高中生数学符号语言掌握现状的调查研究

发布时间：2018-01-11 06:31

本文关键词：高中生数学符号语言掌握现状的调查研究　出处：《华中师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：《全日制义务教育数学课程标准》明确提出要培养学生的“符号意识”。整个中学阶段是学生学习、掌握数学符号语言的关键时期。初中阶段是形成对数学符号语言的感性认识,初步到达简化和加速学生思维过程的训练；而高中阶段是形成对数学符号语言的理性认识,数学符号的宽度、广度、深度各方面都有加深,达到培养锻炼学生的抽象思维的目的。数学符号语言的学习,是学好数学的关键。为此,本研究对高中三个学段的学生进行调查研究,了解他们对数学符号语言的掌握现状。首先,分析数学符号语言研究的背景、研究的意义,并假设学生数学符号语言掌握程度的高低与其数学成绩的好坏呈正相关。认为了解学生数学符号语言的掌握现状,可以为研究“学困生”的问题开辟一条新的研究途径。接着,概述了数学符号语言的相关研究现状,包括数学语言、数学符号感以及数学符号语言的研究现状。其次,对数学符号语言的内涵进行界定,并基于中学数学对数学符号语言的不同形式进行划分。从数学符号的直观形式和传递数学意义的本质内涵两个方面来介绍数学符号语言的特点,在直观形式上,数学符号具有间接性、直观性。在数学符号传递数学意义的本质内涵上,数学符号具有的特点是：传递数学意义的抽象性,复杂性,精确性,规范性。紧接着,介绍数学符号语言的价值,除了介绍其对数学发展的价值外,并联系数学符号与数学思维和中学数学学习的关系来介绍其价值,认为数学符号承载数学知识,是数学知识的载体,是数学思维的依赖工具,其本身具有的美感可以激发学生学习数学的兴趣。之后,概括了数学符号传递数学意义的多样性,即同一个数学符号可以承载不同的数学意义,同一个数学意义也可以由不同的数学符号来表达。再次,指出本研究的调查对象以及具体实施调查的过程。并根据调查收集的数据,运用软件对高中阶段学生掌握数学符号语言的现状进行了分析。本研究获得的结论是：(1)对于同一个数学符号语言,不同的学生有不同的理解,对于同一个数学意义,不同的学生用数学符号语言表达的结果是不同的。(2)普遍学生都认为对数学符号的分析与讲解很重要；(3)数学符号语言掌握的越好的学生,他们的数学成绩就越好,数学符号语言掌握得越不好的学生,他们的数学成绩就越不好;另一方面,得出高中生在学习数学符号语言方面主要存在的困难是：(1)多个数学符号组合在一起时,学生难以理解与表述,即是不能准确理解复合数学符号。(2)学生不能准确、清晰地掌握同一数学符号可以具有不同的数学意义,也不能掌握同一数学意义可以利用多种数学符号来表示,也就是说学生理解的数学符号语言是单一的。(3)在数学符号的表示上存在不准确性、不完整性以及书写的不规范性。(4)不能很好的将数学符号语言与文字语言进行转化。(5)学生在书写或是使用数学符号时,很容易出现负迁移的现象。最后,根据研究的结果,对数学符号语言的教学进行反思。分析概括目前的数学符号语言教学现状,认为老师对数学符号语言的教学对学生掌握数学符号语言程度的影响很大,并针对数学符号语言教学提出了相应的教学建议。
[Abstract]:"The full-time compulsory education mathematics curriculum standard" clearly put forward to cultivate the students "consciousness of symbols". The middle school stage is the key period of learning, to master the language of mathematical symbols. The junior middle school stage is the formation of perceptual knowledge of the language of mathematical symbols, preliminary to simplify and accelerate the process of training students' thinking; and the high school stage is the formation of knowledge the language of mathematical symbols of the rational, mathematical symbol width, breadth, the depth has deepened, to train students abstract thinking. The symbolic language of mathematics learning, the key is to learn mathematics. Therefore, this study investigated three high school schools students, understand their current situation of master mathematics sign language. First, analysis of the language of mathematical symbols in the background, the significance of the research, and assuming that the students master the language of mathematical symbols and their mathematics achievement level That is a positive correlation. To understand the status quo of students to master the language of mathematical symbols, can open up a new way to study the "underachievers". Then, summarizes the related research status of mathematical symbol language, including the language of mathematics, mathematics symbol sense and the research status of mathematical symbol language. Secondly, defines the the connotation of the language of mathematical symbols, and different forms of middle school mathematics mathematical symbol language based on division. From the two aspects of the visual form of mathematical symbols and transfer mathematical meaning essence to introduce the characteristics of mathematical symbol language, in the form of intuition, mathematical symbols is indirect, intuitive. The mathematic essence in mathematical symbols, mathematical symbols with the characteristics are: transfer the meaning of mathematics abstraction, complexity, accuracy and standardization. Then, introduce the language of mathematical symbols The value, in addition to the introduction of the development of mathematics value, and the relationship of mathematical thinking and mathematics learning to introduce its value, bearing the symbol that mathematics knowledge of mathematics, mathematics is the carrier of knowledge, mathematical thinking depends on the tool, its beauty can arouse students' interest in learning mathematics. And summarizes the diversity of mathematical symbols transfer mathematical meaning, namely the same mathematical symbols can carry different mathematical meanings, the same mathematical meaning can be expressed by different mathematical symbols. Thirdly, points out the research object of this paper and the concrete implementation process. According to the survey data collected in the survey, application status the software to master the language of mathematical symbols of the high school students are analyzed. The conclusions are: (1) for the same symbolic language of mathematics, different students have different The understanding for the same mathematical meaning, different students with the mathematical symbol language expression is different. (2) general students that analysis of mathematical symbols and explanation is very important; (3) the better the students master the language of mathematical symbols, their math scores can master the language of mathematical symbols it is not good for students, their mathematics achievement is not good; on the other hand, the main problems in learning mathematical symbol language difficulties of senior high school students are: (1) a number of mathematical symbols when combined together with the students to understand, that is not an accurate understanding of complex mathematical symbols (. 2) students can not accurately and clearly grasp the same mathematical symbols can have different mathematical meanings, they can not grasp the same mathematical meaning can use a variety of mathematical symbols, that is to say the students understand the language of mathematical symbols is single. (3 In the representation of mathematical symbols) are uncertain, incomplete and writing is not normative. (4) not very good will be the language of mathematical symbols and language conversion. (5) students in writing or using mathematical symbols, it is prone to the phenomenon of negative transfer. Finally, according to the study the reflection on the teaching of mathematics symbols. The analysis summarized the mathematical symbol language teaching at present, teachers think of the symbolic language of mathematics teaching for students to master the language of mathematical symbols of large, and according to the mathematical symbol language teaching and puts forward the corresponding teaching suggestions.

【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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