MPCK视角下的圆锥曲线教学研究

发布时间：2018-06-12 04:20

本文选题：学科教学知识 + 数学学科教学知识　；参考：《陕西师范大学》2015年硕士论文

【摘要】：教师的专业发展成为当今一个比较热门的话题,同时,它受到了国内外学者的广泛关注。在教师的专业能力发展的过程中,学科教学知识(Pedagogical Content Knowledge,简称PCK)成为研究的焦点,它是教师的专业知识中所特有的一种知识类型。针对数学教师而言,数学学科教学知识(Mathematics Pedagogical Content Knowledge,简称MPCK)作为一种独特的教学知识,在数学教学中占有重要的地位。与此同时,圆锥曲线对于教师而言是一部分比较特殊的教学内容,这部分内容不仅对教师的理论知识有着较高的要求,也考验着教师其他方面的教学知识和能力。对于学生而言,这部分内容的学习是有一定难度的,不仅需要具备丰富的理论知识,还要具有一定程度的计算能力。将MPCK理论与圆锥曲线进行结合,在MPCK理论的视角下对圆锥曲线的教学进行探索是必要的。论文从圆锥曲线的定义、几何性质、直线和圆锥曲线的位置关系这三个方面进行了教学探究。其中定义的教学主要是揭示圆锥曲线的本质特征,几何性质的教学探究主要引导学生从方程的角度,用数学结合的思想去理解圆锥曲线的几何性质。直线和圆锥曲线的位置关系是本论文的重点部分,从最基本的弦长公式、常见的中点弦问题及直线和圆锥曲线关系中五种最典型的问题进行了探究。目的是让教师从MPCK的视角下进行教学从而提高教学能力,让学生灵活掌握弦长求法、中点弦问题的两种基本处理方法以及五种典型问题的分析、思考规律和常用的处理方法。最后就圆锥曲线的教学进行了思考与展望,提出了在MPCK视角下圆锥曲线教学的一些想法。本文研究的重点是在MPCK理论的视角下的圆锥曲线的教学探究,经过将MPCK理论运用于圆锥曲线的各个部分的内容中,探索出新的教学理论和教学方式,更有利于教学的教学和学生的学习,为高中圆锥曲线的教学提供了一定的教学参考。
[Abstract]:The professional development of teachers has become a hot topic, at the same time, it has been widely concerned by scholars at home and abroad. In the process of teachers' professional ability development, the subject teaching knowledge Pedagogical content knowledge (PCK) becomes the focus of research, and it is a special type of knowledge in teachers' professional knowledge. For mathematics teachers, mathematics pedagogical content knowledge (MPCK), as a unique teaching knowledge, plays an important role in mathematics teaching. At the same time, conic curve is a special part of teaching content for teachers, which not only has higher requirements for teachers' theoretical knowledge, but also tests teachers' teaching knowledge and ability in other aspects. For the students, it is difficult to learn this part of the content, not only need to have rich theoretical knowledge, but also have a certain degree of computing ability. Combining MPCK theory with conic curve, it is necessary to explore the teaching of conic curve from the perspective of MPCK theory. This paper explores the definition of conic curve, geometric properties, the position relationship between straight line and conic curve. The teaching of the definition is mainly to reveal the essential characteristics of the conic curve, and the teaching and research of the geometric properties mainly guide the students to understand the geometric properties of the conic curve from the angle of equation and with the thought of combining mathematics. The relationship between the position of straight line and conic curve is the key part of this paper. The basic formula of chord length, the common mid-point chord problem and the five most typical problems in the relationship between straight line and conic curve are discussed. The purpose is to let teachers teach from the perspective of MPCK to improve their teaching ability, to make students master the method of finding chord length flexibly, two basic methods of dealing with mid-point chord problems, and the analysis, thinking rules and common treatment methods of five typical problems. Finally, the teaching of conic curve is considered and prospected, and some ideas of teaching conic curve under the view of MPCK are put forward. The focus of this paper is to explore the teaching of conic curves from the perspective of MPCK theory. By applying MPCK theory to the contents of various parts of conic curves, a new teaching theory and teaching method are explored. It is more conducive to teaching and students learning, and provides a certain teaching reference for the teaching of conic curve in senior high school.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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