基于几何画板培养学生动态解决几何问题能力的实践研究

发布时间：2018-01-18 03:19

本文关键词：基于几何画板培养学生动态解决几何问题能力的实践研究　出处：《陕西师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：21世纪是以信息技术为主的技术革命,全球化的经济、网络化的信息、知识化的社会是21世纪的三大特征,国与国之间的经济的竞争,实质上是科学技术的竞争,说到底,是教育的竞争。本文是笔者对数学新课程标准研读后,查阅国内外关于几何画板和几何教学相关文献,以及自身教育实习经历和对初中数学几何教学的调研和具体实践的基础上,对基于几何画板动态解决几何问题的现状进行深一步研究。文中采用理论和实践相结合的方法,主要面向初中数学几何课堂教学,通过问卷调查和案例分析发现,学生在解决几何问题时存在的一些障碍,并对此提出如何借助几何画板工具来具体解决几何实际问题的策略,研究结果主要是为了提高中学生的几何学习兴趣,从而培养初中生用动态观念解决几何问题的能力。本文主要分为六部分：第一部分包括研究背景、国内外相关研究现状、研究目的及意义和研究问题与方法；第二部分是相关概念界定和理论基础；第三部分是初中生解决几何动态问题的现状调查,包含调查目的、调查对象、问卷设计、调查结果及初中生解决几何动态问题的现状；第四部分提出借助几何画板动态解决几何问题的策略；第五部分介绍几何画板动态解决初中几何问题的教学实践；第六部分调查研究几何画板能够激发学生解决几何问题的兴趣,引发学生创造性思维,通过几何画板动态解决几何问题的教学能够让学生更加深刻理解以下几点：(1)借助几何画板模拟整个运动过程,把整个运动过程划分为不同的阶段,即就是将几何动态问题问题转化为静止问题；(2)无论运动过程多么复杂、求什么问题,必须先找出不变量,再求出一些由运动而变化的线段的长,最后与整个几何图形联系起来；(3)若是在直角坐标系中的运动,注意将运动的点的坐标变化的过程转化为线段的长,再与几何图形联系在一起；(4)若是与已知表达式图像结合的,必须恰当借用动点是否在已知题设给定的图像上,动点的坐标是否适合图形解析式等特点；(5)若运动过程能分段研究,寻找合理分段点是解题的关键,正确画出每段的图形,运用分段静止图形的策略来解决动态问题；(6)初中几何问题常用等量关系,较多的是相似、锐角三角函数、线段加减、平行且相等、中心对称,轴对称,旋转,勾股定理等知识点。动态几何问题是中考考试重点题型之一,利用几何画板可以提高学生动态几何问题解决能力,有助于学生空间观念的形成,培养学生的创新意识。
[Abstract]:In 21th century, the technological revolution based on information technology, the global economy, the networked information and the knowledge-based society were the three characteristics of 21th century, the economic competition between countries. In essence, it is the competition of science and technology. In the final analysis, it is the competition of education. And their own educational practice experience and junior high school mathematics geometry teaching research and specific practice on the basis of. This paper makes a further study on the present situation of solving geometric problems dynamically based on geometric drawing board. The method of combining theory and practice is adopted in this paper, which is mainly aimed at the teaching of geometry in junior high school mathematics. Through the questionnaire survey and case analysis, it is found that there are some obstacles in solving the geometric problems, and the strategies of how to solve the practical geometric problems with the help of geometric Sketchpad tools are put forward. The main purpose of this study is to improve the interest of middle school students in geometry learning, so as to cultivate the ability of junior high school students to solve geometric problems with dynamic concepts. This paper is divided into six parts: the first part includes the research background. Domestic and foreign related research status, research purpose and significance, research problems and methods; The second part is the definition of relevant concepts and theoretical basis; The third part is a survey of junior high school students to solve geometric dynamic problems, including the purpose of the survey, survey objects, questionnaire design, survey results and junior high school students to solve geometric dynamic problems; In the 4th part, the strategy of solving geometric problems dynamically with the help of geometric drawing board is put forward. Part 5th introduces the teaching practice of geometric drawing board to solve geometry problems in junior high school dynamically. 6th part of the investigation and research on geometric Sketchpad can stimulate students' interest in solving geometric problems and arouse students' creative thinking. The teaching of dynamic solution to geometric problems can make students understand the following points more deeply. (1) with the help of geometric Sketchpad to simulate the whole process of motion, the whole process of motion can be divided into different stages. That is to say, the geometric dynamic problem is transformed into a static problem. 2) no matter how complex the motion process is, we must first find out the invariants, then find out the length of some lines changed by motion, and finally associate with the whole geometry; 3) if the motion is in the rectangular coordinate system, pay attention to the process of changing the coordinate of the moving point into the length of the line segment, and then associate with the geometric figure; (4) if it is combined with the image of known expression, the characteristics of whether the moving point is set on the given image and whether the coordinate of the moving point is suitable for the graphic analytic formula must be properly used. 5) if the motion process can be divided into sections, finding a reasonable segmentation point is the key to solve the problem, draw the graph of each section correctly, and solve the dynamic problem by using the strategy of segmental static figure. The geometric problems of junior high school are often used in the same quantity relation, the more are similar, sharp angle trigonometric function, line segment addition and subtraction, parallel and equal, center symmetry, axisymmetric, rotation. Dynamic geometry problem is one of the key questions in the middle school examination. The use of geometric drawing board can improve students' ability to solve dynamic geometric problems and help students form the concept of space. Cultivate students' innovative consciousness.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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