The Research On Pattern Recognition In Solving The Plane Geometry Problems

Mathematical problem solving is a cognitive process unique to human beings,so also is to solve the problems in plane geometry,including vision,thinking and other advanced cognitive process.Pattern recognition as an important part of mathematical problem solving,in-depth research on it,is conducive to deepening understanding of the cognitive process of solving mathematical problems.On the basis of psychology and mathematics problem solving the existing research results in two major areas,this paper defines the two core concepts in this study.To solve the plane geometry model is defined as: the basic graphics in plane geometry,and the corresponding basic graphics concepts,axioms,theorems,propositions,inference and common conclusion.A class of problems or have the same solution has a problem common structure of the plane geometry,and the commonly used problem-solving skills and problem-solving methods.The pattern recognition of plane geometry in problem solving is defined as: when solving contact problems in plane geometry,the problem of the condition,conclusion,relation,structure statement and the problems of the geometry of understanding,pattern graph mode,the problem of storage problems in plane geometry and then faced with their own cognitive structure in the What are the characteristics of the model in the plane geometry problem solving,and what is the particularity of the model in solving the problem?How to deal with the problem of pattern recognition in plane geometry? This is the research problem of this paper.Third and four chapter is the main part of this research.In the research of the two chapter,theoretical analysis,interview,thinking aloud,experimental research methods by the author,trying to answer the above questions.In the third chapter,the author based on the importance of graphics for plane geometry,analyses the characteristics of plane geometry problem solving the model of plane geometry in problem solving.The model is divided into: graphic mode,mode,mode of three kinds of methods,examples,and discusses the level of overall and subjective model with plane geometry problem solving.Two study of the fourth chapter is the analysis results of the third chapter based on the theory of the the research is mainly to study.A pattern recognition of plane geometry problem solving,the research is mainly to discuss the two methods of pattern recognition of plane geometry in problem solving.The fourth chapter is the conclusion of a study are: 1 to solve the plane geometry problem solving,often starting from the familiar pattern,for multiple graphics mode superposition,separated from the graphical model more superimposed in the graphic pattern in accordance with the goal of problem solving is the key to.2.'s success in the process of solving the problem.Geometric intuition plays an important role.3 when the corresponding to different modes of separated graphics geometry in question,and every figure all accord with the problem-solving goal,pattern recognition in different ways,will correspond to different solutions,which is consistent with the problem-solving goal difficulty and the pattern formation geometry problems often exist the main reason of multi solutions of.4.geometric problem in graphics mode is much significant correlation.Main conclusions are: two research methods of pattern recognition To solve the problems of the same model results do not significantly,but had a significant effect on solving variant problem.Therefore,the plane geometry problem solving model of accumulation,pay special attention to the integrity of the model,not only to build a model of basic graphics and problems of the type and structure,but also the accumulation of corresponding to the problem solving method mode.Pay attention to the whole pattern,pattern recognition of the right is more convenient to solve the variant problem.