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文献检索作业 数学与应用数学09级2班

西华师范大学文献信息检索课综合实习报告

学生姓名：付 松 学号：200908140207 成 绩_____________

院（系）：专业：数学与信息学院数学与应用专业 检索课题（中英文）：微积分与中学数学的应用

and Application of Middle School Mathematics 研究Calculus

一、课题分析

如果将整个数学比作一棵大树,那么初等数学是树的根,名目繁多的数学分支是树枝,而树干的主要部分就是微积分不论是高等数学还是初等数学,其基本方法都是相通的,那么,高等数学微积分方法在中学数学中有着怎样的应用?微积分的思想方法和基本理论有着广泛的应用,除对中学的教学有重要的指导作用外,也能在中学教学的许多问题上起到居高临下和以简驭繁的作用.那么微积分在中学数学中有哪些应用,本文就研究证明恒等式和不等式,判定函数的增减性,求极值,找切线方程等方面的研究与应用 。导数及其应用是微积分中的部分内容，是微积分初步几经

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文献检索作业 数学与应用数学09级2班

修改后进入我国《高中数学课程标准(实验)》的内容，其在概念呈现、内容编排等都有所改革。如何设计这部分的教学，特别是用怎样的视角处理，笔者认为有必要做一些探讨。本文对导数及其应用的内容结构、基本数学思想方法、学习目标及任务、学习初等微积分的课程价值进行了理论研究，同时在实验基础上对导数及其应用的教与学进行了研究。研究表明：(1)微积分中蕴含的思想是信息时代社会公民生活的一种需要，是数学发展的一种动力，微积分对其它领域也有着广泛的应用；(2)学生必须具备的极限思想及理论基础； (3)学生理解导数概念的认知结构发展经历三个层次：作为“具体实际意义”的导数；作为“变化率”的导数；在某点处的导数与导数概念的辨析。并对影响其教与学的因素进行了分析。针对以上调查和分析，对具体内容提出了的教学策略：(1)突出概念本质；(2)防止微积分教学退化成形式；(3)加强数学思想方法的教学；(4)关注与信息技术的整合；(5)加强对数学的文化的渗透；(6)处理好微积分与初等数学的关系；(7)加强初等微积分学习中常见错误的剖析。

If the entire mathematics compared to a tree, then the elementary mathematics is the root of the tree, branches of the numerous branches of mathematics, but the trunk is the main part of the calculus, whether or higher mathematics elementary mathematics, the basic methods are interlinked , then the method of higher

mathematics calculus mathematics in secondary schools has a kind of application? calculus way of thinking and the basic theory has been widely applied, in addition to teaching in secondary schools have an important role in guiding, but also a lot of teaching in secondary schools issues and to play a commanding role in Jane Yu Fan. So calculus in middle school mathematics in which applications, this paper studies have shown that identity and inequality, to determine changes in sexual function, extremum, find the tangent equation, the research and application. Derivatives and its application is part of the Calculus is calculus preliminary

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文献检索作业 数学与应用数学09级2班

revised several times to enter China's \School Mathematics Curriculum Standards (Experimental)\reforms. How to design this part of the teaching, especially in dealing with the perspective of what the author considers it necessary to do some research. In this paper, derivatives and its application in the content and structure, the basic mathematical way of thinking, learning objectives and tasks of elementary calculus courses to learn the value of a theoretical study, while based on the experimental application of the derivative and its teaching and learning was studied. The results show that: (1) Calculus and connotations of the information age as a society need to civic life is a driving force for the development of mathematics, calculus also has a wide range of other areas of the application; (2) Students must have limits Ideological and theoretical basis; (3) students understand the derivative concepts of the cognitive structure of development through three levels: as a \practical significance\of the derivative; as the \rate\derivative; at some point the derivative and derivative Concepts . And the factors affecting the teaching and learning were analyzed. For more investigation and analysis of the specific content of the teaching strategies: (1) to highlight the concept of nature; (2) to prevent calculus teaching to degenerate into a form; (3) to strengthen the teaching of mathematical thinking; (4) concerned with information technology integration; (5) to strengthen the penetration of the culture of mathematics; (6) deal with calculus and elementary mathematical relationship; (7) to strengthen learning in elementary calculus analysis of common errors.

二、该课题主要检索词

微积分(Calculus)中学数学思想方法(School of mathematical thinking)

极值问题(Extremal problem)导数(Derivative)

单调区间(monotone interval) 复合函数(Composite function) 检索表达式：（关键词=微积分）*（关键词=中学数学思想/极值问题）*（关键词=单调区间/导数/复合函数）*全部期刊*年=1980--2011

三、选择检索工具

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