初一学生数学抽象能力的调查研究

发布时间：2019-05-07 08:28

【摘要】：数学抽象作为核心素养之首,对其的关注越来越多.数学的本质是抽象,数学抽象能力的发展对学生学习数学具有重要的意义,考虑到初一的学生正处于是能力发展的关键期,了解初一学生数学抽象能力的情况,具有现实的研究意义.本论文采用文献分析法,调查问卷法和分析法进行研究.首先通过广泛而深入地查阅相关文献资料,并结合苏科版七年级上册数学教材内容,将初一学生数学抽象能力分为两个维度六个成分.编制了一份初一学生数学抽象能力的测试卷,再对测试结果进行数据分析,最后提出相关教学建议.本研究的测试对象为南京市某一所初中的初一部分学生.为了更好地了解学生的情况,在回收测试卷时,随机选取个别学生进行访谈.从初一学生数学抽象能力的整体发展情况,实验班和普通班学生的情况以及不同性别的学生差异情况这三个方面,利用SPSS软件对测试卷的数据进行分析,再对测试卷做归因分析.本文研究主要结论如下:(1)初一学生数学抽象能力整体发展较好;(2)学生在表征型抽象和原理型抽象上存在显著差异,学生表征型抽象要比原理型抽象好;(3)不同性别的学生在数学抽象能力上没有显著差异;(4)实验班和普通班学生数学抽象抽象能力差异显著,实验班学生表征型抽象能力比普通班学生发展好,学生的原理型抽象成绩并无太大的差异.根据研究结果以及教育心理学理论和相关文献,结合具体教学案例,提出四点培养初一学生数学抽象能力的教学建议:(1)借助直观操作,感悟数学抽象;(2)注重观察、分析、类比、猜想、概括等活动的积累;(3)加强数学抽象能力的训练;(4)关注其他素养的培养.
[Abstract]:Mathematical abstraction as the first of the core literacy, more and more attention has been paid to it. The essence of mathematics is abstract, and the development of mathematical abstract ability is of great significance to students' learning of mathematics. Considering that the students of junior high school are in a critical period for the development of their abilities, they are aware of the situation of the abstract ability of junior high school students in the first year of junior high school. Has the realistic research significance. This paper uses the literature analysis method, the investigation questionnaire method and the analysis method to carry on the research. Firstly, the abstract ability of junior high school students is divided into two dimensions and six components by means of extensive and in-depth access to relevant literature materials, and combining with the contents of mathematics textbooks in the first volume of the seventh grade of the Jiangsu edition of junior high school. This paper compiles a test paper of mathematics abstract ability of junior high school students, then analyzes the data of the test results, and finally puts forward some teaching suggestions. The test object of this study is a junior high school student in Nanjing. In order to get a better understanding of the students' situation, individual students were randomly selected for interviews when the test papers were collected. This paper analyzes the data of test paper by using SPSS software from three aspects: the overall development of mathematics abstract ability of junior high school students, the situation of students in experimental class and ordinary class, and the difference between students of different sexes. Then the attribution analysis of the test volume was made. The main conclusions of this paper are as follows: (1) the overall development of mathematical abstraction ability of junior high school students is good; (2) there are significant differences between representational and theoretical abstractions, and the students' representational abstractions are better than those of principle abstractions; (3) there is no significant difference in the abstract ability of mathematics among students of different sexes; (4) there is a significant difference between the experimental class and the ordinary class in the abstract ability of mathematics. The students' representational abstract ability of the experimental class is better than that of the ordinary class, and the students' abstract achievement of the theoretical type is not much different. According to the research results, educational psychology theory and related literature, combined with concrete teaching cases, four teaching suggestions are put forward to cultivate the mathematics abstract ability of junior one students: (1) with the help of visual operation, the understanding of mathematical abstraction is realized; (2) pay attention to the accumulation of activities such as observation, analysis, analogy, conjecture and generalization; (3) strengthen the training of mathematical abstract ability; (4) pay attention to the cultivation of other qualities.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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