【作者】 李萍；

【导师】 叶军；

【作者基本信息】 湖南师范大学 ， 学科教学， 2012， 硕士

【摘要】 本文通过对初中学生及初中教师的问卷调查,结果分析发现大部分师生觉得平面几何比较难学,感觉图形变化性太强,不知道从何下手,主要是不知道怎样去构造辅助图形.于是,本文提出了“初中平面几何中怎样构造辅助图形的研究及实践”的课题.本文研究的重点是归纳三类辅助图形的构造方法,它们分别是构造辅助相似形；构造辅助多边形；构造辅助圆.通过例题分析,寻找构造的条件特征,归纳总结这些特征,找出图形形成的过程.本文还尽可能将这些特征普及化,总结出一个应用性较广的结论,帮助解决其他同类型的题目.本文在教学实践方面例举了两则教学案例.案例一是构造多边形证明勾股定理,案例二是运用圆幂定理构造相似三角形.通过理论研究和教学实践,笔者发现,让学生学会挖掘题目特征非常重要,并引导学生了解哪种题目符合哪种特征,哪种特征需要尝试构造哪种辅助图形,从而较大幅度的提升初中学生平面几何中辅助图形构造的能力.最后,本文针对平面几何中怎样构造辅助图形提出了以下几点教学建议：合理选择、安排教学内容；重视书写表达能力；加强新旧知识的联系；鼓励学生独立研究图形,发现构图过程.更多还原

【Abstract】 According to the questionnaire survey between junior high school students and teachers, the author finds that most teachers and students think it is hard for them to learn plane geometry well, and find the graph variability. They do not know how to make a start. How to design a good auxiliary graph is the main difficulty for them. Now in order to help them to solve this problem, the study "The research and practice about how to design a good auxiliary graph in studying the plane geometry for junior high school students" is mentioned in this paper.Several ways, the main results in this paper, to design three kinds of auxiliary graphs, which include auxiliary similar graphs, auxiliary polygon graph and auxiliary circle, are obtained. By an analysis of some examples, we can help the students to find out the conditional characteristic of the structure and then summarize the characteristics, finally find out a graphic formation process. Moreover, in this paper, the author will try her best to make all the characteristics universal and get a widely applicable conclusion, which is good for them to solve all this kind of questions by the same way.Two teaching examples in teaching practice are considered in this paper:Example No.1:the Proof of the Pythagorean Theorem; Example No.2:Design Similar triangles by Power of a point. According to the theoretical research and Experimental Learning, the author finds that it is really very important to make the students to grasp how to conclude the characteristics of the questions. Meanwhile we should guide them to analysis and classify the questions, then make them to choose the proper auxiliary graph which is correspondence to the questions. All this will extremely promote the students’ ability to design the auxiliary graph in plane geometry. Finally, Some suggestions about how to design an auxiliary graph are given:Make a good schedule of teaching; Pay attention to writing ability; Strength the relationship between unknown and known knowledge; Encourage the students to do research on graph by themselves, and found that the composition process.更多还原