小学低年级学生数学符号意识培养的调查研究

发布时间：2018-10-13 15:43

【摘要】：符号意识是数学课程标准中的一项重要的教学目标,并和数与代数部分内容紧密相连,针对小学数学符号意识的培养也成为了近些年数学学习的重点要点,随着小学数学教学改革的发展,图形等式的教学内容得到了充分的加强。这一部分的教学内容主要涉及到基本图形的认知及等式的基本思维掌握,同时这一内容也很好的反应了学生的符号意识。由于等式思维需要有较高的逻辑思维能力,也受到学生符号意识发展的制约,在小学阶段特别是一、二年级就开展图形等式是否合适成为教学研究的重点。本研究的主要内容是我国小学低段特别是一,二年级学生的符号意识的教育现状。具体地说,本研究主要在讨论以下几个问题:(一)小学一年级生符号意识现状的调查分析研究的具体问题包括一年级生在符号的感知、符号的提炼、符号的运用这三个方面,对学生的具体表现和所展示的特征进行比较研究。(二)一、二年级学生符号意识的差异分析1.一年级学生图形等式推算解题策略的调查分析以具体的一道图形等式推算题为载体,针对一年级学生如何解题进行研究。2.一、二年级学生图形等式推算题解题策略差异分析以两题图形等式推算题为载体,分析一二年级学生的解题策略是否存在差异。同时本研究还调查了学生对图形等式推算问题的情感程度。从而有助于在教学过程中采取更为合适的方式,强化学生对图形推算问题的兴趣,充分提高教学效果。通过调查发现一年级学生在符号意识方面的学习情况总体还是可以的,但在符号的感知,符号的提炼,符号的运用这三个方面的学习存在不同的情况:(1)学生对于数学符号的感知总体情况较为理想:学生对运算符号的感知较好,也能够体会图形在算式中的替代作用。(2)一年级学生还未完全将符号等同数参与列式,在日常语言与数学语言的转换,还存在一定的困难。(3)一年级学生在文字与符号的语言转换中存在较大的困难,欠缺将文字语言的关系符号转化为数学语言的关系符号的能力。我们还发现符号意识的强弱与学生年龄与教学还是存在一定关系的。在调查中我们了解到在一,二年级解决图形推算问题时,两者的通过率相差无几,但在选择解题策略时却有不同。一年级学生没有经过系统地学习,符号意识也没有经过特定地培养,他们相较二年级所能采用的策略更多一些,有依靠生活经验,利用凑数来获得结果,也有利用代数方法计算获得。而二年级学生通过学校的教学及符号意识的培养,相较一年级能够更加系统地理解图形推算问题,更多地采用代数的方法来解决,策略的选择上更加的统一。
[Abstract]:Symbol consciousness is an important teaching goal in mathematics curriculum standard, and it is closely related to the content of numbers and algebra. The cultivation of symbol consciousness in primary school mathematics has also become the key point of mathematics study in recent years. With the development of mathematics teaching reform in primary school, the teaching content of graphic equation has been strengthened. The teaching content of this part mainly involves the cognition of basic graphics and the basic thinking of equality, at the same time, this content also well reflects the students' symbolic consciousness. Because equality thinking needs to have higher logical thinking ability and is restricted by the development of students' symbolic consciousness, whether it is appropriate to carry out graphic equality in primary school, especially in the first and second grade, has become the focus of teaching research. The main content of this study is the current situation of symbolic consciousness of the first and second graders in primary schools in China. Specifically, this study mainly discusses the following issues: (1) the investigation and analysis of the status quo of the symbol consciousness of the first grade students in primary school include three aspects: the perception of the symbol, the extraction of the symbol, and the use of the symbol. A comparative study is made on the students' specific performance and characteristics. (2) the difference analysis of sign consciousness of grade one and grade two. The investigation and Analysis of the Strategy of calculating the Graphics equation of Grade one students based on a specific figure equation calculation problem as the carrier, this paper studies how to solve the problems of the first grade students. 2. Analysis on the difference of problem solving Strategies between the second graders and the second graders the difference of solving strategies between the first and the second graders is analyzed by using the calculation of the two problems as the carrier. At the same time, this study also investigated the students' affective degree to the problem of figure equation extrapolation. Therefore, it is helpful to adopt more suitable ways in the teaching process, to strengthen students' interest in the problem of figure calculation and to fully improve the teaching effect. Through the investigation, it is found that the first grade students' learning situation in the aspect of symbol consciousness is generally OK, but in the sense of symbol, the extraction of symbol, There are different situations in the use of symbols in these three aspects: (1) the overall situation of students' perception of mathematical symbols is ideal: the students' perception of operational symbols is better, Can also understand the substitution of graphics in the formula. (2) the first grade students have not fully participated in the number of symbols to participate in the column, in the daily language and mathematical language conversion, There are still some difficulties. (3) the first grade students have great difficulties in the language conversion between characters and symbols, and they lack the ability to convert the relational symbols of the written language into the relational symbols of the mathematical language. We also find that there is a certain relationship between the strength of symbolic consciousness and students' age and teaching. In the investigation, we know that in the first and second grade solving the problem of figure extrapolation, the passing rate of the two is the same, but in the choice of problem-solving strategies, there are differences. The first graders did not learn systematically, nor did they develop a specific sense of sign. They used more strategies than the second graders. They relied on their life experience and used the numbers to get results. It is also obtained by algebraic calculation. The second grade students can understand the problem of figure calculation more systematically than the first grade through the teaching of school and the cultivation of symbol consciousness, and adopt more algebraic methods to solve the problem, and the choice of strategy is more uniform.
【学位授予单位】：杭州师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G623.5

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