數(shù)形結(jié)合思想在中學(xué)教學(xué)中的應(yīng)用研究

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摘要:如今數(shù)學(xué)教學(xué)理念主要是通過傳授學(xué)生數(shù)學(xué)知識和方法來培養(yǎng)學(xué)生的理解和解題能力。而數(shù)學(xué)又是研究數(shù)與形的一門學(xué)科，并且數(shù)和形是相互聯(lián)系的。所以數(shù)形結(jié)合思想方法在數(shù)學(xué)教學(xué)占有很重要的地位。數(shù)形結(jié)合思想是一種思維方式，可以將數(shù)學(xué)題中的數(shù)形進(jìn)行轉(zhuǎn)換，同時(shí)也可使題目信息更加形象直觀。本文主要講述了數(shù)學(xué)思想之一的數(shù)形結(jié)合思想。首先對數(shù)形結(jié)合思想進(jìn)行了簡單介紹，簡單闡述了國內(nèi)外眾多學(xué)者們對中學(xué)生利用數(shù)形結(jié)合思想解題能力現(xiàn)狀的研究成果以及概括了通過查閱大量的文獻(xiàn)參考總結(jié)出的數(shù)形結(jié)合思想的實(shí)際應(yīng)用和教學(xué)價(jià)值。除此之外還根據(jù)所研究的數(shù)形結(jié)合思想在中學(xué)教學(xué)中的應(yīng)用問題針對中學(xué)這一范圍進(jìn)行了實(shí)際調(diào)查，從學(xué)生和教師兩方面分析得出了關(guān)于在數(shù)形結(jié)合思想教學(xué)過程中存在的問題。最后，整理文獻(xiàn)與調(diào)查結(jié)果總結(jié)出了數(shù)形結(jié)合思想在教學(xué)中的不足，并對如何更加有效的在教學(xué)中應(yīng)用該思想提出了一些建議?？偠灾?，數(shù)形結(jié)合思想的有效運(yùn)用有助于培養(yǎng)學(xué)生的思維能力，增強(qiáng)學(xué)生的解題能力。
關(guān)鍵詞：數(shù)形結(jié)合 解題能力 教學(xué)研究



Research on Application of thought in high school teaching of combining numbers with shapes
Abstract:Modern primarily through the transfer of students ' mathematical knowledge and mathematics teaching method to cultivate students ' ability to understand reconciliation problems. Research and form a discipline of mathematics, and number and are interconnected. Number shape Union method used in the teaching of modern mathematics is particularly important. With combination of number and form ideas in math can be the number of relationships and interaction in the form of space, is a mode of thinking, you can make the topic more visual information. This article focuses on the combination of number and form one of the mathematical ideas, make a brief introduction to it, as well as the evolution in understanding after a combination of number and form of thought by a lot of references to summarize several teaching combined with the practical application of ideas and values, there are scholars on middle school students ' ability of solving thought of using the combination of number and form research results. In addition to literature references also did actual research, drawn from the analysis of both students and teachers on the problems in the combination of number and form ideas in the teaching process, organize documents and summary of survey results besides the lack of combination of number and form of thought in the teaching and how to become more effective in teaching in the ideas put forward some suggestions. In short, effective combination of number and form ideas to help develop students ' thinking ability of reconciliation problems.
Keywords: Several form combining The problem solving ability teaching research


目 錄
第一章 研究背景 1
1.1關(guān)于數(shù)學(xué)思想 1
1.2數(shù)形結(jié)合思想的簡介 2
1.3數(shù)形結(jié)合思想的歷史演進(jìn) 3
第二章 研究內(nèi)容 5
2.1數(shù)形結(jié)合思想解決的問題類型 5
2.2數(shù)形結(jié)合思想在教學(xué)中的作用 5
2.3中學(xué)數(shù)學(xué)中應(yīng)用數(shù)形結(jié)合思想解題現(xiàn)狀的研究 6
第三章 實(shí)例調(diào)查 8
3.1調(diào)查研究的問題 8
3.2調(diào)查研究的對象 8
3.3調(diào)查研究的方法 8
3.4調(diào)查研究的工具 8
3.4.1問卷題目設(shè)計(jì) 8
3.4.2訪談環(huán)節(jié) 9
3.5實(shí)際的實(shí)施 9
3.6數(shù)據(jù)整理統(tǒng)計(jì) 10
第四章 結(jié)果與分析 11
4.1中學(xué)生對數(shù)形結(jié)合思想的涵義、價(jià)值、歷史背景的了解掌握 11
4.2中學(xué)生數(shù)與形之間相互轉(zhuǎn)化的能力 11
4.3數(shù)形結(jié)合過程中的思維特點(diǎn) 12
4.4教師對數(shù)形結(jié)合思想應(yīng)用的教學(xué) 14
第五章 結(jié)論 16
5.1數(shù)形結(jié)合思想在教學(xué)應(yīng)用中存在不足 16
5.2如何有效應(yīng)用數(shù)形結(jié)合思想的教學(xué) 16
結(jié)束語 17
致 謝 18
參考文獻(xiàn) 19
附錄 20