高中生导数及应用学习现状的调查研究

发布时间：2018-02-24 12:37

本文关键词： 极限导数调查　出处：《河北师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：微积分学的重要性,众所周知。毫无疑问,高中生了解、掌握一点微积分初步的知识,会让其受益匪浅。学生既可以感受微积分在研究函数性质和解决实际问题时带来的便利,又可以体会其中的辩证统一思想,还可以学习使用微积分的观点分析和解决问题,开阔视野,提高数学素养,为以后的微积分学习打下坚实的基础。新课标对导数一章的教学也提出了希望和要求:微积分教学要注重导数概念的本质,防止将导数仅仅作为一些规则和步骤来学习,从而忽视了它的思想和价值,通过微积分的学习,让学生体会微积分的科学价值、应用价值以及对人类文化发展的价值。但在实际教学中却发现一些不和谐的现象:学生不能真正理解极限和导数概念的本质,存在模棱两可或死记硬背的现象,知识的迁移能力不够。教师感到自己的知识储备不足,面临进修与教学任务相冲突的尴尬,教学总是疲于应对考试,注重解题训练较多,不能考虑学生的长远发展等等,这也是进行本研究之根源。本研究在阅读了大量相关文献的前提下,通过多视角、“三位一体”式的问卷调卷和访谈(既对高中学生和高中教师进行了问卷调查和访谈,同时还对大学教师进行了访谈),这也是本文的创新之处。以往的研究大多只针对学生或高中教师进行的,结合大学教师的访谈很少。通过问卷和访谈,主要了解以下几个方面的问题:(1)学生方面:了解学生对极限思想的把握和对导数概念本质的理解;在实际问题中,学生正确解释导数实际意义的能力;对导数几何意义理解的深刻程度;以及对导数计算、导数应用的掌握情况。(2)高中教师方面:了解高中数学教师如何处理与导数密切相关的内容,如极限思想、微积分的发展史等。高中教师是否存在“本本主义”以及视野不开阔的情况;教师在教授导数内容时的体会和感受;以及对数学教改有哪些好的建议。(3)大学教师方面:在学生已经具备微积分初步知识的前提下,大学教师在教授导数内容时的体会和感受;以及对高中教师的教学有哪些合理可行的建议。通过对调查数据的统计和分析,得出以下结论:学生对极限概念的把握不尽人意,对导数概念本质的理解不够深刻,对导数几何意义认识不全面,对求导公式和法则的掌握比较熟练,学生具备初步的利用导数解决实际问题的能力。教师对渗透“数学史”基本处于忽略状态,对极限思想的重视付诸行动少,在教学过程中重导数应用轻概念理解,教学水平维持现状者居多。针对调查结果中存在的问题,结合大学教师的访谈结果,笔者给出了相应的教学建议。课堂上应该重视极限思想及概念的介绍,注重学生对导数概念本质的理解,教师也要转变观念,提高认识,具有时代紧迫感。希望这些教学建议能够为学生和一线教师提供有价值的借鉴和参考。
[Abstract]:As everyone knows the importance of calculus. There is no doubt that the understanding of high school students, a preliminary knowledge of calculus, will let benefit. Students can bring calculus to solve practical problems in the study of the nature and function of the convenience, but also can realize the dialectical unity of thinking, can also learn to use calculus ideas to analyze and solve problems, broaden their horizons, improve mathematical literacy, for Calculus Learning and lay a solid foundation. The new curriculum for teaching a derivative also raised the hopes and demands: the essence of calculus teaching should pay attention to the concept of derivative, will prevent to learn just as some derivative rules and procedures, so as to ignore it thought and value, through calculus learning, let students experience the calculus of scientific value, application value and value for the development of human culture. But it is found in practical teaching Some of the students will not understand the essence of the phenomenon: the limit and derivative concept, are ready to accept either course or rote phenomenon, the migration ability of knowledge is not enough. Teachers feel their own lack of knowledge, learning and teaching task conflict faced embarrassment, teaching is always struggling to cope with the examination, focus on problem-solving training more, can not consider students the long-term development and so on, which is also the origin of this study. In this study, reading a lot of literature under the premise, through multi perspective, "three-in-one" type of questionnaire and interviews (both for high school students and high school teachers conducted a questionnaire survey and interviews, also conducted interviews of University Teachers), which is the innovation of this paper. Most previous studies only for students or high school teachers, combining university teacher interviews rarely. Through the questionnaire and interview, mainly to understand Following several aspects: (1) students: students to understand the limit idea and to grasp the nature of the derivative concept understanding; in practice, students ability to explain the actual meaning of the derivative of the profound understanding; the geometric meaning of derivative; and derivative calculation, to grasp the situation of derivative application (2. High school teachers): learn how to deal with high school mathematics teachers is closely related with the derivative content, such as the limit idea, the development of calculus. The history of high school teachers is the existence of "bookishness and vision is not open; teachers' experience in content and feeling of the derivative Professor; and on mathematics teaching reform which have good suggestions. (3) College Teachers: the students already have preliminary knowledge under the premise of calculus, experience of university teachers in the content and feelings of the derivative Professor; and for high school teachers teaching what are reasonable and feasible The suggestion. Through the statistical analysis of the survey data, draw the following conclusion: the students to grasp the concept of limit is, to understand the nature of the derivative concept is not deep enough, the derivatives of geometric significance and incomplete understanding of the derivation and the rules of the master students have more skilled ability, using the derivative preliminary to solve practical problems. Teachers on the permeation of mathematical history "at the neglect of basic state, limit thought attention into action, in the process of teaching the application of the derivative concept of light weight, the teaching level to maintain the status quo mostly. In view of the existing problems in the survey results, combined with the interview results of university teachers, the author provides some suggestions for teaching the classroom. Should pay attention to the introduction of the concept and the limit idea, pay attention to students' understanding of the nature of the derivative concept, teachers should change their ideas, raise awareness, with a sense of urgency. Hope this time Some teaching suggestions can provide valuable reference and reference for students and teachers.

【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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