Teaching Research Of Coordinate System And Parametric Equation

Coordinate system is a powerful tool to realize the combination of number and shape.It is not always simple and effective to describe geometry in rectangular coordinate system.Sometimes,in order to describe geometry more easily by algebraic method,different coordinate systems need to be established.In this paper,based on the three years of 2017-2019 in Ordos City,the first simulation examination of middle school students to choose to do the research,through literature research,interviews,case analysis,according to the interviews with teachers and students' investigation,we find and analyze students' cognitive difficulties and common errors in learning coordinate system and parameter equation.Then we give five optimized coordinate system and parameters Finally,two teaching cases are designed.The conclusion of this paper is as follows:1.Due to the students' inaccurate understanding of the essence of similar concepts,it leads to confusion of any angle,polar angle,tilt angle of straight line,parameter angle of circular parameter equation and parameter angle of ellipse parameter equation.When guiding the students to sort out the wrong questions,they should pay attention to the vertex,beginning,end and range of the above several angles.After the questions,there are the extraction of key points of solving questions and the summary of mathematical ideas and methods It can effectively strengthen the students' understanding of the above-mentioned angles by practicing again.2.Select examples,students in different groups describe the locus ofmoving points in different equation forms.Students can get better personal experience through the comparison of group display process.When the point has obvious rotation,it has obvious advantages to describe the position of the point and describe the geometric relationship with polar coordinates.3.It is good to understand the geometric meaning of parameters in the parameter equation of a straight line by analogy with the number axis.The fixed point in the parameter equation of a straight line analogizes the origin of the number axis.The geometric meaning of the points on the number axis is the distance from the point to the origin,which is transferred to the parameter equation of a straight line.The geometric meaning of the parameters corresponding to the midpoint of the parameter equation of a straight line represents the distance from the corresponding point to the fixed point.This paper is based on the learning of four bases of coordinate system and parameter equation.In fact,coordinate system and parameter equation are widely used in daily life and science and technology field,but the research on application is rarely introduced in this paper.