【摘要】：化歸思想作為高中數(shù)學(xué)中最為重要和基本的思想之一,一直是數(shù)學(xué)教育工作者共同思考和研究的熱點(diǎn).可以說(shuō),整個(gè)高中數(shù)學(xué)內(nèi)容都滲透了化歸思想,而且它還統(tǒng)領(lǐng)著大多數(shù)的數(shù)學(xué)方法,在數(shù)學(xué)中有著不可替代的地位.然而,對(duì)目前數(shù)學(xué)學(xué)科中化歸思想研究的文獻(xiàn)查閱來(lái)看,比較常見(jiàn)的現(xiàn)象是對(duì)化歸的策略和原則等進(jìn)行舉例說(shuō)明,或者是對(duì)化歸的各種手段和方法進(jìn)行闡述,而針對(duì)學(xué)生本身的化歸思維過(guò)程的研究較少,特別是學(xué)生化歸思想的狀況、發(fā)展特點(diǎn)及如何形成化歸思想等研究還不夠系統(tǒng).為此,本研究力求對(duì)高中生數(shù)學(xué)化歸思想進(jìn)行系統(tǒng)的研究,并以函數(shù)教學(xué)為例對(duì)化歸的思維過(guò)程進(jìn)行分析,對(duì)化歸思想的教學(xué)提供一些參考建議.本研究主要采用文獻(xiàn)分析法、訪談法,對(duì)當(dāng)前高中生數(shù)學(xué)函數(shù)化歸進(jìn)行了訪談?wù){(diào)查與案例分析研究.本論文分為以下幾部分:(1)問(wèn)題的提出.通過(guò)對(duì)化歸思想教學(xué)背景的分析,提出化歸思想促進(jìn)數(shù)學(xué)教學(xué),并且在高中數(shù)學(xué)教學(xué)中,運(yùn)用化歸思想解決數(shù)學(xué)問(wèn)題的機(jī)會(huì)較多.(2)相關(guān)研究綜述,對(duì)國(guó)內(nèi)外有關(guān)化歸思想研究的文獻(xiàn)的查閱與分析,掌握化歸思想的研究現(xiàn)狀和動(dòng)態(tài),為本研究的開(kāi)展奠定基礎(chǔ).(3)問(wèn)卷調(diào)查和訪談.選擇某校高一學(xué)生學(xué)作為研究對(duì)象,進(jìn)行問(wèn)卷調(diào)查和訪談,了解目前學(xué)生的化歸思想狀況.(4)個(gè)案研究.通過(guò)對(duì)個(gè)案資料的研究,分析影響學(xué)生化歸能力的因素主要有學(xué)生的原有知識(shí)結(jié)構(gòu)、元認(rèn)知水平及教師的教學(xué)觀,并在此基礎(chǔ)上提出一些思考建議.本研究得到的主要觀點(diǎn)如下:學(xué)生的原有知識(shí)水平是化歸得以實(shí)現(xiàn)的基石;高一學(xué)生的元認(rèn)知水平普遍不高,導(dǎo)致不能對(duì)自身的化歸過(guò)程進(jìn)行有效的調(diào)控;很多學(xué)生都缺乏對(duì)自身原有知識(shí)內(nèi)容進(jìn)行歸納整理,難以快速的化到已知問(wèn)題鏈.此外,我們通過(guò)訪談?wù){(diào)查初步推斷:原有數(shù)學(xué)知識(shí)、元認(rèn)知水平和數(shù)學(xué)教師的教學(xué)觀是高中生數(shù)學(xué)化歸的主要影響因素.
[Abstract]:As one of the most important and basic thoughts in high school mathematics, the thought of conversion has always been a hot spot for mathematics educators to think and study together. It can be said that the whole high school mathematics content permeates the thought of transformation, and it also dominates most mathematics methods, and has an irreplaceable position in mathematics. However, looking up the literature on the thought of transformation in mathematics at present, the more common phenomenon is to give examples of the strategies and principles of transformation, or to elaborate on the various means and methods of transformation. However, there is little research on the process of students' thinking, especially on the condition, development characteristics and how to form the thought of transformation and so on, which are not systematic enough. Therefore, this study tries to make a systematic study on the thought of mathematical transformation of senior high school students, and takes the function teaching as an example to analyze the thinking process of transformation, and provides some reference suggestions for the teaching of the thought of transformation. This research mainly uses the literature analysis, the interview method, has carried on the interview investigation and the case analysis research to the current senior high school student mathematics function reduction. This paper is divided into the following parts: (1) the issue of the proposed. Through the analysis of the teaching background of the thought of transformation, this paper puts forward the idea of transformation to promote mathematics teaching, and in high school mathematics teaching, there are many opportunities to apply the thought of transformation to solve mathematics problems. (2) the related research is summarized. The review and analysis of domestic and foreign literature on the thought of transformation, the present situation and trend of the research on the thought of reversion, lay the foundation for the development of this study. (3) questionnaire investigation and interview. A survey and interview were conducted to find out the current situation of students' thinking. (4) A case study was carried out in the first year of senior high school as the object of study. (4) A case study was carried out in this paper. Through the study of the case data, this paper analyzes the factors that affect the students' ability to return to biochemistry, such as students' original knowledge structure, metacognitive level and teachers' view of teaching. On this basis, some suggestions are put forward. The main points obtained in this study are as follows: students' original level of knowledge is the cornerstone of the realization of transformation, and the metacognitive level of senior one students is generally low, which leads to the inability to effectively regulate and control their own process of transformation; Many students lack to sum up their original knowledge and content, so it is difficult to quickly turn to known problem chain. In addition, we infer that the original mathematics knowledge, metacognitive level and the teaching view of mathematics teachers are the main influencing factors of mathematics transformation of senior high school students.
【學(xué)位授予單位】：江西師范大學(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)：2466183