本文關(guān)鍵詞：上海高中數(shù)學(xué)分類討論思想及其教學(xué)研究　出處：《上海師范大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 上海高中數(shù)學(xué) 數(shù)學(xué)思想方法 分類討論思想 教學(xué)原則 教學(xué)策略

【摘要】：數(shù)學(xué)思想,是數(shù)學(xué)知識內(nèi)容的精髓和靈魂,是對數(shù)學(xué)的本質(zhì)認識.它是把數(shù)學(xué)知識的學(xué)習(xí)和能力的培養(yǎng)有機結(jié)合起來提高個體思維品質(zhì)和數(shù)學(xué)能力的關(guān)鍵,更是一個人數(shù)學(xué)素養(yǎng)的重要內(nèi)涵之一.分類討論思想作為高中階段最重要的數(shù)學(xué)思想之一見于教材的各個章節(jié),在高考中具有舉足輕重的地位.學(xué)生解題時分類討論的意識不強,討論時存在盲目性、主觀性.現(xiàn)有研究偏重解題研究,較少教學(xué)研究.本文緊密結(jié)合教材和高考,為上海高中數(shù)學(xué)教師提供豐厚的分類討論思想教學(xué)資料,希望能為分類討論思想的教學(xué)提供有價值的參考.本文主要進行了如下研究:對現(xiàn)行上海高中數(shù)學(xué)教材做了深入研究,充分挖掘了集合、不等式、函數(shù)、三角函數(shù)、數(shù)列、平面向量、行列式、解析幾何、復(fù)數(shù)、立體幾何、排列組合和概率中蘊含分類討論思想的知識點、例題和習(xí)題,對同類型題做了歸類,對教材中出現(xiàn)的引起分類討論的原因做了總結(jié).然后以引起分類的原因分析了上海近六年高考試題,并對每年高考試題中分類討論的題型、分值、討論因素、知識載體做了統(tǒng)計,得出了高考常以函數(shù)、數(shù)列、解析幾何、向量、集合、不等式等知識為載體考察分段函數(shù)、含參數(shù)的分類討論、排列組合概率、分類給出的公式、設(shè)直線時考慮斜率是否存在、去絕對值討論、不等式的運算性質(zhì)、圖形的不確定性、根據(jù)剩余類討論、結(jié)論不唯一時討論等分類討論內(nèi)容的結(jié)論.根據(jù)以上研究,結(jié)合前人研究和自身十三年的教學(xué)經(jīng)驗,提出了對上海高中數(shù)學(xué)分類討論思想教學(xué)的五項教學(xué)原則和七項教學(xué)策略,并以概念課、公式推導(dǎo)課的教學(xué)設(shè)計為例說明如何進行分類討論思想的教學(xué).其中五項教學(xué)原則為滲透性原則、漸進發(fā)展原則、系統(tǒng)性原則、明確性原則、自我構(gòu)建原則.七項教學(xué)策略:(1)充分挖掘教材中的分類討論思想方法.給出了通過變式把一些例題、習(xí)題改編成分類討論題的例子.(2)重視知識的發(fā)生過程,加強分類討論思想方法的訓(xùn)練和培養(yǎng).對概念教學(xué)不要直接給定義,對公式、定理、性質(zhì)不要過早下結(jié)論.(3)搞好整理總結(jié),進行分類討論思想方法的概括和提煉.總結(jié)了避免或優(yōu)化討論的策略(4)加強解題指導(dǎo),突破分類討論思想的難點.(5)反復(fù)滲透,掌握分類討論重點.對分類討論重點考察內(nèi)容,教學(xué)時要通過不同知識載體反復(fù)滲透分類討論思想.(6)糾錯練習(xí),強化易錯點.(7)重視其它數(shù)學(xué)思想方法.
[Abstract]:Mathematical thought is the essence and soul of mathematical knowledge content and the essential understanding of mathematics. It is the key to improve individual thinking quality and mathematical ability by organically combining the study of mathematical knowledge with the cultivation of ability. As one of the most important mathematical ideas in senior high school, the classified discussion thought can be found in every chapter of the textbook. In the college entrance examination has a pivotal position. Students' awareness of problem solving classification discussion is not strong, the discussion exists blindness, subjectivity. The existing research emphasis on problem solving research. This article closely combines the teaching materials and the college entrance examination to provide the rich classified discussion ideological teaching materials for the senior high school mathematics teachers in Shanghai. Hope to provide a valuable reference for the teaching of classified discussion ideas. This paper mainly carried out the following research: the current senior high school mathematics textbooks in Shanghai have done in-depth research, fully excavated the set, inequality, function. Trigonometric functions, sequence of numbers, plane vectors, determinants, analytic geometry, complex number, solid geometry, permutation and combination, and probability are the knowledge points, examples and exercises of classification and discussion. This paper summarizes the reasons that cause the classification discussion in the teaching materials, and then analyzes the questions of the college entrance examination in Shanghai in the past six years with the reasons of the classification, and discusses the types, scores and discussion factors of the questions classified in the examination questions of the college entrance examination every year. The knowledge carrier has made statistics and obtained that the college entrance examination often uses function, number series, analytic geometry, vector, set, inequality and other knowledge as the carrier to investigate the piecewise function, including the classification and discussion of parameters, the probability of arrangement and combination. The formulas given by the classification consider whether the slope exists, the absolute value is removed, the operation property of the inequality and the uncertainty of the graph are considered when the straight line is set, and discussed according to the remaining class. According to the above research, combined with the previous studies and their own 13 years of teaching experience. This paper puts forward five teaching principles and seven teaching strategies to discuss the classified teaching of high school mathematics in Shanghai. The teaching design of formula derivation course as an example shows how to carry on the teaching of the classified discussion thought, among which five teaching principles are permeability principle, progressive development principle, systematic principle and clear principle. Self-construction principle. Seven teaching strategies: 1) fully excavate the thinking method of classification discussion in the textbook. An example of adapting exercises into classified discussion questions. (2) pay attention to the process of knowledge, strengthen the training and cultivation of thinking methods of classification discussion. Do not directly define the concept teaching, and give formulas and theorems. Do not prematurely draw conclusions. 3) do a good job in sorting out and summing up ideas and methods of classification discussion. Summarize the strategies to avoid or optimize discussion. 4) strengthen the guidance of problem solving. Break through the difficulty of classification discussion. 5) repeatedly infiltrate, grasp the focus of classification discussion. In teaching, we should repeatedly infiltrate into different knowledge carriers to discuss the idea of classification. 6) the error-correcting exercises should be strengthened, and the error-prone point should be strengthened. 7) other mathematical thinking methods should be emphasized.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6

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