中学数列中的探索性问题浅析.docx
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中学数列中的探索性问题浅析,摘要数列是高中数学的重要内容，又是学习高等数学的基础。高考对本章的考察比较全面，数列探索性考查每年都不会漏。有关数列试题经常是综合题，探索性问题是高考的热点，常在数列解答题中出现。本章中还蕴含着丰富的数学思想，在主观题中重考查函数与方程，转化与归化，分类讨论等重要思想，以及配方法，换元法，待定...
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中学数列中的探索性问题浅析
摘要
数列是高中数学的重要内容，又是学习高等数学的基础。高考对本章的考察比较全面，数列探索性考查每年都不会漏。有关数列试题经常是综合题，探索性问题是高考的热点，常在数列解答题中出现。本章中还蕴含着丰富的数学思想，在主观题中重考查函数与方程，转化与归化，分类讨论等重要思想，以及配方法，换元法，待定系数法等基本数学方法。在解决综合题和探索性问题中加深对基础知识，基本技能和基本数学思想方法的认识，沟通各类知识的联系，形成更完整的知识网络，提高分析问题和解决问题的能力，培养学生善于分析题意，富于联想，以适应新的背景，新的设问方式，提高学生用函数的思想，方程的思想研究数列问题的自觉性，培养学生主动探索的精神和科学理性的思维方法
关键词：高中数学 探索性 数学思想方法 思维方法
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 录
引言……………………………………………………………………………………2
第一章条件探索性问题……………………………………………………………3
1.1 利用分析法解决条件探索性题………………………………………………4
1.2 利用联想法解决条件性探索题………………………………………………5
1.3利用观察法解决条件性探索问题………………………………………………6
1.4利用逻辑推理法解决条件探索性问题…………………………………………7
1.5 利用综合法解决条件探索性问…………………………………………………8
第二章结论性探索性问题……………………………………………………………9
2.1 利用先探索结论后论证法解决结论探索性题…………………………………10
2.2利用特殊情形解决结论探索性题…………………………………………………11
2.3利用变量归一论证解决结论探索性题……………………………………………12
第三章 存在探索性问题………………………………………………………………13
3.1利用数值结论论证解决结论探索性题……………………………………………14
3.2利用图形结论论证解决结论探索性题……………………………………………15
3.3利用函数结论论证解决结论探索性题………………………………………………16
第四章 规律探索性问题…………………………………………………………………17
4.1利用透彻分析法解决规律探索性问题………………………………………………18
4.2利用发现规律法解决规律探索性问题………………………………………………19
4.3利用猜想结论法解决规律探索性问题………………………………………………20
结论……………………………………………………………………………………………21
致谢………………………………………………………………………………………………22
参考文献…………………………………………………………………………………………23
摘要
数列是高中数学的重要内容，又是学习高等数学的基础。高考对本章的考察比较全面，数列探索性考查每年都不会漏。有关数列试题经常是综合题，探索性问题是高考的热点，常在数列解答题中出现。本章中还蕴含着丰富的数学思想，在主观题中重考查函数与方程，转化与归化，分类讨论等重要思想，以及配方法，换元法，待定系数法等基本数学方法。在解决综合题和探索性问题中加深对基础知识，基本技能和基本数学思想方法的认识，沟通各类知识的联系，形成更完整的知识网络，提高分析问题和解决问题的能力，培养学生善于分析题意，富于联想，以适应新的背景，新的设问方式，提高学生用函数的思想，方程的思想研究数列问题的自觉性，培养学生主动探索的精神和科学理性的思维方法
关键词：高中数学 探索性 数学思想方法 思维方法
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 录
引言……………………………………………………………………………………2
第一章条件探索性问题……………………………………………………………3
1.1 利用分析法解决条件探索性题………………………………………………4
1.2 利用联想法解决条件性探索题………………………………………………5
1.3利用观察法解决条件性探索问题………………………………………………6
1.4利用逻辑推理法解决条件探索性问题…………………………………………7
1.5 利用综合法解决条件探索性问…………………………………………………8
第二章结论性探索性问题……………………………………………………………9
2.1 利用先探索结论后论证法解决结论探索性题…………………………………10
2.2利用特殊情形解决结论探索性题…………………………………………………11
2.3利用变量归一论证解决结论探索性题……………………………………………12
第三章 存在探索性问题………………………………………………………………13
3.1利用数值结论论证解决结论探索性题……………………………………………14
3.2利用图形结论论证解决结论探索性题……………………………………………15
3.3利用函数结论论证解决结论探索性题………………………………………………16
第四章 规律探索性问题…………………………………………………………………17
4.1利用透彻分析法解决规律探索性问题………………………………………………18
4.2利用发现规律法解决规律探索性问题………………………………………………19
4.3利用猜想结论法解决规律探索性问题………………………………………………20
结论……………………………………………………………………………………………21
致谢………………………………………………………………………………………………22
参考文献…………………………………………………………………………………………23
