本文關(guān)鍵詞： 類比思想 高中數(shù)學(xué) 數(shù)學(xué)教學(xué)引入　出處：《華中師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：類比思想是高中數(shù)學(xué)一種重要的思維方法,在整個高中數(shù)學(xué)的教學(xué)與學(xué)習(xí)過程起著非常重要的作用。在數(shù)學(xué)史上,很多重要定理的發(fā)現(xiàn)和相關(guān)概念得到的性質(zhì)結(jié)論都與類比有關(guān),波利亞曾說過:“類比是一個偉大的引路人”。學(xué)生熟練掌握類比思想,可以幫助他們對不同的數(shù)學(xué)概念、性質(zhì)結(jié)論和定理有一個清晰地認識和理解,這樣有助于學(xué)生對數(shù)學(xué)知識進行整合歸納,對于數(shù)學(xué)學(xué)習(xí)具有非常重要的意義。本文旨在對整個高中數(shù)學(xué)教學(xué)中涉及類比關(guān)系的知識點按照類比形式進行總結(jié),并根據(jù)實際課堂教學(xué)引入如何應(yīng)用類比思想展開具體說明,在此針對數(shù)學(xué)課堂上三種類型的課,分別是概念課、定理講解課、單元小結(jié)課,對這三種類型的課舉例說明如何在教學(xué)引入上恰當?shù)乩妙惐人枷?并給出教案分析和設(shè)計。本文從以下4個方面進行研究:第一部分主要介紹類比思想在高中數(shù)學(xué)教學(xué)中的研究背景,國內(nèi)外關(guān)于類比的研究現(xiàn)狀和研究意義;第二部分主要介紹類比的概念和在數(shù)學(xué)教學(xué)的幾種形式,將人教A版高中數(shù)學(xué)課本中涉及到相似的知識點對應(yīng)總結(jié)歸納到不同形式下,并把類比思想用于高中數(shù)學(xué)課堂上三種不同類型的課上,分別是概念課的引入、定理講解課的引入、單元小結(jié)課的引入,同時分別進行舉例說明在高中數(shù)學(xué)課堂引入如何采用類比思想,介紹具體實施步驟:類比教學(xué)的準備,類比教學(xué)的實施,驗證類比結(jié)論;第三部分將類比思想運用于課堂教學(xué)引入中,分別舉例說明上述三種不同類型課的教學(xué)設(shè)計,并針對教學(xué)設(shè)計提出教學(xué)反思;最后對本文的研究內(nèi)容進行總結(jié),發(fā)現(xiàn)使用類比思想作為一個切入點時,可以使課堂效果達到事半功倍,然后分析研究中的不足之處,期望這些總結(jié)可以為教師在進行類比教學(xué)的時候提供一定的參考。
[Abstract]:The thought of analogy is an important method of thinking in high school mathematics, which plays a very important role in the teaching and learning process of mathematics in senior high school. Many of the discoveries of important theorems and the nature of the related concepts are related to analogy. Polia once said, "analogy is a great guide." students are proficient in the idea of analogy, which can help them understand different mathematical concepts. The nature of the conclusion and theorem has a clear understanding and understanding, which is helpful for students to integrate mathematical knowledge, The purpose of this paper is to summarize the knowledge about analogy relation in the whole senior high school mathematics teaching according to the form of analogy, and to explain how to apply the analogy thought to the actual classroom teaching. In view of the three kinds of classes in mathematics classroom, they are concept class, theorem explaining class, unit summary lesson. Examples are given to illustrate how to introduce the analogy thought into the teaching. The first part mainly introduces the research background of analogy thought in mathematics teaching in senior high school, the research status and significance of analogy at home and abroad; The second part mainly introduces the concept of analogy and several forms of mathematics teaching. And the analogy thought is applied to three different kinds of high school mathematics classes, namely, the introduction of concept class, the introduction of theorem explaining class, the introduction of unit summary class, the introduction of the introduction of the concept class, the introduction of the theorem explanation class, the introduction of the unit summary class. At the same time, examples are given to illustrate how to adopt analogy in high school mathematics classroom, and the concrete steps are introduced: preparation of analogy teaching, implementation of analogy teaching, verification of analogical conclusion; The third part applies the analogy thought to the classroom teaching, explains the teaching design of the three kinds of courses mentioned above with examples, and puts forward the teaching reflection on the teaching design. Finally, it summarizes the research contents of this paper. It is found that the use of analogy thought as an entry point can make the classroom effect double the result with half the effort, and then analyze the shortcomings of the research, and hope that these conclusions can provide some reference for teachers in the process of analogical teaching.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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