Teaching Analytic Geometry From The Perspective Of HPM

Analytic Geometry is not only one of the most important chapters in Mathematics,but also the key problem in the college entrance exam.First of all,analytic geometry is the bridge between geometry and algebra.Then,it provides the essential research method for modern technology.Moreover,analytic geometry provides guidelines for mathematic teaching.Nowadays,there are some disadvantages in the textbook for Analytic Geometry,for example:the introduction of concept is a little bit unnatural,the link of concepts is not coherent,the derivation of formula is not suitable for students,and so on.As a result,students may be tired with mathematics learning.Instructional design based on HPM will solve these problems.Action research is adopted in this survey,which is based on HPM.At first,I made a depth investigation on the textbooks for Analytic Geometry that published from 1800 to 1950,in order to draw the outline of the history of some elements in analytic geometry.And then instructional method is designed to forecast the problems students will face based on the similarity of history.The design will be adjusted after the practice and the reaction of students.There're four HPM design occurred in the article:11.1 The inclination and slope of the straight line,11.2 The straight line,11.4 The distance from a point to a straight line,12.1 Curve and equation.The article is aimed at solving the following three questions:1.What's the view of students on HPM?2.Can HPM help students to overcome the obstacles that may occur in the traditional class?3.Whether the similarity between students and history exists or not?We make the inclusion after the four steps of action research:1.Students are curious about history of mathematics and they like the classroom mixed with HPM.This type of class can motivate the enthusiasm and creation of students.2.On some extent,HPM can solve the obstacles of students in some regions.However,HPM is not omnipotent,but just one of the modes of class.3.There is similarity between the sequence of students logic and the development of mathematics concepts.Above of all,HPM is an effective mode to teach analytic geometry,and it is worth using HPM to have class for teachers in middle school.