平面几何概念教学探讨

发布时间：2018-08-28 15:17

【摘要】：数学概念教学是初中数学教学的重要内容。学生只有准确地理解数学中的各种概念,才能更好地掌握各种数学法则、公式、定理以及思想,最终应用所学知识去解决实际问题。几何教学有助于培养学习者合情推理的正确逻辑思维能力和严谨的数学思想品质与精神。几何概念是数学概念的重要组成部分,引导学生正确地理解几何概念是提高几何教学质量的关键。笔者通过对初中平面几何概念教学的观察,发现很多学生不会应用几何概念解决问题,原因是学生并没有真正地理解几何概念。多年来教师以文字形式表述几何概念的做法是诠释几何概念的主要形式,在概念形式上的抽象说教现象还很严重,对某些几何概念讲解不够透彻,不能很好地让学生体验到几何概念的内涵,从而影响了学生的学习效果。本研究主要以皮亚杰的“发生认识论”、建构主义中的APOS理论以及奥苏贝尔的有意义学习理论中的概念教学部分为理论指导,并结合当前初中平面几何概念教学的现状,运用Van Hiele几何教学理论进行平面几何概念教学研究。对初中阶段平面几何基本概念进行认定后发现:这些概念除切线的概念要求达到Van Hiele几何思维水平3的层次外,其他的基本概念只要求学生达到水平1或水平2的层次。本论文研究的创新之处在于:用Van Hiele几何教学理论对初中阶段平面几何基本概念进行认定并针对部分几何基本概念进行教学设计,为教师在进行平面几何概念教学时提供借鉴和参考。最后,为促进学生能够更好地从其中的一个思维水平顺利地过渡到下一个思维水平,笔者在论文结尾提出了一些教学建议。
[Abstract]:Mathematics concept teaching is an important content in junior high school mathematics teaching. Only by accurately understanding all kinds of concepts in mathematics can students master all kinds of mathematical rules, formulas, theorems and ideas, and finally apply the knowledge they have learned to solve practical problems. Geometry teaching is helpful to cultivate learners' correct logical thinking ability and rigorous mathematical thinking quality and spirit. Geometry concept is an important part of mathematics concept. Guiding students to understand geometry concept correctly is the key to improve the quality of geometry teaching. By observing the teaching of plane geometry concept in junior high school, the author finds that many students can't solve the problem by applying geometric concept, the reason is that the students do not really understand the concept of geometry. Over the years, teachers' practice of expressing geometric concepts in the form of words has been the main form of interpretation of geometric concepts. Abstract preaching in the form of concepts is still very serious, and some geometric concepts are not sufficiently explained thoroughly. It can not let students experience the connotation of geometric concept, thus affecting the learning effect of students. This study is guided by Piaget's Theory of occurrence epistemology, the APOS theory of constructivism and the concept teaching part of Ausubel's meaningful learning theory, and combined with the present situation of plane geometry concept teaching in junior high school. Using Van Hiele geometry teaching theory to carry on the plane geometry concept teaching research. After identifying the basic concepts of plane geometry in junior middle school, it is found that except the tangent concept which requires the level of Van Hiele geometric thinking level 3, the other basic concepts only require students to reach the level of level 1 or level 2. The innovation of this paper lies in: using Van Hiele geometry teaching theory to identify the basic concepts of plane geometry in junior middle school and to design some basic concepts of geometry. For teachers in the teaching of plane geometry concept to provide reference and reference. Finally, in order to promote the students to better transition from one of the level of thinking to the next level of thinking, the author puts forward some teaching suggestions at the end of the paper.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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