高中生数学符号学习现状的调查研究

发布时间：2019-02-23 14:32

【摘要】：数学是由概念、公式、命题等组成的知识体系,而数学符号又是数学概念、公式、命题等的抽象化,是数学的重要组成部分,对学生的数学学习起着奠基性的重要作用。高中数学中的符号自成体系,主要包括元素符号、关系符号、运算符号及辅助符号等。通过自己作为学生的学习体会及参加教育实习期间对高中学生的观察和访谈发现,影响高中生数学学习的因素有很多,但缺乏对数学符号学习的理解、识记及迁移是造成其学习数学困难的主要原因。因此对高中数学符号的研究是非常有必要的,希望研究过程中发现的问题及提出的建议对当前的数学符号教学提供事实依据及参考。本研究在对国内外相关文献梳理的基础上,运用文献法、问卷调查法和访谈法对高中生数学符号学习现状进行了研究。研究的主要问题有:(1)高中生数学符号学习的现状如何。(2)高中生数学符号学习的具体表现及成因是什么。(3)提高高中生数学符号学习的途径有哪些。研究发现学生对数学符号学习的困难主要有:(1)元素符号:①对于符号的认识仅停留于表面;②难以辨识同一符号在不同位置的含义。(2)关系符号:①难以理解符号的实质;②难以准确判断符号间的关系。(3)运算符号:①难以理解运算符号的内涵;②对复杂运算的运算能力较弱;③难以对符号进行熟练运用;④难以克服“先入为主”的思维定势。(4)辅助符号:①只注重形式,不注重本质。综合分析,学生学习数学符号的困难有以下几点:难以理解符号的实质和内涵、难以对数学符号进行有效加工、难以对数学符号进行熟练运用。产生这些困难的主要原因有:思维方向较为单一、已有知识对新知识的负影响很大、缺乏主动性,对教师过分依赖。针对学生数学符号学习的现状及具体表现,分析其成因,提出了以下几点教学建议:1、深刻剖析数学符号的内涵和实质;2、注重分析数学符号间的联系与区别;3、引导学生多角度联想;4、提高学生对数学符号的转换和运用能力;5、注重提高学生的运算能力;6、注重提高学生的自主性。
[Abstract]:Mathematics is a knowledge system composed of concepts, formulas and propositions, and mathematical symbols are abstractions of mathematical concepts, formulas and propositions, which is an important part of mathematics and plays an important role in students' mathematics learning. The symbols in high school mathematics consist of element symbols, relational symbols, operational symbols and auxiliary symbols. Through their own learning experience as a student and the observation and interview with senior high school students during their educational practice, it is found that there are many factors that affect high school students' mathematics learning, but lack of understanding of mathematical symbol learning. Memorization and transfer are the main reasons for their difficulty in learning mathematics. Therefore, it is very necessary to study the mathematical symbols in senior high school. It is hoped that the problems found in the course of the research and the suggestions made will provide a factual basis and reference for the current teaching of mathematical symbols. On the basis of combing the relevant literature at home and abroad, the present situation of high school students' mathematical symbol learning is studied by means of literature, questionnaire and interview. The main problems are as follows: (1) the present situation of mathematical symbol learning in senior high school students, (2) what are the concrete manifestations and causes of mathematical symbol learning in senior high school students, and (3) what are the ways to improve the learning of mathematical symbols in senior high school students. The study found that students' difficulties in learning mathematical symbols are as follows: (1) Elemental symbols: (1) the understanding of symbols is only on the surface; 2it is difficult to identify the meaning of the same symbol in different positions. (2) Relational symbol: it is difficult to understand the essence of the symbol; (2) it is difficult to judge the relationship between symbols accurately; (3) the operational symbol: 1it is difficult to understand the connotation of the operational symbol; (2) the calculation ability of complex operation is weak; (3) it is difficult to use symbols skillfully; (4) it is difficult to overcome the preemptive thinking pattern. (4) Auxiliary symbol: 1 only pays attention to form but not essence. Comprehensive analysis shows that students have the following difficulties in learning mathematical symbols: it is difficult to understand the essence and connotation of symbols, to process them effectively and to use them skillfully. The main reasons for these difficulties are: the direction of thinking is relatively single, the negative influence of existing knowledge on new knowledge is great, the lack of initiative and over-dependence on teachers. According to the present situation and concrete performance of students' mathematical symbol learning, this paper analyzes its cause of formation and puts forward the following teaching suggestions: (1) deeply analyzing the connotation and essence of mathematical symbol, (2) paying attention to analyzing the connection and difference between mathematical symbols, and putting forward some teaching suggestions as follows: 1. Third, guide students' multi-angle association; (4) improve students' ability to convert and use mathematical symbols; (5) pay attention to improving students' ability of calculation; (6) pay attention to improving students' autonomy.
【学位授予单位】：西北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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