高中生数学符号语言表征能力的调查研究

发布时间：2018-06-15 03:18

本文选题：数学符号语言 + 表征能力内涵　；参考：《南京师范大学》2015年硕士论文

【摘要】：数学符号语言在数学教育中占有重要的地位,许多高中生感觉数学越来越难学的一个主要原因是不理解数学符号语言,因此研究高中生对数学符号语言的表征能力具有十分重要的意义。首先,笔者在查阅相关的教育教学理论的基础上,结合国内外有关数学符号语言教育方面研究成果,试着对数学符号语言表征能力的内涵和层次进行了界定,并从数学符号的用途这一角度对高中阶段的数学符号进行了重新分类。其次对高一到高三的286名学生进行了问卷调查和数学符号语言表征能力的调查测试,并对测试卷中出现的具体问题进行了访谈,以此了解学生在数学符号语言表征过程中的真实想法,进一步探究对数学符号表征的过程。对问卷结果和测试结果收集来的数据运用统计的方法从不同年级、不同学业成绩水平,不同性别等角度作了进一步的分析。再次根据统计结果和访谈,分析了影响高中生数学符号表征能力的因素。笔者认为主要是两大类因素：一是外部环境因素,包括课程和目标设置,教师的符号教学观和教师的符号教学方法观。二是内部环境因素,包括学生的符号语言知识、符号意识,以及一些智力和非智力因素。最后,根据结果分析,提出了自己的一些见解,得出了一些结论：(1)从总体来看,高中生对数学符号语言的表征能力水平一般,并且学生的数学符号语言表征能力并没有随着知识的增多或年级的增高而显著提高。(2)不同学业成绩的学生在符号语言表征能力方面存在显著差异,学优生的表征能力远远超过中等生和学困生,这一结果充分表明对数学符号的表征能力与学业水平成绩是密切相关的,对数学符号语言的表征能力也成为影响学困生数学学习的一个重要因素。(3)不同性别的学生在符号语言表征能力方面总体不存在显著差异。(4)教师对数学符号语言教学的忽视是导致学生数学符号表征能力低下的一个重要原因。(5)提高学生数学符号语言表征能力应从对符号的感知,对符号语义的分析,对符号意义的建构,对符号的运用等层面进行训练。(6)培养学生的数学符号表征能力需要教师转变片面的知识教学观、解题方法观,也应树立符号教学观。本研究得出最后结论：培养学生对数学符号语言的表征能力是提高学生数学学习能力的一种有效的,可行的,具有可操作性的方法和途径。
[Abstract]:Mathematical symbolic language plays an important role in mathematics education. Many senior high school students feel that one of the main reasons why mathematics is becoming more and more difficult to learn is their lack of understanding of mathematical symbolic language. Therefore, it is of great significance to study the representation ability of high school students in mathematical symbolic language. First of all, the author tries to define the connotation and level of mathematical symbolic language representation ability on the basis of consulting relevant educational and teaching theories and combining with the research results of mathematical symbolic language education at home and abroad. From the point of view of the use of mathematical symbols, the paper reclassifies the mathematical symbols in senior high school. Secondly, 286 students from Senior one to Senior three were investigated and tested by questionnaire and mathematical symbolic language representation, and the specific problems in the test paper were interviewed. In order to understand the students' real ideas in the process of mathematical symbolic language representation, and further explore the process of mathematical symbolic representation. The results of the questionnaire and the data collected from the test results were further analyzed from different grades, different academic achievement levels and different genders by statistical methods. Based on the statistical results and interviews, this paper analyzes the factors that affect the mathematical symbol representation ability of senior high school students. The author thinks that there are two kinds of factors: one is the external environmental factors, including curriculum and goal setting, teachers' concept of teaching symbols and teachers' view of teaching methods of symbols. Second, internal environmental factors, including students' knowledge of symbolic language, symbolic awareness, and some intelligence and non-intelligence factors. Finally, based on the analysis of the results, the author puts forward his own opinions and draws some conclusions. On the whole, the level of high school students' ability to express mathematical symbolic language is general. Moreover, the students' mathematical symbolic language representation ability did not improve significantly with the increase of knowledge or grade. (2) there were significant differences in the symbolic language representation ability among students with different academic achievements. The representation ability of eugenics is much higher than that of secondary students and students with learning difficulties. This result shows that the representation of mathematical symbols is closely related to academic achievement. The representation ability of mathematical symbolic language has also become an important factor to affect the mathematics learning of students with learning difficulties.) there is no significant difference between students of different genders in the aspect of symbolic language representation. 4) Teachers teach mathematical symbolic language. The neglect of learning is an important reason for the students' poor representation of mathematical symbols. (5) to improve the students' ability of representation of mathematical symbols should be based on the perception of symbols. The analysis of symbolic semantics, the construction of symbolic meaning and the training of the use of symbols etc.) to cultivate students' mathematical symbol representation ability requires teachers to change their one-sided knowledge teaching view, problem-solving method view and symbolic teaching view. The final conclusion of this study is that it is an effective, feasible and operable way to improve students' mathematical learning ability by cultivating students' representation ability of mathematical symbolic language.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【共引文献】