Teaching Design Based On The Idea Of ??transformation From The Perspective Of HPM

The thought of transformation is the soul of mathematics.Taking solid geometry as the carrier,this paper examines the imagination of space,and at the same time,focuses on the infiltration and transformation of thinking in teaching.Through extensive investigation,it is shown that the establishment of the concept of solid geometry is a "hard bone" for students to learn geometry,and its difficulty coefficient is mainly reflected in two aspects: one is the high requirement for space imagination ability;it is difficult to understand the principle of equal product in ancestor.This study is based on the HPM angle of view.We sort out the order of historical development.According to the similarity of history,we analyze the obstacles that students may encounter in the process of learning.Therefore,the corresponding teaching design is designed.For the students and for the teacher,the flexible application of the thought is of great benefit to the study,the rational use of the mathematical history knowledge can make the whole mathematical process more effective with half the effort.Based on this,the purpose of this paper is to study the following three questions:1.What are the students' cognition and obstacles to the principle of ancestor?2.How do teachers integrate mathematical history into the teaching of geometry?3.Which mathematical historical materials related to solid geometry are suitable as teaching materials?Through the research we make the inclusion after the researsh:1.There is a positive correlation between students' cognition of ancestral principle and their interest in learning.In the process of solving the problem,the importance of integrating mathematics history into study was not recognized.2.In view of the importance of solid geometry in high school and even in college entrance examination,teachers have maintained a positive attitude.More and more teachers will use educational software to assist in teaching.3.In order to make mathematics teaching develop more vigorously,the selection of mathematics history should be wide in scope,great in influence,far away in meaning,in order to make the mathematics teaching develop more vigorously.To sum up,the teaching of mathematics history into solid geometry has educational significance and value,and it is worth popularizing and practicing.