向量教学中的问题及对策研究

【作者】 王银立；

【导师】 毛东明；

【作者基本信息】 东北师范大学 ， 教育， 2008， 硕士

【摘要】 新一轮数学课程改革从理念、内容到实施,都发生了巨大变化。其中,尤其值得注意的是,直到19世纪末20世纪初才发展起来的“向量教学”,以其在物理学、工程学、空间物质结构中的广泛应用,而备受人们所关注,进而很快形成了一套具有优良运算通法的数学体系,现已被纳入中学数学基础课程中,成为这次数学新教材改革的一大亮点。向量是近代数学中最基本的概念之一,具有代数与几何的双重身份,是沟通几何、代数的桥梁。具有丰富的实际背景和应用价值,是解题的基本工具。向量知识在许多国家的中学数学教材中,早就成了一个基本的教学内容。但在我国,因为其刚刚进入中学数学教材,各方面的研究都处于起步阶段,特别是关于向量进入中学教材必要性及可行性研究与教学对策研究更是薄弱。向量进入中学教材是否必要又是否可行,如何在新理念下开展向量的教学工作,这是本文着重探讨的问题。在研究过程中,笔者采用文献法,对向量相关文献作出综述,了解了关于向量教学最前沿的科研成果;利用调查法掌握了普通高中的教师和学生对向量教学的认识;用实验法对笔者设置的教学策略进行了试验;行动研究使笔者所做实验的实施增加了信度和效度。实验过程中,笔者充分运用现代教学理念指导教学实践,仔细研究,认真反思,对如何开展向量教学提出以下建议:1.针对多数教师和学生认为向量概念难于理解,在教学实践中要注重向量概念的教学,要注重对向量内容和教学要求的把握2.针对在解题时向量的工具作用没有得到充分贯彻,在教学时要发挥向量的解题工具作用3.针对学生对向量的应用价值认识不多,对向量运算的实际背景不甚清楚,教学时要加强向量与现实生活的联系4.针对学生学习方法单一,学习兴趣不高,教学时要充分发挥学生的主体作用,体现学生的主动学习原则。更多还原

【Abstract】 The new-round mathematics curriculum reform, from the ideas, contents and implementations, has been changed grently, Among then,“the vector mathematics”---which developed and applied at the turn of the 19th century to the 20th,with its wide application in moderm mathematics. Physics,Engineering.and Spatial matter structure, has been noticed greatly. Further more, it has formed a mathematics system system with a set of fine operation passing methods. Today it has been brought into the basic mathematics curriculum in middle school and became a flashpiont in this new mathematics curriculum reform..In many countries, vector as a basic course content,has already been included in the mathenatics for middle school students.However,in our country as it just has been applied in the middle school mathematics curriculum, the study of vector is still in its start stage. And the reseach of its is even weaker.It is necessary to bring vector into middle school mathematics course. However, how a teacher advances his vector teachering under a new education idea is what I want to go further in this paper attentively.During the research, the writer uses documental method,and describes the relative data,and also uses investigation method to survey the questions about the vector in the middle school teachering,and experimental validity and relibility.I fully use modern educational concepts in my teachering pratice, including documentation,investigation,combrination the operation with study in this process,I study it carefully,design it accurately,put it into practice boldly and think it over. I give many suggestions on how to advance vector teaching in this paper:1)In the opinion of most teachers and students,it is difficult for them to understand the conceot of vector.so in the teaching process,we should pay more attention to its concept and grasp the demand and the content of vector properly.2)Its function as tools can not be put in to effect.When the students are doing exercises,thus we should bring this function into full play.3) In the teaching process,we should pay attention to its dackground and introduction,and improve our teaching by using geometry mapping skills of its,At the same time,I use new curriculum reform concepts properly:“grouping,cooperation and research”in my teaching in order to bring the initiative of students into main body,and embody the principle that students should study actively.4)With this teaching method,we should strengthen the relations between wector and its application,attach the importance to infiltrate mathematics ideas and methds into it.Especially,we should know that vector analysis a very important role at the core in vector teaching.更多还原