高中生在“导数应用”学习中的常见错误研究

发布时间：2018-02-01 02:20

本文关键词： 高中生导数应用常见错误教学建议　出处：《重庆师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：导数是指当自变量的增量趋于零时,因变量的增量与自变量的增量之商的极限。在高中数学课程中,导数是解决函数、不等式,分析解析几何、数列和生活最优化等问题的有效工具。利用导数解题,把复杂问题简单化,能够快速准确的解决问题,但是高中生在“导数应用”中常犯的诸多错误却严重影响了相关问题的顺利解决。本文研究的目的在于了解高三学生学习导数知识部分特别是导数应用的常见错误及其产生原因,为教师提供简单有效的教学建议,提高解决导数应用综合性难题的得分率,进而提高学生的自信心,为学生进入更高层次的学习做准备。本研究运用作品分析法和试卷分析法,对高三学生“导数应用”的课后作业和测试卷进行了研究,总结出高三学生在“导数应用”学习中的常见错误及其原因,主要表现为:(1)知识性错误。包括概念模糊不清、题意理解错误、运算法则记忆不准确、忽视隐含条件。(2)逻辑性错误。包括虚假论证、充要条件混乱。(3)策略性错误。包括分类标准不统一、转化问题不等价、构造函数困难、数形结合不准确。(4)心理性错误。包括畏难情绪、局部成就感造成的错误。通过文献研究和访谈法分析了学生产生错误的原因,提出了如下教学建议:(1)重视基础知识讲解和学习,重点区分个别概念(以在某点的切线和过某点的切线、极值点和不可导点、求函数的单调区间和已知单调函数求参数的取值范围为例进行说明);(2)重视归纳总结全面复习,主要对应条件(以任意、存在性问题为例进行说明);(3)深入分析题目,注重方法选择(以构造函数、分类讨论为例进行重点说明);(4)关注学生心理健康。
[Abstract]:Derivative is the limit of the quotient of the increment of dependent variable and independent variable when the increment of independent variable tends to 00:00. In high school mathematics, derivative is the solution function, inequality and analytic geometry. Effective tools for solving problems such as sequence of numbers and optimization of life. Using derivative to solve problems, complex problems can be simplified to solve problems quickly and accurately. But high school students in the "derivative application" The purpose of this study is to understand the common mistakes in the learning of derivative knowledge, especially the application of derivative, and the causes. To provide teachers with simple and effective teaching advice, improve the derivative application of comprehensive problems to solve the scoring rate, and then improve the self-confidence of students. In order to prepare students for a higher level of study, this study uses work analysis and test paper analysis to study the "derivative application" homework and test paper of senior three students. This paper summarizes the common mistakes and their causes in the study of "derivative application" among the senior high school students, which are mainly manifested in the knowledge errors of "1: 1", including vague concepts, wrong understanding of the meaning of questions and inaccurate memorization of arithmetic rules. Ignore the implicit condition. 2) logical error. Including false argument, necessary and sufficient confusion. 3) strategic errors, including the classification criteria are not uniform, the problem of transformation is not equivalent, and the constructor is difficult. Mental errors, including the fear of difficulties, the errors caused by local sense of achievement, and the analysis of the causes of students' errors through literature research and interviews. This paper puts forward the following teaching advice: 1) pay attention to the explanation and study of basic knowledge, and focus on distinguishing individual concepts (such as tangent at a certain point and tangent at a certain point, extremum and non-differentiable point). The monotone interval of the function and the range of values of the known monotone function are illustrated as examples. (2) pay attention to summing up comprehensive review, the main corresponding conditions (take arbitrary, existential problem as an example to explain; (3) deeply analyze the topic, pay attention to the choice of method (take constructor, classification discussion as an example to explain emphatically; Pay attention to the mental health of students.
【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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