數(shù)形結合思想在中學教學中的應用研究

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



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關于數(shù)學思想 1
1.2數(shù)形結合思想的簡介 2
1.3數(shù)形結合思想的歷史演進 3
第二章 研究內(nèi)容 5
2.1數(shù)形結合思想解決的問題類型 5
2.2數(shù)形結合思想在教學中的作用 5
2.3中學數(shù)學中應用數(shù)形結合思想解題現(xiàn)狀的研究 6
第三章 實例調查 8
3.1調查研究的問題 8
3.2調查研究的對象 8
3.3調查研究的方法 8
3.4調查研究的工具 8
3.4.1問卷題目設計 8
3.4.2訪談環(huán)節(jié) 9
3.5實際的實施 9
3.6數(shù)據(jù)整理統(tǒng)計 10
第四章 結果與分析 11
4.1中學生對數(shù)形結合思想的涵義、價值、歷史背景的了解掌握 11
4.2中學生數(shù)與形之間相互轉化的能力 11
4.3數(shù)形結合過程中的思維特點 12
4.4教師對數(shù)形結合思想應用的教學 14
第五章 結論 16
5.1數(shù)形結合思想在教學應用中存在不足 16
5.2如何有效應用數(shù)形結合思想的教學 16
結束語 17
致 謝 18
參考文獻 19
附錄 20