數(shù)形結(jié)合思想方法的有效策略研究

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目 錄
第一章 引言
1.1 問(wèn)題的提出……………………………………………………………………5
1.2 研究的目的和意義……………………………………………………………6
1.3 研究的思路和方法……………………………………………………………7
第二章 國(guó)內(nèi)外數(shù)形結(jié)合思想方法研究綜述
2.1 國(guó)內(nèi)數(shù)形結(jié)合思想研究………………………………………………………8
2.2 國(guó)外數(shù)形結(jié)合思想研究………………………………………………………9
2.3 研究現(xiàn)狀的思考………………………………………………………………9
第三章 數(shù)形結(jié)合思想方法
3.1 數(shù)、形的發(fā)展及其特點(diǎn)………………………………………………………11
3.2 數(shù)形結(jié)合思想概念及其特點(diǎn)…………………………………………………11
3.3 數(shù)形結(jié)合分類及其特點(diǎn)………………………………………………………12
第四章 數(shù)形結(jié)合思想方法教學(xué)策略的舉例
4.1 由數(shù)化形………………………………………………………………………15
4.2 以形助數(shù)………………………………………………………………………17
4.3 數(shù)形結(jié)合思想的升華----無(wú)字證明…………………………………………19
致謝………………………………………………………………………………………23
參考文獻(xiàn)…………………………………………………………………………………24



摘要 數(shù)學(xué)是一門研究數(shù)量關(guān)系和空間形式的科學(xué)。數(shù)學(xué)的研究對(duì)象大體分成兩類，表示數(shù)量關(guān)系的數(shù)，和表示空間形式的形。在數(shù)學(xué)上，數(shù)是代數(shù)學(xué)、分析學(xué)的研究對(duì)象，形則是幾何學(xué)的研究對(duì)象。雖然它們研究的內(nèi)容和使用的方法各有區(qū)別，但中間沒(méi)有不可逾越的鴻溝。學(xué)生從“數(shù)”角度理解“形”，從“形”角度理解“數(shù)”對(duì)數(shù)學(xué)學(xué)習(xí)有著重要的作用。
數(shù)形結(jié)合思想方法的實(shí)質(zhì)是把抽象的數(shù)學(xué)語(yǔ)言和形象直觀的幾何圖形聯(lián)系在一起，使代數(shù)的抽象概念和幾何圖形具體形象相互轉(zhuǎn)化、聯(lián)系、滲透，讓復(fù)雜的數(shù)學(xué)問(wèn)題簡(jiǎn)單化，更快速、更便捷解決數(shù)學(xué)問(wèn)題。它是富有數(shù)學(xué)特點(diǎn)的信息轉(zhuǎn)換，是一柄雙刃的解題利劍。
在分析數(shù)學(xué)結(jié)合思想方法實(shí)質(zhì)的基礎(chǔ)上提出：由數(shù)化形，根據(jù)數(shù)量關(guān)系畫出圖形，通過(guò)對(duì)圖像的觀察、分析來(lái)解決數(shù)學(xué)問(wèn)題的教學(xué)策略。以形助數(shù)的策略，其實(shí)質(zhì)是圖形運(yùn)用數(shù)字計(jì)算將問(wèn)題表達(dá)精確。同時(shí)研究了“數(shù)形結(jié)合”思想方法的升華----無(wú)字證明，它以鮮明的直觀和簡(jiǎn)捷的表達(dá)形式使復(fù)雜問(wèn)題更容易解決、理解，讓數(shù)學(xué)變得更加有吸引力、更充滿活力。對(duì)培養(yǎng)學(xué)生的創(chuàng)新精神，開拓學(xué)生思維有著積極的意義。

關(guān)鍵詞： 數(shù)形結(jié)合 思想方法 教學(xué)策略 無(wú)字證明


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