高中生数形结合能力的现状调查及策略

发布时间：2019-06-06 17:08

【摘要】：数与形是数学研究的重要主题,数与形的结合有着悠久的历史。从毕达哥拉斯“万物皆数”开始就将数和形紧密的联系在一起。笛卡尔创立的解析几何是数形结合模式的典范,极大地推动了数形结合的发展。数和形也是数学中的两个最基本的概念,他们相互联系并相互论证。在《义务教育数学新课程(2011年版)》中明确指出：数形结合是探索数学新知识的重要方法之一。因此,数形结合一向是教学的重点,也是历年高考的必考内容。新一轮课改更加注重学生探索和创新能力的培养,这对学生数形结合思想的理解以及运用数形结合解题的能力,提出了更高的要求,也对教师的教学提出了新的挑战。因此,有必要对数形结合思想在解题中的应用以及学生数形结合解题能力现状进行研究分析,从而给出一些教学上的策略建议。本文试图在总结前研究成果的基础上,以教材为依据,以教育实践经验为参考,深入研究数形结合在高中数学中的应用方面,并通过问卷调查、口头访谈和课堂实践的方式,了解学生数形结合解题能力现状。并在充分分析结果的基础上,探讨教师应如何培养学生数形结合能力。使其不单成为学生快速有效解题的方法,而且更高层次的,使其上升为一种数学思想,并内化为学生的数学素养。具体里来说,本文共分5章内容：第一章绪论,主要阐述问题研究的背景和意义；第二章文献综述,主要总结前人的研究成果,包括数形结合的演变简史、数形结合的理论依据和数形结合的教育价值。第三章数形结合在中学数学解题中的应用,总结并用实例说明了数形结合应用的三种类型：以形辅数、以数助形和数形并重。而在运用数形结合解题中应遵循等价性原则、双向性原则和等价性原则,最后根据对近几年高考统计分析,总结高考对数形结合思想考察的特点；第四章对数形结合思想应用的现状做实证调查,发现学生对数形结合思想的理解比较狭隘,学生对数形结合思想的应用能力不强。主要原因是学生构图能力不强、学生对同一知识点的数表征和形表征的对应关系较弱。但相对来说学生“以形思数”的能力要强于“以数思形”的能力。第五章根据第四章调查研究所发现的问题给出一些策略性建议,包括转变教师观念、用好教材中的素材、注重数学语言的教学和合理利用信息技术加强数与形的对应。
[Abstract]:Number and shape are important topics in mathematical research, and the combination of number and shape has a long history. Since Pythagoras, everything has been closely linked to form. The analytic geometry created by Descartes is a model of numerical combination model, which greatly promotes the development of numerical combination. Number and form are also the two most basic concepts in mathematics, which are related to each other and demonstrated to each other. In the New Mathematics Curriculum of compulsory Education (2011 Edition), it is clearly pointed out that the combination of numbers and shapes is one of the important methods to explore the new knowledge of mathematics. Therefore, the combination of numbers and shapes has always been the focus of teaching, but also the required content of the college entrance examination over the years. The new round of curriculum reform pays more attention to the cultivation of students' exploration and innovation ability, which puts forward higher requirements for the understanding of students' thought of combining number and shape and the ability to use the combination of number and form to solve problems, and also puts forward new challenges to teachers' teaching. Therefore, it is necessary to study and analyze the application of the thought of combination of numbers and shapes in problem solving and the present situation of students' ability to solve problems, so as to give some strategic suggestions in teaching. On the basis of summing up the previous research results, taking the teaching materials as the basis, taking the educational practice experience as the reference, this paper attempts to deeply study the application of the combination of numbers and shapes in senior high school mathematics, and through questionnaires, oral interviews and classroom practice. To understand the present situation of students' problem-solving ability combined with number and shape. On the basis of full analysis of the results, this paper probes into how teachers should cultivate students' ability of combining numbers and shapes. So that it not only become a fast and effective method for students to solve problems, but also a higher level, so that it rises to a kind of mathematical thought, and internalizes it into students' mathematical literacy. Specifically, this paper is divided into five chapters: the first chapter is the introduction, which mainly expounds the background and significance of the problem research; The second chapter is a literature review, which mainly summarizes the previous research results, including the brief history of the evolution of the combination of numbers and forms, the theoretical basis of the combination of numbers and forms and the educational value of the combination of numbers and forms. In the third chapter, the application of number-form combination in middle school mathematics problem solving is summarized and illustrated with an example: the auxiliary number of the number, the weight of the auxiliary number and the number of the number. In using the combination of number and form to solve the problem, we should follow the principle of equivalence, the principle of two directions and the principle of equivalence. Finally, according to the statistical analysis of the college entrance examination in recent years, this paper summarizes the characteristics of the thought of the combination of logarithm and form in the college entrance examination. In the fourth chapter, we make an empirical investigation on the present situation of the application of logarithmic combination thought, and find that students have a narrow understanding of the thought of numerical combination, and the application ability of students' thought of logarithmic combination is not strong. The main reason is that the students' composition ability is not strong, and the corresponding relationship between the number representation and the shape representation of the same knowledge point is weak. But relatively speaking, students' ability of thinking in shape is stronger than that of thinking in shape. The fifth chapter gives some strategic suggestions according to the problems found in the fourth chapter, including changing the teachers' concept, making good use of the materials in the teaching materials, paying attention to the teaching of mathematical language and making rational use of information technology to strengthen the correspondence between numbers and shapes.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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