中學(xué)數(shù)列中的探索性問題淺析


摘要
數(shù)列是高中數(shù)學(xué)的重要內(nèi)容，又是學(xué)習(xí)高等數(shù)學(xué)的基礎(chǔ)。高考對本章的考察比較全面，數(shù)列探索性考查每年都不會漏。有關(guān)數(shù)列試題經(jīng)常是綜合題，探索性問題是高考的熱點(diǎn)，常在數(shù)列解答題中出現(xiàn)。本章中還蘊(yùn)含著豐富的數(shù)學(xué)思想，在主觀題中重考查函數(shù)與方程，轉(zhuǎn)化與歸化，分類討論等重要思想，以及配方法，換元法，待定系數(shù)法等基本數(shù)學(xué)方法。在解決綜合題和探索性問題中加深對基礎(chǔ)知識，基本技能和基本數(shù)學(xué)思想方法的認(rèn)識，溝通各類知識的聯(lián)系，形成更完整的知識網(wǎng)絡(luò)，提高分析問題和解決問題的能力，培養(yǎng)學(xué)生善于分析題意，富于聯(lián)想，以適應(yīng)新的背景，新的設(shè)問方式，提高學(xué)生用函數(shù)的思想，方程的思想研究數(shù)列問題的自覺性，培養(yǎng)學(xué)生主動探索的精神和科學(xué)理性的思維方法

關(guān)鍵詞：高中數(shù)學(xué) 探索性 數(shù)學(xué)思想方法 思維方法




SUMMARY
Sequence is an important content of high school mathematics，Is the basis of learning advanced mathematics. The university entrance exam this chapter examine more comprehensive, Exploratory examination every year does not leak. About the sequence of test questions often is a comprehensive topic, Exploratory problem is one of the hot issues college entrance examination. Often appear in the sequence of solution. This chapter also contains abundant mathematical thinking,In the subjective topic examination function and equation, Classification to discuss such important thought, And the method, change element method, the basic mathematical methods such as method of undetermined coefficients. In solving the problem of the comprehensive topic and exploratory about basic knowledge, basic skills and the understanding of the basic mathematical thought method, and communication of all kinds of knowledge, to form a more complete knowledge network, improve the ability to analyze and solve problems, cultivate students' analytical and full of lenovo, to adapt to the new background, new way, establish to improve the students by the concept of function and equation of thought research series problem consciousness, trains the student to take the initiative to explore the spirit and scientific and rational way of thinking
Key words: high school mathematics exploratory
mathematics thoughtway thinking method



目 錄

引言……………………………………………………………………………………2
第一章條件探索性問題……………………………………………………………3
1.1 利用分析法解決條件探索性題………………………………………………4
1.2 利用聯(lián)想法解決條件性探索題………………………………………………5
1.3利用觀察法解決條件性探索問題………………………………………………6
1.4利用邏輯推理法解決條件探索性問題…………………………………………7
1.5 利用綜合法解決條件探索性問…………………………………………………8
第二章結(jié)論性探索性問題……………………………………………………………9
2.1 利用先探索結(jié)論后論證法解決結(jié)論探索性題…………………………………10
2.2利用特殊情形解決結(jié)論探索性題…………………………………………………11
2.3利用變量歸一論證解決結(jié)論探索性題……………………………………………12
第三章 存在探索性問題………………………………………………………………13
3.1利用數(shù)值結(jié)論論證解決結(jié)論探索性題……………………………………………14
3.2利用圖形結(jié)論論證解決結(jié)論探索性題……………………………………………15
3.3利用函數(shù)結(jié)論論證解決結(jié)論探索性題………………………………………………16
第四章 規(guī)律探索性問題…………………………………………………………………17
4.1利用透徹分析法解決規(guī)律探索性問題………………………………………………18
4.2利用發(fā)現(xiàn)規(guī)律法解決規(guī)律探索性問題………………………………………………19
4.3利用猜想結(jié)論法解決規(guī)律探索性問題………………………………………………20
結(jié)論……………………………………………………………………………………………21
致謝………………………………………………………………………………………………22
參考文獻(xiàn)…………………………………………………………………………………………23