分析中小学关于“圆”的教材内容设计

发布时间：2018-03-29 08:51

本文选题：圆　切入点：教材比较　出处：《广州大学》2016年硕士论文

【摘要】：圆是几何数学中一类特殊的曲线,虽然其性质比较简单,但其应用却非常广泛.本文通过对三种不同版本数学教材中圆的内容进行分析比较,从学生认知角度、学习行为角度、激励动机和兴趣角度等加以分析探索这些教材的共性和差异,挖掘其优点,审视其不足.期望能为一线教师的课堂教学提供一些参考,并能为中小学数学教材建设做出一点小小贡献.迄今为止,国内学者对不同版本教材中圆内容的系统研究还不是很多,而且这些研究也仅是对“圆”的某一部分进行的研究,缺乏从小学至初中再到高中这一体系的研究,而这却对全面认识“圆”内容很重要.本文采用文献法、内容分析法和比较研究法作为研究工具,在已有研究成果的基础上,对人教版、苏教版和北师大版三个版本小学、初中以及高中所涉及到的圆的内容进行了系统的研究.得到以下结论:1.在内容编排框架方面.北师大版中圆的内容总课时数最多,苏教版教材中“圆”的内容初次出现是在五年级下册,相对于人教版和北师大版都要早一个学期.2.在栏目设计方面.苏教版教材栏目最为丰富,难度梯度的设置非常合理;人教版教材栏目设置的实用性较强;北师大版教材栏目设置简单,但却精炼.3.在内容顺序编排方面.三个版本教材大致相同,差异主要体现在具体内容的安排顺序上,例如“弧、弦、圆心角”、“垂径定理”的顺序有较大差别.4.在“圆”的内容广度和深度方面.苏教版教材中知识点中的命题最多,且内容安排深度最深;而人教版教材以概念形式出现的知识点最多.人教版和北师大版教材难度分布属于倒U型,深度水平适中.三个版本教材的内容广度有明显差异,课程总体难度较高.5.在概念的引入方式方面.三个版本教材中均以多种不同的方式对概念进行引入,人教版注重生活实例和动手操作两种方式,北师大版教材使用较多的是常设问题和直接定义的方式,苏教版教材各种方式数量均衡.6.在例题呈现方式方面.三个版本教材的共同点体现在纯数学例题所占比例最高.其中苏教版例题数量最多、难度偏向简单;北师大版教材例题数量少、难度合理;人教版例题数量多、难度较高,引入部分贴近生活且较有趣味性.8.在圆周率内容的编排部分,人教版教材重视引入设计,概念表述准确、严谨;苏教版教材引入部分繁琐,概念表述严谨,补充内容充实;北师大版教材引入部分精简,但概念表述不够严谨,课后补充内容充实、详细.最后,值得说明的是,要全面对比三个不同版本教材中“圆”的内容,仅对教材进行理论分析还远远不够,如能了解不同版本设计的差异对教学效果的影响,通过对使用不用教材地区的学生进行检测反馈性分析,相信能更准确地对之予以准确的分析比较,这也是值得今后进一步探索的问题.
[Abstract]:Circle is a special kind of curve in geometric mathematics. Although its nature is relatively simple, its application is very wide. This paper analyzes and compares the contents of circle in three different versions of mathematics textbooks, from the perspective of students' cognition and learning behavior. The motivational motivation and interest angle are analyzed to explore the commonness and difference of these teaching materials, to excavate their advantages, to examine their shortcomings, and to provide some references for the classroom teaching of front-line teachers. And can make a little contribution to the construction of mathematics textbooks in primary and secondary schools. Up to now, there are not many systematic studies on the circular content in different versions of textbooks by domestic scholars, and these studies are only a part of the "circle". There is a lack of research on the system from primary school to junior high school to senior high school, which is very important to fully understand the content of "circle". This paper uses literature method, content analysis method and comparative research method as research tools, based on the existing research results. This paper makes a systematic study on the contents of the circle involved in the three versions of the edition of the people's Education, the Su Education and the Beijing normal University. In the elementary school, junior middle school and senior high school, the following conclusions are drawn: 1. In terms of the content arrangement framework, the total class hours of the content in the circle edition of the Peking normal University are the largest. The first appearance of the content of "Yuan" in the teaching materials of the Su education edition is in the fifth grade, which is one semester earlier than that of the people's edition and the Beijing normal University edition. 2. In the field of column design, the teaching material column of the Su education edition is the most abundant, and the setting of the difficulty gradient is very reasonable. The column setting of the teaching material of the personal education edition is more practical; the column of the edition of the Beijing normal University is simple, but it is refined. 3. In the content order arrangement, the three versions of the textbook are roughly the same, and the difference is mainly reflected in the arrangement order of the specific content. For example, the order of "arc, string, center angle" and "vertical diameter theorem" is quite different. 4. In the scope and depth of the content of "circle", the proposition of knowledge points is the most in the teaching material of Su Jiao edition, and the content arrangement is the deepest; However, the teaching materials of personal education have the most knowledge points in the form of concept. The difficulty distribution of the teaching materials of personal education and Beijing normal University belongs to the inverted U type and the depth is moderate. There are obvious differences in the content and breadth of the three versions of textbooks. The overall difficulty of the course is relatively high. 5. In the three versions of textbooks, the concepts are introduced in many different ways. The people's Education Edition pays attention to the two ways of life example and hands-on operation. The textbooks used in the Peking normal University edition are mostly permanent problems and the way they are directly defined. The common points of the three versions of textbooks are that the proportion of pure mathematical examples is the highest. Among them, the number of examples in the Soviet edition is the most, and the difficulty is simple; The number of examples in Beijing normal University textbook is small, the difficulty is reasonable, the number of examples is more and the difficulty is higher in the edition of human education, the introduction of part is close to life and more interesting. 8. In the part of arranging the contents of the circular ratio, the teaching materials of human education pay attention to the introduction of design, and the concept is expressed accurately. Rigorous; the introduction of the Soviet edition of teaching materials is cumbersome, the concept is strictly expressed, and the supplementary content is enriched; the Peking normal University edition introduces some streamlining, but the concept statement is not rigorous enough, and the supplementary content after class is substantial and detailed. Finally, it is worth explaining that, In order to compare the contents of "circle" in three different versions of textbooks, it is far from enough to make a theoretical analysis of the teaching materials. If we can understand the influence of the differences in the design of different versions on the teaching effect, It is believed that it can be more accurately analyzed and compared with the students who do not use teaching materials. This is also a problem worthy of further exploration in the future.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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