本文選題：數(shù)學(xué)思維 + 類比思想�。� 參考：《南京師范大學(xué)》2015年碩士論文

【摘要】：培養(yǎng)數(shù)學(xué)思維能力是高中數(shù)學(xué)教學(xué)強(qiáng)調(diào)的內(nèi)在要求和重要任務(wù),類比思維作為數(shù)學(xué)思維的重要組成部分,在高中數(shù)學(xué)教學(xué)中需要被高度重視并廣泛應(yīng)用。針對(duì)當(dāng)前高中數(shù)學(xué)教師和學(xué)生應(yīng)用類比思想更多的出于自發(fā)性和隨機(jī)性,缺乏系統(tǒng)性和規(guī)范性,與《普通高中數(shù)學(xué)課程標(biāo)準(zhǔn)(實(shí)驗(yàn)稿)》目標(biāo)對(duì)教師應(yīng)用類比教學(xué)和對(duì)學(xué)生掌握類比思維方法提出的要求存在差距,對(duì)此,本文對(duì)類比思想在高中數(shù)學(xué)教學(xué)中的應(yīng)用情況展開了研究。本文在查閱大量國(guó)內(nèi)外類比思想研究文獻(xiàn)的基礎(chǔ)上,對(duì)當(dāng)前關(guān)于類比思想研究及應(yīng)用的現(xiàn)狀、特點(diǎn)進(jìn)行綜述,發(fā)掘類比思想與數(shù)學(xué)乃至高中數(shù)學(xué)的密切聯(lián)系,提出類比思想在高中數(shù)學(xué)教學(xué)應(yīng)用的必要性和可行性,通過(guò)找出影響類比思想教學(xué)的內(nèi)在因素,避免日常類比教學(xué)產(chǎn)生的局限性,從而掌握類比思想教學(xué)策略的一般原則和基本環(huán)節(jié)�；陬惐人枷朐跀�(shù)學(xué)學(xué)科發(fā)展的密切聯(lián)系,開展類比教學(xué)在高中數(shù)學(xué)教學(xué)中的應(yīng)用研究顯得尤為重要。本文立足高中數(shù)學(xué)教學(xué)目標(biāo)及實(shí)際需要,通過(guò)高中數(shù)學(xué)教學(xué)中類比思想的應(yīng)用,闡述了類比思想的科學(xué)性、聯(lián)系性和聯(lián)想性,以及類比思想在教學(xué)中的實(shí)效性。重點(diǎn)突出對(duì)高中數(shù)學(xué)蘇教版教科書中類比內(nèi)容進(jìn)行應(yīng)用研究,運(yùn)用文獻(xiàn)研究、課堂觀察法、個(gè)人訪談、問(wèn)卷調(diào)查等研究方法,系統(tǒng)地從高中數(shù)學(xué)課堂的教與學(xué)兩個(gè)方面進(jìn)行綜合研究,動(dòng)態(tài)與靜態(tài)分析相結(jié)合,理論與實(shí)證分析相結(jié)合,既分析教師運(yùn)用類比思想的教學(xué)策略情況,又研究高中學(xué)生運(yùn)用類比思想學(xué)習(xí)的情況,力圖呈現(xiàn)高中數(shù)學(xué)教學(xué)中教師和學(xué)生關(guān)于類比思想的應(yīng)用現(xiàn)狀,尋找出類比思想與高中數(shù)學(xué)切入點(diǎn)和契合點(diǎn),通過(guò)設(shè)計(jì)運(yùn)用類比思想教學(xué)的一般路徑,總結(jié)出類比思想在高中數(shù)學(xué)教學(xué)應(yīng)用中的基本規(guī)律,并就如何提高類比教學(xué)策略的效果提出意見和建議。通過(guò)研究,得出結(jié)論包括：在高中數(shù)學(xué)教學(xué)中注重應(yīng)用類比思想,有助于展示數(shù)學(xué)的內(nèi)在和諧和數(shù)學(xué)知識(shí)的統(tǒng)一性,豐富教師的教學(xué)手段,實(shí)現(xiàn)教學(xué)目標(biāo)；通過(guò)運(yùn)用類比思想教學(xué)策略,可以激發(fā)學(xué)生主動(dòng)參與數(shù)學(xué)探究積極性,引導(dǎo)學(xué)生在學(xué)習(xí)數(shù)學(xué)知識(shí),掌握數(shù)學(xué)技能的過(guò)程中形成創(chuàng)新擴(kuò)散思維；學(xué)生在高中數(shù)學(xué)學(xué)習(xí)中恰當(dāng)?shù)剡\(yùn)用類比推理,能夠提高他們解決問(wèn)題的能力、攻克難題的信心和數(shù)學(xué)學(xué)習(xí)效率。希望本論文對(duì)類比思想在高中數(shù)學(xué)課堂教學(xué)中進(jìn)一步擴(kuò)大應(yīng)用范圍的研究有一定幫助。
[Abstract]:It is an internal requirement and an important task to cultivate mathematics thinking ability in senior high school mathematics teaching. As an important part of mathematics thinking, analogical thinking needs to be attached great importance to and widely used in high school mathematics teaching. In view of the present high school mathematics teacher and student application analogy thought more out of spontaneity and randomness, the lack of systematic and normative, There is a gap between the goal of ordinary Senior Middle School Mathematics Curriculum Standard (Experimental draft) and the requirements of teachers' application of analogy teaching and students' mastery of analogical thinking methods. This paper studies the application of analogy thought in mathematics teaching in senior high school. On the basis of consulting a large number of domestic and foreign literature on analogical thought research, this paper summarizes the present situation and characteristics of the research and application of analogy thought, and explores the close relationship between analogy thought and mathematics, even mathematics in senior high school. This paper puts forward the necessity and feasibility of the application of analogy thought in mathematics teaching in senior high school, and by finding out the internal factors that influence the teaching of analogy thought, it avoids the limitation of daily analogy teaching. In order to master the general principles and basic links of analogical ideological teaching strategy. Based on the close relationship between the thought of analogy and the development of mathematics, it is very important to carry out the research on the application of analogy teaching in mathematics teaching in senior high school. Based on the goal and practical needs of mathematics teaching in senior high school, this paper expounds the scientific, associative, associative and practical effects of analogy thought through the application of analogy thought in mathematics teaching in senior high school. Emphasis is placed on the applied research on the analogical content in the textbooks of senior high school mathematics education, including literature research, classroom observation, personal interviews, questionnaires and other research methods. This paper systematically studies the teaching and learning of mathematics classroom in senior high school, combines the dynamic and static analysis, the theory and the empirical analysis, analyzes the teachers' teaching strategies using analogy thought. It also studies the situation of high school students' learning with analogy thought, and tries to present the present situation of the application of analogy thought between teachers and students in high school mathematics teaching, and find out the starting point and the point of convergence between analogy thought and senior high school mathematics. By designing the general path of analogical thought teaching, this paper sums up the basic law of the application of analogy thought in mathematics teaching in senior high school, and puts forward some suggestions on how to improve the effect of analogy teaching strategy. The conclusions are as follows: paying attention to the thought of applying analogy in mathematics teaching in senior high school is helpful to show the inherent harmony of mathematics and the unity of mathematics knowledge enrich the teaching means of teachers and realize the teaching goal; Through the use of analogy thought teaching strategy, it can stimulate students' initiative to participate in mathematical inquiry enthusiasm, guide students to form innovative and diffusive thinking in the process of learning mathematical knowledge and mastering mathematical skills. Students can improve their ability to solve problems, solve problems with confidence and study efficiency by using analogy reasoning properly in senior high school mathematics learning. It is hoped that this paper will be helpful to further expand the scope of application of analogical thinking in senior high school mathematics classroom teaching.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

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本文編號(hào)：2116106