基于几何画板的高中数学中轨迹问题探究

发布时间：2018-05-28 19:27

本文选题：几何画板 + 圆锥曲线　；参考：《延边大学》2015年硕士论文

【摘要】：高中数学中的轨迹问题一直是困扰广大师生的难题,无论是教师的教亦或是学生的学都存在着困难,尤其涉及到有关动态性以及抽象性的问题更是难以攻克。几何画板利用“几何元素在动态状态下保持几何关系间的不变性”这一原理,将抽象的、动态的数学模型直观的呈现在学生面前,给学生视觉的冲击,将抽象问题问题直观化,帮助学生更深刻的探究问题。本文以建构主义理论、信息加工学习理论、几何直观、记忆表象和数形结合思想为理论基础,通过文献综合法、比较法以及问卷调查法来研究如何在解决圆锥曲线的轨迹问题中应用几何画板。学生通过观察几何画板在运动中保持不变的数学规律,在头脑中动态性的建构轨迹生成。本文以新课程人教A版选修2-1为参考,制作了有关椭圆、双曲线、抛物线的相关课件,通过设计如何在教学中引入几何画板,关键是使学生亲自动手操作几何画板来绘制轨迹的生成,从而在学生的头脑中建构动态性思维过程。通过结合某市高中二年级学生及教师对几何画板的应用情况的调查结果,表明多数学生对教师应用几何画板教学态度积极,在操作过程中激发了学生的主体意识,提高了解决问题的能力；针对高中数学解析几何中的轨迹问题的解决做出了具体的阐述,学生可以根据文中的具体操作制作课件,从而观察到轨迹的动态性生成。研究过程中也发现了一些不足,对于初步接触通过几何画板来观察轨迹生成,对培养学生的动态性思维有一定的限制；对于初步接触通过几何画板来观察轨迹生成,对培养学生的动态性思维有一定的限制；对教师在几何画板的操作方面存在较高要求。针对研究过程中发现的不足,提出如下建议：合理调控时间,教师在教授重点、难点后可以试着让学生亲自动手操作几何画板；学校应该组织数学教师定期的学习和培训；开设数学实验课。几何画板不能代替学生思考,但是可以帮助学生更好的思考,通过直观的演示,从本质上看待数学问题,通过观察运动的图形来发现其中不变的几何规律。
[Abstract]:The problem of trajectory in high school mathematics has always been a difficult problem for teachers and students. It is difficult for both teachers and students to learn. Especially, it is difficult to overcome the problem of dynamic and abstract. The geometric sketchpad uses "geometric elements to keep the invariance between geometric relationships in dynamic state". In this paper, the theory of constructivism, the theory of information processing, the geometric intuition, the memory table and the combination of numbers are used as the theoretical basis and the literature synthesis method, which is based on the theory of constructivism, information processing and learning, geometric intuition, memory and number form. The comparison method and the questionnaire survey method are used to study how to apply the Geometric Sketchpad in the solution of the trajectory of the conical curve. By observing the constant mathematical rules of the geometric sketchboard in the movement, the dynamic construction trajectory in the mind is generated. This paper makes a reference to the selection of 2-1 of the new curriculum human teaching A edition, and makes the ellipse, hyperbola and throwing. Through the design of the geometric sketchboard in the teaching, the key is to make the students personally manipulate the geometric drawing board to create the trajectory, so as to construct the dynamic thinking process in the students' mind. By combining the investigation results of the application of the two grade students and teachers to the Geometric Sketchpad in a high school in a city, the results show that Most of the students have a positive attitude to the teaching of geometric sketchboards. In the process of operation, the students' subjective consciousness is aroused and the ability to solve the problem is improved. The solution of the trajectory problem in the analytical geometry of high school mathematics is explained. The students can make the courseware according to the specific operation in the text, thus the track is observed. In the process of dynamic formation, some shortcomings have also been found in the research process. For preliminary contact to observe trajectory generation through geometric sketchpad, there is certain limitation on the training of students' dynamic thinking. There are high requirements for the operation of the sketchboard. In view of the deficiencies found in the research process, the following suggestions are put forward: reasonable control of time, teachers in the teaching of emphasis, the difficulties can be tried to let students personally manipulate the geometric sketchboard; the school should organize regular learning and training of mathematics teachers; set up a mathematical experiment course. Geometric Sketchpad can not. Instead of thinking about the students, they can help students to think better, look at the mathematical problems in essence through a visual demonstration, and discover the invariable geometric rules by observing the graphics of the movement.
【学位授予单位】：延边大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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