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上海初中生几何变换理解困难及教学对策研究

【作者】 葛秦

【导师】 鲍建生;

【作者基本信息】 华东师范大学, 学科教学(数学)(专业学位), 2017, 硕士

【摘要】 几何变换思想由于其对于几何论证具有统一性和规律性,其发展在数学教育现代化进程中占据了极其重要的位置.然而,无论从课标教材本身、教师的实施课程及学生的实际掌握还是从历年中考的考察结果来看,几何变换无疑从初学时的简单易操作转变为了中考时人人头疼的难点.因此本文就上海初中生在几何变换理解上存在的困难及教师相应的教学对策展开了研究.本文采用结合布鲁纳的理解表征理论和Byer的理解层次理论制定的衡量学生几何变换理解困难的研究框架,结合SPSS软件进行问卷的定量分析,再对部分学生及教师采取访谈形式进行定性分析.从而得出上海初中生对几何变换的理解存在以下困难:1.概念理解单一化、机械化,表象匮乏2.旋转对称与轴对称内部及相互关系理解混淆3.有无格点作图中关系理解矛盾造成这些困难的原因主要有概念本身的迷惑性、关系理解的单向性、问题的不同阐述方式以及不同年级变换内容的隐性关联.最后本文就以上理解困难及原因结合教材进行了相关教学对策研究并给出了教学建议:强调概念内部与概念之间本质关联与区别、借助多媒体软件动态演示增强理解、引入无格点作图加深理解、合理组织教材,互相渗透,突出隐性关联,并对课标提出相应的建议.

【Abstract】 The development of geometric transformation thought in the process of modernization education occupies an extremely important position because geometric transformation thought makes the geometric demonstration with uniformity and regularity. However, no matter from the standard, content, implementation, acquisition of the curriculum to the results of past years’ examinations, geometric transformation undoubtedly changes from simple easy to operate in the beginner to the difficulty of the high school entrance exam. This thesis carries out research on the difficulties of understanding of geometric transformation and the corresponding teaching strategies of junior middle school students in Shanghai.Quantitative analysis is based on the research framework combined with Bruner’s understanding representation theory and Byer’s understanding hierarchy theory and SPSS. Qualitative analysis is based on interviews of students and teachers. Thus eliciting the following difficulties of understanding the geometric transformation of junior middle school students in Shanghai:1. Simplification, mechanization of conception understang; lacking of representation2. Internal and mutual relational clutter between rotational symmetry and axisymmetric symmetry3. Understanding contradiction of the relationship between lattice drawing and off-lattice drawingThe mainly causes of these difficulties are the confusing of the concepts, unidirectional understanding of the relationship, various description of the problems and the implicit association between different grades.Finally in this thesis, studies on the teaching strategies are carried out and teaching suggestions are also included:emphasizes the natural association and difference between internal and mutual conception, enhancing understanding with the aid of multimedia software, introduction of off-lattice drawing to comprehend intensely, reasonally organizing the teaching material, interpenetrating, developing implicitly association, and putting forward corresponding suggestions on curriculum standard.

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  • 【网络出版投稿人】 华东师范大学
  • 【分类号】G633.6
  • 【下载频次】89
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