数形结合思想方法在解题中的应用.doc

数形结合思想方法在解题中的应用

13300字 36页

摘要
数学思想方法作为数学知识内容的精髓，是数学的一种指导思想和普遍适用的方法。它能使人们领悟数学的真谛，懂得数学价值，学会数学地思考和解决问题。它能把知识的学习、能力的培养和智力的发展有机地结合起来。因此数学思想方法作为数学教育的重要内容，己日益引起人们的注意。
加强数学思想方法教学，能使学生从盲目的学习转化为有意义的学习，从题海中解脱出来，真正做到举一反三，触类旁通，大大缩短了学生在黑暗中摸索的过程，真正提高学生的学习效益，做到“高分高能”。数学是研究空间形式和数量关系的科学，因此数形结合思想是重要的数学思想方法之一，从数的概念的形成和发展，到微积分的产生及现代数学各分支学科的形成，都是与数形的完美结合分不开的。“数”与“形”也是贯穿整个中小学数学教材的两条主线，“数”与“形”的相互转化、结合更是解题的重要方法。从更高的理论层次总结数形结合思想的形成与发展，探索数形结合思想方法在解题中的应用。试图给予数形结合思想方法一个较为完整的诠释，并给其它数学思想的研究提供一个范例。本文主要从以下几个方面进行阐述：（1）研究意义与背景，国内外情况，方法与思路（2）理论依据（3）以形助数在奥数，高考中的广泛应用，以数辅形的应用（4）数形结合思想方法自身的意义与提高学生运用此种方法解题能力的方法

关键词

数学思想方法 数形结合思想方法 奥数 高考 以形助数 以数辅形

Abstract
Mathematical thought method as the essence of mathematics knowledge content, is a kind of guiding ideology of mathematics and universally applicable method. It can make people understand the true essence of mathematics, know the mathematical value, learn to think and solve mathematical problems. It can put the knowledge learning, ability cultivation and the development of intelligence organically. So mathematical thought method as the important content of the mathematics education has increasingly aroused people's attention.
To strengthen the teaching of mathematics thought method, which can make students from blind study into meaningful study, to escape from the crowd, really extrapolate, instance, greatly shorten the process of students in the dark, to improve the students' learning efficiency, achieve the "high energy". Mathematics is the science of space form and quantity relationship, so the number form combining ideas is one of important mathematics thought method, from the concept of the number of the formation and development of the calculus of generation and the formation of all branches of modern mathematics and are the perfect combination of number form and inseparable."Number" and "form" is throughout the entire primary and secondary school mathematics teaching material's two main line, "number" and "shape" of mutual transformation, combining but also the important method of solving problems. From a higher theoretical level to summarize the formation and development of several form combining ideas, explore the number form combining ideas method in the application of problem solving. Try to give the number form combining ideas method is a more complete explanation, and to other research provides an example of mathematical thinking.This article mainly expounds from the following several aspects: (1) the research significance and the background, domestic and international situation, method and train of thought (2) the theoretical basis for (3) to help function, to help form the mathematical olympiad, widely used in the college entrance examination (4) the number form combining ideas the method itself and the significance of improve students' ability in using this method the problem solving method
keywords
Mathematical thinking method Several form combining ideas
Mathematical olympiad The university entrance exam
To help function In a number of auxiliary


目录
第一章绪论
1.1研究背景与意义 ······························1
1.2国内研究现状 ······························2
1.3研究内容与方法 ······························2
第二章 理论依据
2.1建构主义学习理论······························3
2.2脑科学原理 ······························4
2.3数形结合思想方法在高中数学教学中的地位，作用··5
第三章广泛应用
3.1以形助数，代数问题几何化
3.1.1在奥数中的应用 ······················9
3.1.2在高考题的应用 ······················13
3.2以数辅形，几何问题代数化 ·····················24
第四章如何培养学生的数形结合思想 ············29
第五章论文结束感谢语 ······················30
参考文献 ······················31