初中数学中的数形结合研究

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摘要数学思想方法就是数学中所蕴含的一般思维规律，具有高度的概括性和抽象性，难于一般知识的理解和掌握。初中学习中，主要的思想方法包括数形结合思想、函数思想、化归思想、方程思想等等。素质教育的提出对学生的能力有了更高的要求，此时在教学中思想方法的渗透就尤为重要。数学思想方法的教学是数学教学的有机组成部分。渗透数形结合的思想也是课标要求之一，如何让学生具有数形结合的思维能力，哪些数学知识内容包含着数形结合的思想，是本文需要讨论的问题。本文研究的基本内容包括：初中数学思想方法教学现状（以个人经历为主）；初中数学思想方法教学中存在的问题；初中数学中数形结合思想渗透的内容及举例；如何在初中数学中渗透数形结合思想；初中数学数形结合思想课程教学方案设计。拟解决的主要问题包括：初中数学中数形结合思想的运用的系统分类；如何在实际课堂中渗透数形结合思想；如何运用现在教育技术辅助思想渗透。本文采用的研究方法有：文献研究法；调查法；比较分析法；跨学科研究法；观察法。47611

The general thinking of mathematics method of thinking in mathematics it is that, with a high degree of generality and abstraction, it is difficult to understand and grasp the general knowledge. Junior high school learning, the main thinking methods including thought, combination of number and shape function, transformation, equation thought etc.. Put quality education ability of students have higher requirements, it is particularly important to penetrate the teaching thought and method. Mathematics thinking method teaching is an organic part of mathematics teaching. One of the infiltration number shape union thought and curriculum requirements, how to make students have the number shape union thinking ability, mathematical knowledge which contains several form combining ideas, is the need to discuss the issue. The basic content of this paper includes: teaching situation in junior high school mathematics thinking method (based on personal experience based); there are junior high school mathematics teaching method in junior middle school mathematics problems; the combination of Ideological Penetration of the content and examples; how to infiltrate the number shape union thought in mathematics of junior high school; the junior middle school mathematics “the combination of number and shape” teaching design of ideological course. Including the main problems to be solved: junior high school mathematics “the combination of number and shape” thinking of using the classification system; how to infiltrate the number shape union thought in the actual classroom; how to use the modern educational technology assisted ideological penetration. The research methods used in this paper are: literature study; investigation; analysis; cross disciplinary research method; observation method.

毕业论文关键词：数形结合; 思想渗透; 教学实践

Keyword: The number shape union thought; permeability; teaching practice

1初中数学数形结合教学现状5

2 文献资料整理及感想5

3 初中数学中的数形结合思想（内容及典例）6

3.1数与代数6

3.2图形与几何8

3.3 概率与统计9

3.4 综合与实践9

4 如何在初中数学中渗透数形结合思想10

4.1思想方法渗透需要教师的耐心和自身教学技能的“修炼”11

4.2应加强数学定理的探索和证明11

4.3合理运用教育学和心理学知识11

1 初中数学数形结合教学现状（个人经历为主）

从2014年9月19日开始，我在杭州市桐庐县叶浅予中学进行了为期三个月的教学实习。我实习的班级是初二（4）班（此年段一共六个班）。在这段时间里，他们学习的内容是不等式和三角形部分（包括全等三角形，等腰三角形，直角三角形等）。我听了不下50节数学课，其中包括我的导师平时教学活动时上的课（即这个班的数学老师兼班主任）、几位优秀老师上的市公开课、还有我的同学（实习生）上的课。就数形结合思想而言，我想从这三类不同主体，不同情境下的课堂活动来具体描述。