新课标下立体几何画图识图能力培养的研究

发布时间：2018-01-20 16:24

本文关键词： 新课标立体几何画图和识图教学策略　出处：《鲁东大学》2015年硕士论文　论文类型：学位论文

【摘要】：教育部在2003年颁布《普通高中数学课程标准（实验稿）》（以下简称“新课标”），自此中学数学课程改革进入了新阶段。新课标进一步明确了立体几何教学的具体任务，即“培养发展学生的空间想象能力、推理论证能力、运用图形语言进行交流的能力以及几何直观的能力”。新课标教学内容的设计遵循从整体到局部，从具体到抽象的原则，强调借助实物模型，通过整体观察，直观感知，操作确认，思辩论证，度量计算，引导学生多角度、多层次地揭示空间图形的本质；重视合情推理与逻辑推理的结合，注意适度形式化，发展空间想象能力。培养学生几何学习的兴趣，增进学生对几何本质的理解是立体几何教学的关键。画图和识图教学是学习立体几何的基础，是教学的重点和难点。画图能力是把平面图形转成直观形象的过程，识图能力就是把平面或空间图形所代表的图形语言，转化成符号语言和文字语言的能力。从某种意义上说立体几何学习过程就是一个数学识图的过程。学生从平面几何的学习转入立体几何的学习需要过渡，这一过程始于画图和识图教学。因此，研究学生学习立体几何过程中的图形感知、识别障碍，帮助他们克服困难，会有效地促进学生的立体几何学习。本文以培养学生画图识图能力为着眼点，通过加深学生对几何体的点、线、面以及部分与整体的关系的理解，培养学生掌握画图规则，弄清画法原理，训练基本作图能力。通过问卷、测试和访谈对学生立体几何图形感知障碍进行调查，从中我们得到重要信息就是：部分学生画图识图能力薄弱（包括不会画简单的立体图形、画图识图习惯不好、没有直观图和三视图的作图概念等），空间想象能力和空间观念缺失，空间点、线、面之间位置关系的错误判断、初中几何知识的负迁移以及其他画图和识图问题都或多或少地影响立体几何学习。本文在调查研究的基础上对几何教学提出相应的教学策略：立体几何教学要重视基础图形的教学，培养学生的良好画图习惯；通过细心观察周围建筑和身边物体，借助实物模型和动手操作，，培养学生的几何直观能力；运用计算机软件的图形演示功能，增加学生图形感；强化知识的正迁移，增强立体几何的学习能力。
[Abstract]:In 2003, the Ministry of Education promulgated the Mathematics Curriculum Standard of General Senior High School (Experimental draft) (hereinafter referred to as "New Curriculum Standard"). Since then, the middle school mathematics curriculum reform has entered a new stage. The new curriculum standard further clarifies the specific task of solid geometry teaching, that is, "to develop students' ability of spatial imagination and reasoning and argumentation". The teaching content of the new curriculum standard follows the principle of from whole to part, from concrete to abstract, and emphasizes the aid of physical model and the whole observation. Intuitionistic perception, operation confirmation, argumentation, measurement and calculation, guide students to reveal the essence of spatial graphics from different angles and levels; Attach importance to the combination of reasonable reasoning and logical reasoning, pay attention to the appropriate formalization, develop the ability of spatial imagination, and cultivate students' interest in geometry learning. To improve students' understanding of the essence of geometry is the key to the teaching of solid geometry. Drawing and graphics teaching are the basis of learning solid geometry and are the emphasis and difficulty of teaching. Drawing ability is the process of transforming plane graphics into visual images, and the ability to recognize drawings is the graphic language represented by plane or spatial graphics. In a sense, the learning process of solid geometry is a process of mathematical graph recognition. Students need to transition from plane geometry to solid geometry. This process begins with drawing and graphics teaching. Therefore, the study of students in the process of learning three-dimensional geometry graphics perception, identify obstacles, help them overcome the difficulties. This paper focuses on the cultivation of students' ability of drawing graphics, through deepening the students' understanding of the points, lines, surfaces and the relationship between part and whole of geometry. To train students to master drawing rules, understand the principles of painting, train the basic ability of drawing. Through questionnaires, tests and interviews to investigate the perception of students three-dimensional geometry obstacles. From which we get the important information: some students are weak in drawing graphics (including the ability to draw simple three-dimensional graphics, drawing habits, no intuitive drawing and three-view drawing concept, etc.). The spatial imagination ability and the spatial concept lack, the spatial point, the line, the plane between the position relations mistake judgment. The negative transfer of geometry knowledge in junior high school and other drawing and mapping problems have more or less influence on the learning of solid geometry. Based on the investigation and research, this paper puts forward the corresponding teaching strategies for geometry teaching. The teaching of solid geometry should pay attention to the teaching of basic graphics. Cultivate students' good drawing habits; Through careful observation of the surrounding buildings and objects, with the help of the physical model and hands-on operation, the students' geometric intuitive ability is trained. Using the graphic demonstration function of computer software to increase the students' sense of graphics; Strengthen the positive transfer of knowledge and enhance the learning ability of solid geometry.
【学位授予单位】：鲁东大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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