Research On The Process Of Transforming Plane Geometry And Solid Geometry In Middle School Mathematics

Geometry knowledge is the main content of textbooks for junior high school and senior high school.As a continuation and in-depth of the three-dimensional geometry as plane geometry,it shows that they are related in content and way of thinking.In terms of content,the nature and calculation of plane geometry are performed in two-dimensional space.After entering high school,geometry knowledge rises from two-dimensional angles to three-dimensional angles,turning into three-dimensional spatial pattern recognition,but it is still closely related to plane content.In terms of the way,the relationship between plane geometry and solid geometry is mainly reflected in the construction of analogy and transformation.Therefore,in the in-depth study,we should find the correct method of learning,training problem-solving thinking,so as to improve the ability of mathematical analysis,calculation,and imagination to achieve the requirements of mathematical literacy.This paper takes the pedagogic theory as a guide,combined with the results of the mathematics problem-solving thinking theory and the geometry education theory,adopts literature research methods,comparative methods and other research methods to improve the content of plane geometry and solid geometry.The two teaching cases embody the influence of the construction process of plane geometry and solid geometry on geometry learning,making the geometric content and teaching system more systematic and complete.This paper has the following five parts:The first chapter is a review mainly that summarizes the main idea and content of this paper.The second chapter mainly introduces the theoretical basis of the article and lays the foundation for the whole idea of the article.The third chapter is about the transformation and embodiment of transformation construction process in plane geometry and solid geometry.It is the focus of this article.Firstly,the expansion and extension of plane geometry to three-dimensional geometry are expounded in terms of thinking and content.The main application is analogy thinking.Secondly,the application of plane geometry knowledge in solid geometry is described,reflecting the idea of transformation.The transformation process of point,line and surface in geometry is described in detail in four aspects.Finally,the planarization of the twoaspects of space angle and distance will reveal the formation process of spatial graphics in detail.It is shows the important role of inductive transformation and analogy in learning two kinds of geometry.The fourth chapter designed two teaching cases concerning the cultivation of mathematical geometry building ability in middle schools.Both cases demonstrate the application of the third part in the teaching process in the form of actual teaching process.One is "Triangle Geometry",which uses students' familiar architectural graphics to guide students' understanding of geometric models,embodying analogy ideas.The other is the“determination of the parallel relationship between a straight line and a plane”.The solution is to “find it” and use transformational thinking to find a line that matches the meaning of the problem.The fifth chapter is the conclusions and recommendations of related research.In the conclusion,it is believed that the exploration of the construction process of plane geometry and three-dimensional geometry has a positive guiding significance for teachers' teaching and students' learning.Through the analysis of analogy and transformation process,it is emphasized that teachers pay attention to the cultivation of geometric thinking from two-dimensional space to three-dimensional space in teaching.Appropriate teaching methods and flexible teaching methods are the preconditions for them to master the strategy.At the same time,students should actively train mathematics thinking in their study,pay attention to the connection and transformation of knowledge points,and clearly understand the framework of plane geometry and solid geometry knowledge.In addition,for the direction of the inquiry and the conclusions obtained in the article,the article gives some suggestions for teaching and learning for reference.