初中生数学思维结构特征分析的个案研究

发布时间：2018-08-13 11:54

【摘要】：学生学习数学的目的不仅仅是为了数学知识的学习,更多的应该是学会数学的思维,在生活中运用数学思维来分析和解决问题。数学思维是数学学习的重要部分,初三的数学学习对于初中生的数学思维更是形成的重要阶段,教师应更多的让学生经历数学的学习过程,充分暴露学生数学学习的过程。本文利用建构主义理论、文化生态学理论、联结主义理论、认知主义学习理论和波利亚“怎样解题”理论,为初中生数学思维的研究奠定了丰富的理论基础。本研究的目的是学生能够认识数学思维,尊重数学思维在数学学习中的重要地位,期望可以更好的为研究初中生数学思维机构特征服务。通过本文的研究促使更多的学生有针对性的形成完善的数学思维,实现学生挖掘潜在的能力,教师培养提供好的依据。在本文中对初三某班的学生进行试卷收集、访谈和课堂观察,充分搜集能够体现学生数学思维的资料。通过对学生四次月考试卷中的解答题进行选择,在数与代数和图形与几何部分,选取10道题,分析学生在解题过程中体现的直觉思维、逻辑思维和形象思维的频次与相互之间联系的频次,对数学思维之间的整合与频次的结果进行分类,划分出懒隋型、单一型、杂糅型和完整型。再对学生进行访谈和课堂观察,对资料进行整理,具体分析各类型的表现形式和所包含的学生种类的人数,在表现形式的基础上总结出影响因素为学习兴趣、学习态度、自控力、学校班级环境、知识建构过程和反思归因。通过对类型和影响因素的分析,总结出结论：学生的数学思维结构特征的类型；初中生逻辑思维意识较弱；初中生数学思维差异的主要原因。给出的三条建议是：对学生进行积极心理培训,发展积极心理品质；帮助养成良好的数学思维,及时反思；把课堂交给学生,提升数学思维的发展空间。
[Abstract]:The purpose of students learning mathematics is not only to learn mathematics knowledge, but also to learn the thinking of mathematics, to use mathematical thinking to analyze and solve problems in life. Mathematics thinking is an important part of mathematics learning. The mathematics learning of junior high school students is an important stage of the formation of mathematics thinking. Teachers should let students experience the learning process of mathematics and fully expose the process of students' mathematics learning. Using constructivism theory, cultural ecology theory, connectionism theory, cognitive learning theory and Polia's theory of "how to solve problems", this paper lays a rich theoretical foundation for the study of junior high school students' mathematical thinking. The purpose of this study is that students can understand mathematical thinking, respect the important position of mathematical thinking in mathematical learning, and hope to better serve for the study of mathematical thinking institutional characteristics of junior high school students. Through the research of this paper, more and more students can form perfect mathematical thinking, realize the students' potential ability, and provide a good basis for teacher training. In this paper, the students of a class of junior high school students are collected, interview and classroom observation, which can fully collect the information that can reflect the students' mathematical thinking. Through the selection of the answer questions in the students' fourth monthly examination papers, 10 questions are selected in the parts of number and algebra, graphics and geometry, and the intuitionistic thinking of the students in the process of solving the problems is analyzed. The frequency of logical thinking and image thinking and the frequency of interrelation between them are classified into three types: lazy Sui type, single type, mixed type and complete type. Then the students are interviewed and observed in class, the materials are sorted out, and the expression forms of each type and the number of students included are analyzed concretely. On the basis of the form of expression, the author concludes that the influencing factors are learning interest, learning attitude, and so on. Self-control, school class environment, knowledge construction process and reflection attribution. Through the analysis of the types and influencing factors, the conclusion is drawn: the types of students' mathematical thinking structure, the weak sense of logical thinking of junior high school students, and the main reasons of the difference of junior high school students' mathematical thinking. The three suggestions are: to train students in positive psychology and develop positive psychological quality; to help cultivate good mathematical thinking and to reflect on it in time; to give the class to students to promote the development space of mathematical thinking.
【学位授予单位】：延边大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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