The Reverse Reasoning Of Plane Geometry And It’s Teaching Research

The teaching about reverse analysis of plane geometry pushes to train students to do reverse thinking and reverse analysis of reasoning. Inverse analysis of reasoning, by definition, is an opposition of the deformation.It starts from the conclusion to seek the conditions, and it is required due to performing at the equivalent or half an equivalent variant,and it forms a series of equivalent or semi-equivalent deformation chain,so it can lead to find the conditions to meet the needs of the subject criteria. Especially in the teaching and learning in plane geometry, the method of reverse analysis of reasoning is called universal approach. So the problem can be taught easily and be learned simply.The thesis firstly describes some international and domestic subjects of geometry analysis, which pushing the understanding of the background. Then I present my own views in accordance with the current situation of it’s teaching in addition to expect to open the bottleneck of learning the knowledge of geometry plane. The thesis is mainly to explore the following three questions:1:junior high school students’the cognitive status of using the method of inverse analysis to solve the titles of plane geometry.Through some interviews of junior high school students and classroom teachers, I found that junior high school students doesn’t often used the method of inverse analysis to think the questions. And Students’ set thinking is clearly,only part of the students which participate in the mathematical competition occasionally produce the ideas of inverse analysis.This situation causes some difficulties to push the teaching of using the method of inverse analysis to solve titles about the plane geometry.2:the suitable types of plane geometry’titles by using the inverse analysis method.In accordance with the characteristics of reverse reasoning, I summary several types of adverse inference principles about the plane geometry analysis. Combining with a variety of angles about inverse analysis, I sum up the characteristics and scopes of various types about kinds of questions.The analysis perspectives include:inverse analysis of geometric transformations, inverse and negative analysis in the inverse proof, the same method of inverse analysis about indirect proof proposition.3:the teaching model of inverse analysis.By combining with my own teaching practice and teaching cases,I offer several methods of plane geometry’analysis for the demonstration aim to guide students to learn to classify, to choose the angle to think about the kinds of questions,and to determine the direction of solving the conversion problems.So such experience can push students to complete the knowledge of inverse analysis, and students are able to independently establish a process of knowledge construction:finding the law, the formation of skills, learning to summarize, a deeper impression. It is to achieve a high degree of teaching and research.At the same time, in order to inspect that the thesis can really make the student’s ability developed, I make a survey in the form of a questionnaire of students’ ability to know the difference of the ability.The effect confirms the usefulness of this type of learning method and the effectiveness of plane geometry to solve problems, and ultimately the efficiency of teaching and learning.The first layer of this article is intended to make students to know that they are not afraid of the titles of plane geometry, so that they can get full points when solving the plane geometry’ titles; the second layer is intended to learn basic modes of solving problems:observation, analysis, choosing the direction to solve the problem; the third layer is intended to reflect the ideas on teaching issues from the discovery of the problems, expanding the problems, researching questions, solving problems. By pushing the integrity of the process teachings clearly displayed, it can reflect the development of mathematical thinking.