数形结合思想方法的有效策略研究.doc
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数形结合思想方法的有效策略研究,11000字24页目录第一章 引言1.1问题的提出51.2研究的目的和意义61.3研究的思路和方法7第二章 国内外数形结合思想方法研究综述2.1国内数形结合思想研究82.2国外数形结合思想研究92.3研究现状的思考9第三章 数形结合思想方法3.1数、形的发展及其特点113.2数形结合思想概...
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数形结合思想方法的有效策略研究
11000字 24页
目 录
第一章 引言
1.1 问题的提出……………………………………………………………………5
1.2 研究的目的和意义……………………………………………………………6
1.3 研究的思路和方法……………………………………………………………7
第二章 国内外数形结合思想方法研究综述
2.1 国内数形结合思想研究………………………………………………………8
2.2 国外数形结合思想研究………………………………………………………9
2.3 研究现状的思考………………………………………………………………9
第三章 数形结合思想方法
3.1 数、形的发展及其特点………………………………………………………11
3.2 数形结合思想概念及其特点…………………………………………………11
3.3 数形结合分类及其特点………………………………………………………12
第四章 数形结合思想方法教学策略的举例
4.1 由数化形………………………………………………………………………15
4.2 以形助数………………………………………………………………………17
4.3 数形结合思想的升华----无字证明…………………………………………19
致谢………………………………………………………………………………………23
参考文献…………………………………………………………………………………24
摘要 数学是一门研究数量关系和空间形式的科学。数学的研究对象大体分成两类，表示数量关系的数，和表示空间形式的形。在数学上，数是代数学、分析学的研究对象，形则是几何学的研究对象。虽然它们研究的内容和使用的方法各有区别，但中间没有不可逾越的鸿沟。学生从“数”角度理解“形”，从“形”角度理解“数”对数学学习有着重要的作用。
数形结合思想方法的实质是把抽象的数学语言和形象直观的几何图形联系在一起，使代数的抽象概念和几何图形具体形象相互转化、联系、渗透，让复杂的数学问题简单化，更快速、更便捷解决数学问题。它是富有数学特点的信息转换，是一柄双刃的解题利剑。
在分析数学结合思想方法实质的基础上提出：由数化形，根据数量关系画出图形，通过对图像的观察、分析来解决数学问题的教学策略。以形助数的策略，其实质是图形运用数字计算将问题表达精确。同时研究了“数形结合”思想方法的升华----无字证明，它以鲜明的直观和简捷的表达形式使复杂问题更容易解决、理解，让数学变得更加有吸引力、更充满活力。对培养学生的创新精神，开拓学生思维有着积极的意义。
关键词： 数形结合 思想方法 教学策略 无字证明
based on methodology of number shape combination ，
study on effective strategies
Abstract Mathematics is the study of quantitative relations and spatial forms of science.The research object of mathematics were divided into two groups, showing the number of relations, and representation of spatial form of shape.In mathematics, the number is the research object algebra, analysis, geometry shape is the object of study.Although the content and methods of their research were different, but there is no impassable gulf between.The students from "number" perspective "shape", from the "shape" perspective "number" on the mathematics learning plays an important role.
The essence of methodology of number shape combination is the abstract mathematical language and visual image geometry together,The abstract concepts and geometric algebra specific image transformation, contact, permeability, let the complex mathematical problems easier, faster, and more convenient to solve mathematical problems.It is the conversion of information rich features of mathematics, is a double-edged sword of problem solving.
In the analysis of mathematics thinking method combining is proposed based on a number of essential: shape, according to the relationship between the number of draw graphics, to solve mathematical problems through observation, analysis of the image of the teaching strategies. To help shape strategy, its essence is the use of digital computing the precise expression pattern problem. At the same time, the "combination" thought method sublimation --- proofs without words, it is to express the form vivid intuitive and simple to complex problem is easier to solve, understanding, make mathematics more attractive, more full of vitality. The cultivation of students' innovative spirit, has the positive significance to develop the students' thinking.
Key word: combination of number and form thoughtway instructional strategies
Proofs without words
11000字 24页
目 录
第一章 引言
1.1 问题的提出……………………………………………………………………5
1.2 研究的目的和意义……………………………………………………………6
1.3 研究的思路和方法……………………………………………………………7
第二章 国内外数形结合思想方法研究综述
2.1 国内数形结合思想研究………………………………………………………8
2.2 国外数形结合思想研究………………………………………………………9
2.3 研究现状的思考………………………………………………………………9
第三章 数形结合思想方法
3.1 数、形的发展及其特点………………………………………………………11
3.2 数形结合思想概念及其特点…………………………………………………11
3.3 数形结合分类及其特点………………………………………………………12
第四章 数形结合思想方法教学策略的举例
4.1 由数化形………………………………………………………………………15
4.2 以形助数………………………………………………………………………17
4.3 数形结合思想的升华----无字证明…………………………………………19
致谢………………………………………………………………………………………23
参考文献…………………………………………………………………………………24
摘要 数学是一门研究数量关系和空间形式的科学。数学的研究对象大体分成两类，表示数量关系的数，和表示空间形式的形。在数学上，数是代数学、分析学的研究对象，形则是几何学的研究对象。虽然它们研究的内容和使用的方法各有区别，但中间没有不可逾越的鸿沟。学生从“数”角度理解“形”，从“形”角度理解“数”对数学学习有着重要的作用。
数形结合思想方法的实质是把抽象的数学语言和形象直观的几何图形联系在一起，使代数的抽象概念和几何图形具体形象相互转化、联系、渗透，让复杂的数学问题简单化，更快速、更便捷解决数学问题。它是富有数学特点的信息转换，是一柄双刃的解题利剑。
在分析数学结合思想方法实质的基础上提出：由数化形，根据数量关系画出图形，通过对图像的观察、分析来解决数学问题的教学策略。以形助数的策略，其实质是图形运用数字计算将问题表达精确。同时研究了“数形结合”思想方法的升华----无字证明，它以鲜明的直观和简捷的表达形式使复杂问题更容易解决、理解，让数学变得更加有吸引力、更充满活力。对培养学生的创新精神，开拓学生思维有着积极的意义。
关键词： 数形结合 思想方法 教学策略 无字证明
based on methodology of number shape combination ，
study on effective strategies
Abstract Mathematics is the study of quantitative relations and spatial forms of science.The research object of mathematics were divided into two groups, showing the number of relations, and representation of spatial form of shape.In mathematics, the number is the research object algebra, analysis, geometry shape is the object of study.Although the content and methods of their research were different, but there is no impassable gulf between.The students from "number" perspective "shape", from the "shape" perspective "number" on the mathematics learning plays an important role.
The essence of methodology of number shape combination is the abstract mathematical language and visual image geometry together,The abstract concepts and geometric algebra specific image transformation, contact, permeability, let the complex mathematical problems easier, faster, and more convenient to solve mathematical problems.It is the conversion of information rich features of mathematics, is a double-edged sword of problem solving.
In the analysis of mathematics thinking method combining is proposed based on a number of essential: shape, according to the relationship between the number of draw graphics, to solve mathematical problems through observation, analysis of the image of the teaching strategies. To help shape strategy, its essence is the use of digital computing the precise expression pattern problem. At the same time, the "combination" thought method sublimation --- proofs without words, it is to express the form vivid intuitive and simple to complex problem is easier to solve, understanding, make mathematics more attractive, more full of vitality. The cultivation of students' innovative spirit, has the positive significance to develop the students' thinking.
Key word: combination of number and form thoughtway instructional strategies
Proofs without words
