本文選題：構(gòu)造 + 構(gòu)造性思維�。� 參考：《深圳大學(xué)》2017年碩士論文

【摘要】：奧林匹克數(shù)學(xué)競(jìng)賽作為國(guó)際性的數(shù)學(xué)聯(lián)賽,有很多教育家、研究者們對(duì)數(shù)學(xué)競(jìng)賽中的思想方法進(jìn)行了系統(tǒng)的論述.其中構(gòu)造性的思想方法作為重要的數(shù)學(xué)方法,在奧林匹克競(jìng)賽的命題和解題中都有著廣泛的應(yīng)用.已有的有關(guān)數(shù)學(xué)“構(gòu)造性思維”的研究主要是針對(duì)一些具體題目的構(gòu)造性解法,對(duì)構(gòu)造性思維的本質(zhì)、競(jìng)賽數(shù)學(xué)中涉及到的構(gòu)造性思維解題分類缺乏系統(tǒng)的研究.本文通過(guò)往年中學(xué)數(shù)學(xué)競(jìng)賽中涉及到的構(gòu)造法習(xí)題進(jìn)行實(shí)例分析,從不同的題型如何分類、以及構(gòu)造法在不同數(shù)學(xué)學(xué)科中的運(yùn)用兩個(gè)角度出發(fā)研究當(dāng)今背景下中學(xué)數(shù)學(xué)競(jìng)賽中涉及到的的構(gòu)造性思維.本文首先概述了構(gòu)造性思維的研究背景、國(guó)內(nèi)外研究歷史和現(xiàn)狀及構(gòu)造性思維的理論依據(jù).其次結(jié)合以往數(shù)學(xué)競(jìng)賽的題目對(duì)構(gòu)造法解題的原則、策略和特例進(jìn)行探討,同時(shí)配合競(jìng)賽題目對(duì)運(yùn)用構(gòu)造法解題提出自己的觀點(diǎn).然后通過(guò)對(duì)以往研究文獻(xiàn)和競(jìng)賽題目的整理分析提出了不同數(shù)學(xué)競(jìng)賽題型中的幾類構(gòu)造法應(yīng)用,包括存在性命題的結(jié)論構(gòu)造、否定命題的反例構(gòu)造和轉(zhuǎn)化問(wèn)題形式的推演構(gòu)造.最后通過(guò)對(duì)以往競(jìng)賽題目的整理分析,將初等數(shù)論、代數(shù)、幾何、組合數(shù)學(xué)中運(yùn)用構(gòu)造法解題的題目進(jìn)行分析說(shuō)明,詳細(xì)的探討如何在中學(xué)數(shù)學(xué)競(jìng)賽中根據(jù)具體的題目條件或結(jié)論特征恰當(dāng)?shù)倪\(yùn)用構(gòu)造性思想方法.文章的最后論述了構(gòu)造性思維的教學(xué)誤區(qū)和培養(yǎng)建議,包括怎樣運(yùn)用構(gòu)造法解題、構(gòu)造法解題的誤區(qū)、構(gòu)造性思維的培養(yǎng)建議,希望對(duì)競(jìng)賽數(shù)學(xué)的教學(xué)和構(gòu)造性思維的培養(yǎng)提供有價(jià)值的參考.
[Abstract]:As an international mathematics league, there are many educators and researchers who systematically discuss the thought and method of the Olympic mathematics competition. As an important mathematical method, the constructive thinking method is widely used in the proposition and problem solving of the Olympic competition. The existing research on "constructive thinking" in mathematics is mainly aimed at the constructive solution of some specific topics, but there is no systematic study on the nature of constructive thinking and the classification of structural thinking problems involved in contest mathematics. In this paper, by analyzing the construction exercises involved in mathematics competitions in middle schools in previous years, how to classify different types of questions is given in this paper. And the application of the construction method in different mathematics subjects from two angles to study the constructional thinking involved in the middle school mathematics competition under the background of the present day. This paper first summarizes the research background of constructive thinking, the research history and present situation at home and abroad, and the theoretical basis of constructive thinking. Secondly, this paper discusses the principles, strategies and special cases of solving problems by structural method in combination with the topics of previous mathematical competitions, and at the same time puts forward its own views on the use of structural methods in solving problems with competition topics. Based on the analysis of previous research papers and competition topics, this paper puts forward several kinds of constructional application of different mathematical contest question types, including the conclusion construction of existence proposition, the counterexample construction of negation proposition and the deductive construction of transformation problem form. Finally, through the analysis of the previous competition topics, the problems in elementary number theory, algebra, geometry and combinatorial mathematics are analyzed and explained by using the construction method to solve the problems. This paper discusses in detail how to apply the constructive thinking method according to the specific subject condition or the conclusion characteristic in the middle school mathematics contest. At the end of the article, the author discusses the teaching misunderstandings and training suggestions of constructive thinking, including how to solve problems by constructional method, and how to cultivate constructive thinking. It hopes to provide valuable reference for the teaching of competitive mathematics and the cultivation of constructive thinking.
【學(xué)位授予單位】：深圳大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

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