小学生对图形与变换内容理解水平的调查研究

发布时间：2018-04-10 02:36

本文选题：小学生　切入点：图形变换　出处：《东北师范大学》2015年硕士论文

【摘要】：在科技迅速发展的当今社会,对几何学的要求越来越高,对空间几何结构的思维能力在很多领域都是非常必要的。中小学的教学工作作为优秀人才培养的摇篮,也在不断的加强与发展着几何教学的体系。随着欧美、俄罗斯、日本等国将动态几何学纳入了小学课本,我国于2010年的新课程标准也对运动的几何学非常重视。“图形与变换”部分的教学,成为了小学数学的重要组成部分。本研究以皮亚杰几何发展理论、范希尔几何认知理论和教材理论为基础,对小学教材的编写合理性进行深入研究。在对不同两地有代表性的四所小学的小学生进行问卷检测后,进行大量的数据统计,分析学生掌握“图形与变换”知识的理解水平,来完善这部分的教材理论。笔者通过对北京师范大学版与人民教育出版社出版的两种主流教材的对比,发现了很多差异性的东西,显然在教学侧重点,教学顺序的分歧值得研究,并合理的优化教材。笔者希望本研究可以为我国的基础教育贡献出自己的一份绵薄之力。通过本文的研究笔者得到了如下的主要结论：一：整体上二到六年级小学生的“图形与变换”理解水平主要结论有：1 随着年龄的升高对“图形与变换”知识的理解程度越强,对于知识的发展阶段主要有3个阶段阶段一小学二年级：学生大多处于几何认知的水平0,少数处在水平1。阶段二小学三到五年级：大部分学生处于几何认知水平的水平1阶段,处在水平0与水平2阶段的学生较少。阶段三小学六年级：学生主要发展到几何认知水平的水平2阶段。2 男女性别差异,导致的理解水平差异不显著。3 同年级学生的水平也略有差异。并且年级越低水平差异性越大,小学高年级差别较小。二：“图形与变换”主要三部分内容具体结论：1 平移在小学生的理解上最好,其次是对称,旋转问题最为复杂。2 对称与平移问题比较直观,小学二、三、四年级的学生都很好理解与习得。3 旋转问题多涵盖平移在其中,不易理解,适合五年级开始学习,六年级综合应用。
[Abstract]:With the rapid development of science and technology, the requirement of geometry is getting higher and higher, and the thinking ability of spatial geometry structure is very necessary in many fields.As the cradle of the cultivation of outstanding talents, the teaching work of primary and middle schools is constantly strengthening and developing the system of geometry teaching.With the introduction of dynamic geometry into primary school textbooks in Europe and America, Russia and Japan, the new curriculum standards in 2010 also attach great importance to sport geometry.The teaching of Graphics and Transformation has become an important part of primary mathematics.Based on Piaget's theory of geometric development, van hill's theory of geometric cognition and textbook theory, this paper makes a deep study on the rationality of compiling textbooks in primary schools.After the questionnaire test on the pupils of four primary schools in different places, a large number of data and statistics are carried out, and the understanding level of the students' mastering the knowledge of "graphics and transformation" is analyzed to perfect this part of the textbook theory.By comparing the two kinds of mainstream textbooks published by Beijing normal University and people's Education Publishing House, the author finds a lot of differences, which are obviously focused on teaching, the difference of teaching order is worth studying, and the reasonable optimization of teaching materials.I hope this research can contribute to our basic education.The main conclusions of this paper are as follows: firstly, the understanding level of "graphics and transformation" in grade two to six pupils on the whole is that the understanding level of "figure and transformation" is stronger with the increase of age, and the understanding level of "figure and transformation" is stronger with the increase of age.For the development of knowledge, there are three stages: the second grade of primary school: most of the students are at the level of geometric cognition 0, and the few at level 1.Stage 2 Primary School Grade 3 to Grade 5: most of the students are at level 1 of geometric cognition level, and less students are at level 0 and level 2.Stage 3 primary school grade six: students mainly develop to the level of geometric cognition level 2 stage .2 gender differences, resulting in no significant difference in the level of understanding of the same grade students' level is also slightly different.And the lower the grade is, the greater the difference is, the lower the grade is, the smaller the difference is.Two: "Graphics and Transformation" the main three parts of the concrete conclusion: 1 translation is the best in the understanding of primary school students, followed by symmetry, rotation is the most complex .2 symmetry and translation problem is more intuitive, primary school, two, three,The fourth grade students have a good understanding and acquisition of 3. 3 rotation problem covers translation in it, difficult to understand, suitable for the fifth grade to start learning, sixth grade comprehensive application.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G623.5

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