初中生几何证明阅读理解水平的调查研究

发布时间：2018-07-05 10:03

本文选题：初中生 + 几何证明　；参考：《东北师范大学》2017年硕士论文

【摘要】：几何教学是数学教学中的一个重要组成部分,几何内容也是初中数学课程的主要内容之一。几何课程内容的改革,历来都是国内外数学教育改革的热点和焦点问题。当前对几何证明理解的实证研究,主要集中在学生对所给证明问题的反应及学生依据教师或他们自己的观点对不同证明方法的选择上,而本文则是通过几何证明的阅读理解这一角度来研究此类问题,从中发现学生在几何证明阅读理解中存在的问题,并提出相应的教学建议。本文利用杨凯琳教授的几何证明阅读理解模型,将学生的几何证明阅读理解划分为四个水平,即表层理解水平、识别元素理解水平、串联元素理解水平和综合性理解水平,并根据各水平的标准,编制测试问卷,通过对初二学生的调查问卷结果统计及分析,得出如下结论:1.学生的几何证明阅读理解水平表现出层级递减趋势。2.学生对于几何相关知识的理解大多停留在工具性理解,只有少数学生对所学知识能达到关系性理解。3.学生在几何证明阅读理解中存在的问题主要有以下几点:(1)学生审题能力有待加强,只能知道题目中明确给出的已知条件,而不会挖掘隐含条件;更换论题,将题目中的已知条件看成特殊条件;还有漏题的情况。(2)在学习几何基本图形的概念和性质时,理解不够深刻,常停留在表面,对于一些基本图形的性质掌握不牢,在做题时不能做到灵活应用,遇到基本图形时,没有第一时间在头脑中反映出其对应的性质。(3)在证明过程中犯逻辑关系错误。在证明过程中应用判定定理时,易忽略其成立的条件;用未证明的论据来证明论题。(4)书写证明过程时,不完整,不能够将有关的推理组合成一个完整的证明过程。4.针对研究中发现的问题,给出教师如下建议:(1)加强几何基本图形的教学;(2)加强对学生审题、识图和作图能力的培养;(3)重视对学生逻辑思维能力的培养;(4)加强几何证明过程书写规范的教学。
[Abstract]:Geometry teaching is an important part of mathematics teaching, and geometry content is also one of the main contents of mathematics course in junior high school. The reform of geometry course content has always been the hot spot and focal point of mathematics education reform at home and abroad. The current empirical research on the understanding of geometric proof mainly focuses on the students' response to the problem of proof given and the choice of different methods of proof according to the teachers'or their own views. This paper studies this kind of problems from the angle of reading comprehension of geometric proof, finds out the problems existing in the reading comprehension of geometric proof, and puts forward corresponding teaching suggestions. In this paper, using Professor Yang Kailin's geometric proof reading comprehension model, students' geometric proof reading comprehension is divided into four levels, namely, surface level, recognition level, serial element level and comprehensive level. According to the standards of each level, the questionnaire is compiled. Through the statistics and analysis of the results of the questionnaire, the following conclusions are drawn: 1. Students' geometric proof shows that the level of reading comprehension shows a decreasing trend of hierarchy. 2. Most of the students' understanding of geometric related knowledge lies in the instrumental understanding, and only a few students can reach the relational understanding of what they have learned. The main problems in reading comprehension of students in geometric proof are as follows: (1) the students' ability to examine questions needs to be strengthened, they can only know the known conditions clearly given in the questions, not the hidden conditions, and change the topics. The known conditions in the subject are regarded as special conditions; there are also missing problems. (2) in learning the concepts and properties of basic geometric figures, the understanding is not deep enough and often stays on the surface, and the properties of some basic graphics are not well grasped. It can not be used flexibly when it comes to problems. When it comes to basic graphics, it does not reflect its corresponding properties in the mind at the first time. (3) mistakes in logic relations are made in the process of proof. It is easy to ignore the condition that the judgment theorem is applied in the process of proof, and to prove the thesis with the unproved argument. (4) when writing the proof process, it is not complete and can not combine the relevant reasoning into a complete proof process. In view of the problems found in the study, the following suggestions are given: (1) to strengthen the teaching of basic geometric graphics; (2) to strengthen the examination of students' questions. (3) pay attention to the cultivation of students' logical thinking ability; (4) strengthen the teaching of the writing criterion of geometric proof process.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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