初三学生数学类比推理能力调查研究

发布时间：2018-03-09 03:16

本文选题：初三数学　切入点：类比推理能力　出处：《扬州大学》2017年硕士论文　论文类型：学位论文

【摘要】：2011年的时候,教育部制定并颁布了《义务教育数学课程标准》,在这一标准中重点强调了在数学课堂中要注重发展学生的推理能力,并指出推理能力的发展应存在于整个义务教育阶段的数学学习过程中。自此之后无论是硕、博论文还是期刊都开始把关注的重点从教学中应用类比推理转向了如何利用教学来培养学生的类比推理能力。目前来说,对于学生类比推理能力的研究主要集中在高中,关于初中生类比推理能力的研究较少。本文通过查找、阅读大量文献总结了关于类比推理的四个重要理论:Gentner的结构映射理论、Holyoak的实用图示理论、Ross的样例理论和Piaget的结构阶段理论;从类比推理最早研究者、实施过程、实施原则和分类四个方面对类比推理进行了文献综述;根据高纪平从类比的两个对象的相似性的属性特征将类比分为:性质类比、关系类比、结构类比、方法类比和命题类比五种形式。通过调查问卷重点研究了两个学校初三学生数学类比推理能力的现状:初三学生在关系类比、方法类比、结构类比以及命题类比方面的类比推理能力都不是很高,但在性质类比方面的类比推理能力最高;最小值关系类比推理能力高于运算关系类比推理能力;计数方法高于数形结合类比推理能力,对于计数法的类比,简单的问题可以进行正确的类比,但是对于比较复杂,数字比较大的,有难度的问题,小部分综合能力比较强的学生还是能够通过观察、思考,进行正确地类比得出准确答案的,但是大部分的学生做题盲目,缺乏系统性,研究问题不透彻。通过调查问卷的形式对初三数学教师类比推理教学进行了调查与分析,可以得到:大多数的教师是通过参加新课程培训的时候才知道“类比推理”的,认为现行的教科书对于类比推理相关内容的安排还算合理,在教学中能够做到有意识的使用“类比推理”,大部分教师认为在讲授新课、例题讲解环节类比教学的效果比较好。一些更加切实有效的提高学生类比推理的能力的策略也要认真地去寻找、去探索、去实践。紧接着从教师教学、学生自身和评价体系三个方面总结了培养学生数学类比推理能力的策略;又从与事例做类比和与旧知识的类比两个方面具体阐述了类比推理在初中数学教学中的应用。
[Abstract]:In 2011, the Ministry of Education formulated and promulgated the Mathematics Curriculum Standard for compulsory Education, in which the emphasis was placed on developing students' reasoning ability in mathematics classes. It is pointed out that the development of reasoning ability should exist in the process of mathematics learning in the whole compulsory education stage. In both papers and journals, the focus of attention has shifted from applying analogical reasoning in teaching to how to use teaching to develop students' ability of analogical reasoning. At present, the research on students' ability of analogical reasoning is mainly focused on senior high school. There are few researches on the ability of analogy reasoning of junior high school students. Reading a great deal of literature, we summarize four important theories on analogical reasoning:: Gentner's structural mapping theory and Holyoak's practical schema theory, Ross's sample theory and Piaget's structural stage theory, from the perspective of the earliest researchers of analogical reasoning, the process of implementation. According to Gao Jiping's attribute characteristics of similarity between two objects, analogy is divided into three parts: nature analogy, relation analogy, structure analogy, and so on. Methods five forms of analogy and propositional analogy were used to study the present situation of mathematical analogical reasoning ability of junior high school students in two schools by questionnaire: the third grade students in the relation analogy, the method analogy, the third grade students in the relation analogy, the method analogy in the middle school. The ability of analogy reasoning in structure analogy and propositional analogy is not very high, but the ability of analogy reasoning in nature analogy is the highest, the ability of analogy reasoning in minimum value relation is higher than that in operation relation analogy reasoning. The method of counting is superior to the ability of numeral-form combined analogy reasoning. For the analogy of counting method, simple problems can be compared correctly, but for the more complicated, the larger numbers, the more difficult problems, A small number of students with relatively strong comprehensive abilities are still able to come up with accurate answers through observation, thinking, and correct analogy, but most of them are blind and lack of systematicness in doing problems. Through the investigation and analysis of analogical reasoning teaching of junior high school mathematics teachers in the form of questionnaire, it can be concluded that most teachers know "analogy reasoning" only when they take part in the new curriculum training. It is considered that the current textbook is reasonable for the arrangement of the related contents of analogical reasoning, and can consciously use "analogical reasoning" in teaching. Most teachers think that they are teaching new lessons. Some more practical and effective strategies to improve students' ability of analogical reasoning should also be carefully sought, explored, and practiced. Then, from the perspective of teachers' teaching, This paper summarizes the strategies of cultivating students' ability of analogical reasoning in mathematics from the aspects of students themselves and evaluation system, and expounds the application of analogy reasoning in mathematics teaching in junior high school from two aspects: making analogy with examples and analogy with old knowledge.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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