中小学圆形知识分布及其教学研究

发布时间：2018-04-02 04:35

本文选题：义务教育阶段　切入点：平面几何　出处：《延安大学》2016年硕士论文

【摘要】：几何课程与教学改革一直是数学教育研究的热点,其在培养学生三维空间能力、形象思维能力、合情推理、解析几何观念的树立等方面发挥着重要作用。圆形是贯穿义务教育阶段和高中阶段的几何课程内容中的重点内容之一,历来有很多研究者对其进行了多角度、多层面、多维度的研究和论述,但总体来看,在现有的聚焦平面几何中圆形知识的研究成果中,大多是从几何学的整体角度出发对整个平面几何开展的研究,鲜少出现具体的、有针对性地、专门性地对中小学圆形知识展开详尽的、系统的、专门的研究。本文以现行的中小学数学教材为研究介质,对平面几何中编排的中小学圆形知识及其分布进行系统研究,并结合最新颁布的中小学数学课程标准对之予以理论高度的解读,对圆形知识在中小学各个学段的呈现方式和编排做一细致的分析。同时,根据SOLO分类理论分析评价在学习圆形知识的过程中,学生几何思维水平的具体分析和学生回答相关问题时思维结构水平的特点,最后参照本文的研究成果对中小学数学教材中的平面几何中圆形知识的实际教学和学生的学习提出了若干教学建议.本文主要采用理论分析法、内容分析法和教学片段分析法等研究方法。本文共有5个章节。第1章重在介绍几何课程在国内外研究的历史和现状,在详实阐述和归类关于几何研究的文献综述的基础上,提出了本文拟研究的问题,阐明了研究的目的与意义,介绍了研究的方法与框架。第2章则主要是聚焦义务教育阶段和高中阶段圆形知识在各个学段的呈现方式给予深入分析,对中小学平面几何中圆形知识的内容分布展开了系统、全面的梳理,并结合数学新课标的相关规定探讨了各个学段圆形知识的相互衔接问题,接下来是对中小学的圆形知识进行简单的类别分析。第3章首先引入和大致概括了SOLO分类理论,及该理论提出的理论基础;然后,运用该分类理论有的放矢地分析了中小学各学段圆形知识中最具有典型性和代表性的实际课堂教学片段展开几何思维水平的分析。第4章在以上章节研究成果的基础上,对中小学四个学段中涉及到平面几何中的圆形知识的教学提出了一些具体的、可行的、有针对性的建议。第5章中在反思论文的不足和正视研究的局限性的同时,为今后继续研究中小学圆形知识的实际教学提供一些更好地设想。
[Abstract]:The reform of geometry curriculum and teaching has always been a hot topic in mathematics education. It plays an important role in cultivating students' three-dimensional spatial ability, image thinking ability, reasonable reasoning and the establishment of analytic geometry concept.Roundness is one of the most important contents of geometry curriculum in compulsory education and senior high school. Many researchers have studied and discussed it from many angles, levels and dimensions, but generally speaking,In the existing research results of circular knowledge in plane geometry, most of them are carried out from the perspective of geometry as a whole.A detailed, systematic and specialized study of circular knowledge in primary and secondary schools.Based on the current mathematics teaching materials of primary and middle schools, this paper makes a systematic study on the circular knowledge and its distribution of primary and secondary schools arranged in plane geometry, and gives a theoretical interpretation of it in combination with the newly promulgated mathematics curriculum standards in primary and secondary schools.This paper makes a detailed analysis of the presentation and arrangement of circular knowledge in each learning section of primary and secondary schools.At the same time, according to the analysis of SOLO classification theory, the concrete analysis of students' geometric thinking level and the characteristics of students' thinking structure level when answering related questions in the process of learning circular knowledge.Finally, according to the research results of this paper, some teaching suggestions are put forward for the practical teaching of circular knowledge in plane geometry and the study of students in primary and middle school mathematics textbooks.This article mainly uses the theory analysis method, the content analysis method and the teaching fragment analysis method and so on research method.There are five chapters in this paper.The first chapter focuses on introducing the history and present situation of the research of geometry course at home and abroad. On the basis of elaborating and classifying the literature review of geometry research in detail, the paper puts forward the problems to be studied in this paper, and expounds the purpose and significance of the research.The research method and framework are introduced.The second chapter mainly focuses on the presentation of circular knowledge in the compulsory education stage and the senior middle school stage, and makes a thorough analysis of the distribution of circular knowledge in the plane geometry of primary and secondary schools.Combined with the relevant regulations of the new mathematics curriculum standard, this paper discusses the problem of the interconnectedness of the circular knowledge of each learning section, and then makes a simple analysis of the circular knowledge in primary and secondary schools.Chapter 3 introduces and generalizes the SOLO classification theory and the theoretical basis of the theory.By using the classification theory, this paper analyzes the geometric thinking level of the most typical and representative segments of practical classroom teaching in the circular knowledge of the middle and primary schools.In chapter 4, on the basis of the research results of the above chapters, some concrete, feasible and targeted suggestions are put forward for the teaching of circular knowledge in plane geometry in four sections of primary and secondary schools.Chapter 5, while reflecting on the shortcomings of the thesis and facing the limitations of the research, provides some better ideas for the further study of the practical teaching of circular knowledge in primary and secondary schools.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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