數(shù)形結(jié)合思想方法在解題中的應(yīng)用

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摘要
數(shù)學(xué)思想方法作為數(shù)學(xué)知識(shí)內(nèi)容的精髓，是數(shù)學(xué)的一種指導(dǎo)思想和普遍適用的方法。它能使人們領(lǐng)悟數(shù)學(xué)的真諦，懂得數(shù)學(xué)價(jià)值，學(xué)會(huì)數(shù)學(xué)地思考和解決問(wèn)題。它能把知識(shí)的學(xué)習(xí)、能力的培養(yǎng)和智力的發(fā)展有機(jī)地結(jié)合起來(lái)。因此數(shù)學(xué)思想方法作為數(shù)學(xué)教育的重要內(nèi)容，己日益引起人們的注意。
加強(qiáng)數(shù)學(xué)思想方法教學(xué)，能使學(xué)生從盲目的學(xué)習(xí)轉(zhuǎn)化為有意義的學(xué)習(xí)，從題海中解脫出來(lái)，真正做到舉一反三，觸類(lèi)旁通，大大縮短了學(xué)生在黑暗中摸索的過(guò)程，真正提高學(xué)生的學(xué)習(xí)效益，做到“高分高能”。數(shù)學(xué)是研究空間形式和數(shù)量關(guān)系的科學(xué)，因此數(shù)形結(jié)合思想是重要的數(shù)學(xué)思想方法之一，從數(shù)的概念的形成和發(fā)展，到微積分的產(chǎn)生及現(xiàn)代數(shù)學(xué)各分支學(xué)科的形成，都是與數(shù)形的完美結(jié)合分不開(kāi)的?！皵?shù)”與“形”也是貫穿整個(gè)中小學(xué)數(shù)學(xué)教材的兩條主線，“數(shù)”與“形”的相互轉(zhuǎn)化、結(jié)合更是解題的重要方法。從更高的理論層次總結(jié)數(shù)形結(jié)合思想的形成與發(fā)展，探索數(shù)形結(jié)合思想方法在解題中的應(yīng)用。試圖給予數(shù)形結(jié)合思想方法一個(gè)較為完整的詮釋?zhuān)⒔o其它數(shù)學(xué)思想的研究提供一個(gè)范例。本文主要從以下幾個(gè)方面進(jìn)行闡述：（1）研究意義與背景，國(guó)內(nèi)外情況，方法與思路（2）理論依據(jù)（3）以形助數(shù)在奧數(shù)，高考中的廣泛應(yīng)用，以數(shù)輔形的應(yīng)用（4）數(shù)形結(jié)合思想方法自身的意義與提高學(xué)生運(yùn)用此種方法解題能力的方法

關(guān)鍵詞

數(shù)學(xué)思想方法 數(shù)形結(jié)合思想方法 奧數(shù) 高考 以形助數(shù) 以數(shù)輔形

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


目錄
第一章緒論
1.1研究背景與意義 ······························1
1.2國(guó)內(nèi)研究現(xiàn)狀 ······························2
1.3研究?jī)?nèi)容與方法 ······························2
第二章 理論依據(jù)
2.1建構(gòu)主義學(xué)習(xí)理論······························3
2.2腦科學(xué)原理 ······························4
2.3數(shù)形結(jié)合思想方法在高中數(shù)學(xué)教學(xué)中的地位，作用··5
第三章廣泛應(yīng)用
3.1以形助數(shù)，代數(shù)問(wèn)題幾何化
3.1.1在奧數(shù)中的應(yīng)用 ······················9
3.1.2在高考題的應(yīng)用 ······················13
3.2以數(shù)輔形，幾何問(wèn)題代數(shù)化 ·····················24
第四章如何培養(yǎng)學(xué)生的數(shù)形結(jié)合思想 ············29
第五章論文結(jié)束感謝語(yǔ) ······················30
參考文獻(xiàn) ······················31