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(一) 本单元教学在平面解析几何的教学中的地位和作用根据中学数学教学的总要求,以及该学科的教学要求,不难看出:直线和圆锥截线是该学科教学的重点。然而两相比较,圆锥截线的教学则又是重点中的重点。理由如下: 1.圆锥截线的教学,是使学生对于直角坐标系中曲线和方程的相互关系的认识,达到全面、深刻的极重要(也是最后)的阶段。曲线和方程的相互关系是指:曲线方程的概念,已知曲线求它的方程,已知曲线的方程求作曲线。这些知识虽然在第一章内作了较系统的阐述,然而由于学生是初次学习,很难使他们一下子就牢固地掌握住这些知识的实质;在第二章直线中,这些知识又得到了进一步的印证,但是由于所处理的曲线十分简单,因此还不能使学生对这些知识得到全面、深刻的认识。而圆锥截线则能充分地体现出这些知识的精神实质。譬如,由曲线求它的方程的关键问题之一,是能根据曲线的特征,妥善地选择坐标系。这一点,是决定解析法是否简便的关键。对于圆锥截线的讨论,
(A) The position and function of this unit teaching in the teaching of plane analytical geometry According to the general requirements of middle school mathematics teaching and the teaching requirements of the discipline, it is not difficult to see that the straight line and the conic section are the key points of the teaching of this subject. However, comparing the two, the teaching of the conic section is the focus of the focus. The reasons are as follows: 1. The teaching of the conic section is to make the students understand the relationship between the curves and the equations in the Cartesian coordinate system and reach a comprehensive and profoundly important (and final) stage. The relationship between curves and equations refers to the concept of curve equations. Known curves find their equations. The equations of known curves are obtained as curves. Although this knowledge was systematically elaborated in the first chapter, it is difficult for them to firmly grasp the essence of these knowledge because the students are learning for the first time; in the second chapter, this knowledge was acquired again. Further confirmation, but because the curve is very simple, so students can not have a comprehensive and profound understanding of these knowledge. The conic section can fully reflect the spiritual essence of these knowledge. For example, one of the key issues in finding its equation from a curve is to properly select a coordinate system based on the characteristics of the curve. This point is the key to determining whether the analytical method is simple or not. For the discussion of the conic section,