初二学生全等三角形学习情况的调查与研究

发布时间：2018-04-12 14:23

本文选题：全等三角形 + 空间观念　；参考：《河北师范大学》2017年硕士论文

【摘要】：在当今时代,几何的教与学不仅是数学课程的重要问题,也是教学改革的重大问题。几何不仅能够培养学生的空间想象力,而且对逻辑推理能力的培养也非常重要。在几何教学中,作为初中数学严格演绎推理开端的全等三角形的学习,对以后的数学学习将会产生深远的影响。因此,本文选取石家庄市区重点中学的初二年级普通学生为研究对象,采用文献研究法、访谈法、作业分析法和问卷调查法,研究初二年级学生全等三角形的学习情况,并将学生遇到的困难分类整理并进行归因分析,最后提出相应的教学策略,对于全等三角形这部分知识的教学可以起到一定的理论参考价值和实践指导意义。通过调查与研究,笔者发现初二年级普通学生在学习《全等三角形》一章时,大部分学生掌握比较扎实,能够运用所学知识解决问题,但是也有少部分学生掌握不佳,具体表现在(1)基础知识方面:对概念和关键词语不理解;(2)空间观念方面:识图能力薄弱,不能分析出研究对象或对应元素,空间想象力较差,受思维定势影响严重以及灵活运用相关信息处理图形的能力不强;(3)推理能力方面:理不清命题的条件和结论,不能恰当选择或运用定理以及思维不严谨,表达不规范;(4)应用意识方面:不能将实际问题抽象成数学问题,数学建模能力较差,不能将所学知识与实际相联系,不能用数学知识解决实际问题以及知识迁移能力较差;(5)数学多元表征能力方面:对文字语言所表达的题意不理解,不能实现等价转换以及表征方式不规范。针对此种现象,笔者从全等三角形的概念教学和命题教学两个方面提出相应的教学建议:(1)加强全等三角形概念教学:创设合理的教学情境,探究全等三角形的定义;运用变式教学,深化对全等三角形概念的理解;加强概念对问题解决的应用指导作用。(2)加强全等三角形命题教学:学生充分参与课堂,探究三角形全等的判定定理;加强证明训练,注重推理能力的培养;增强命题的运用能力,培养学生的数学应用意识。
[Abstract]:Nowadays, the teaching and learning of geometry is not only an important problem in mathematics curriculum, but also a major problem in teaching reform.Geometry can not only cultivate students' spatial imagination, but also the ability of logical reasoning.In geometry teaching, as the beginning of strict deductive reasoning in junior high school mathematics, the study of full triangle will have a profound influence on the later mathematics learning.Therefore, this article selects the second grade ordinary students of Shijiazhuang urban key middle school as the research object, uses the literature research method, the interview method, the homework analysis method and the questionnaire survey method, studies the junior high school student's complete triangle study situation.The difficulties encountered by the students are classified and analyzed, and the corresponding teaching strategies are put forward, which can play a certain theoretical reference value and practical guidance significance for the teaching of this part of knowledge.Through investigation and research, the author found that most of the students in the second grade in the study of the chapter "Total Triangle" have a relatively solid grasp, can use the knowledge to solve problems, but also a small number of students do not master well.In terms of basic knowledge: not understanding the concept and key words, the spatial concept: weak ability of map recognition, unable to analyze the object of study or corresponding elements, poor spatial imagination,Influenced seriously by the thought set and the ability of flexible use of relevant information to deal with graphics is not strong in reasoning ability: the condition and conclusion of illegibility of propositions cannot be properly selected or applied, and the thinking is not rigorous.Application consciousness: practical problems cannot be abstracted into mathematical problems, the ability of mathematical modeling is poor, and the knowledge learned cannot be related to practice.We can not solve practical problems with mathematical knowledge and the ability of knowledge transfer is poor. 5) in terms of multi-representation ability of mathematics, we do not understand the question meaning expressed in the written language, can not realize equivalent conversion, and the representation is not standardized.In view of this phenomenon, the author puts forward the corresponding teaching suggestions from the two aspects of concept teaching and proposition teaching of full triangles) strengthening the concept teaching of full triangles: creating reasonable teaching situations and exploring the definition of full triangles;Using variant teaching to deepen the understanding of the concept of the whole triangle, to strengthen the application of the concept to the application of problem-solving, to strengthen the teaching of the proposition of the whole triangle: to fully participate in the classroom, to explore the judgment theorem of the whole triangle;Strengthen the training of proof, pay attention to the cultivation of reasoning ability, strengthen the ability of using propositions and cultivate students' consciousness of mathematics application.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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