士论文

【摘要】：高中数学中立体几何部分内容是高中数学课程核心内容之一,是培养学生空间想象能力的重要载体之一。立体几何初步是安排在学生刚考入高中的第一个学期学习的,学生习惯用平面几何的思维来学习立体几何,这种讲究空间观念、空间想象能力的几何学习起来较难找到正确有效的学习方法。总之,在立体几何的教学中无论是教师的教还是学生的学都还存在一些需要研究和解决的问题。本文的目的在于试图弄清学生在学习的过程中存在的问题,并分析其中原因,提出相应对策进一步提高学生在立体几何这一模块的解题能力。本文重点通过立体几何的教学实践来研究如何培养高中生的解题能力。本文的研究问题是：通过对少数民族地区县级重点高中高二理科学生的立体几何的解题现状分析,从不同方面寻找解题能力不高的原因是什么?根据这些问题,提出一些切实可行的做法,设计给出一些教学案例。本文主要采用问卷调查法、数据统计分析法、访谈法和教学实验法。2015年9月至10月,在开展立体几何教学实验之前,我们根据学学生在立体几何解题过程中可能出现的几个我们感兴趣问题编制调查问卷,对某中学高二理科501位学生进行调查；并在此基础上编制测试卷,对学生立体几何解题现状进行整理、分类、统计,得出以下结论。学生在立体几何解题时遇到的困难主要是：(1)缺乏立体感,识图、辨图、画图、想图困难,图像表征理解不到位。(2)对定义,定理等基本知识理解模糊不清。(3)割裂学习立体几何整体知识,不成体系,思维缺乏生长点。(4)对问题的等价转化的能力较弱。2015年11月至2015年12月,在立体几何教学过中程进行教学实验,探究怎样在教学过程中贯彻解题能力的培养的方法途径。2016年1月,对本次的教学实验进行总结,对实验获得的数据用SPSS进行数据分析。通过实践表明,本文的研究对一线教师开展立体几何教学有一定的借鉴作用,对学生学习立体几何快速入门,有效提高学习效率,提高学生的解题能力等方面有较好的教学促进作用。
[Abstract]:Solid geometry in senior high school mathematics is one of the core contents of high school mathematics curriculum and one of the important carriers to cultivate students' spatial imagination ability. Stereo geometry was initially arranged for students to study in the first semester of high school. Students are accustomed to learning solid geometry with plane geometry thinking, which stresses the concept of space. It is difficult to find a correct and effective learning method for geometric learning of spatial imagination. In short, there are still some problems to be studied and solved in the teaching of solid geometry. The purpose of this paper is to try to find out the problems existing in the process of students' learning, analyze the reasons, and put forward corresponding countermeasures to further improve the students' ability to solve problems in the module of solid geometry. This paper focuses on the teaching practice of solid geometry to study how to cultivate the ability of solving problems of senior high school students. The research question of this paper is: through the analysis of the present situation of solving the three-dimensional geometry problems of the senior high school students in key senior high schools at the county level in minority areas, what are the reasons why the ability of solving problems is not high from different aspects? According to these problems, some practical methods are put forward and some teaching cases are designed. This paper mainly adopts questionnaire survey, statistical analysis of data, interview and teaching experiment. From September to October 2015, before carrying out the teaching experiment of solid geometry, We compiled a questionnaire based on a few questions of interest that may arise in the course of solving a three-dimensional geometry problem, and conducted a survey of 501 students of science in a middle school, and based on this, we prepared a test paper. The present situation of students' solid geometry problems is sorted, classified and counted, and the following conclusions are drawn. The difficulties encountered by students in solving the problems in solid geometry are mainly the lack of three-dimensional sense, the difficulty of recognizing drawings, distinguishing drawings, drawing pictures, thinking of drawings, and the difficulty of understanding the representation of images. The basic knowledge, such as the theorem, is indistinct. 3) the ability to learn the whole knowledge of solid geometry is not systematic, and the thinking lacks the growing point. (4) the ability of equivalent transformation to the problem is weak. November 2015 to December 2015, The teaching experiment was carried out in the middle course of the teaching of solid geometry, and the way of how to carry out the cultivation of the ability of solving problems in the teaching process was explored. In January 2016, the teaching experiment was summarized, and the data obtained from the experiment was analyzed with SPSS. The practice shows that the research in this paper can be used as a reference for first-line teachers in the teaching of solid geometry, and it can be used as a reference for students to learn solid geometry quickly and improve their learning efficiency effectively. Improving students' ability of solving problems and so on has a better promoting effect in teaching.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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