The Application Of Polya’s "Problem Solving Table" In The Stereoscopic Geometry

Since ancient times, the problem solving is an important part in the learning of mathematicscurriculum. Mathematic problem solving can be seen as a kind of problem solving. In April1980, theAmerican Association of mathematics teacher propose that " the problem solving must be the core ofMathematics teaching in the middle school ". The slogan has been proposed, aroused strong repercussionsin the international community and triggered a boom of Polya’s problem solving thinking, a lot of research.Polya’s problem-solving thinking embodied in the "how to solve problem". In the process of studying theseresults, I found which case dispersion relatively larger, while the comprehensive analysis of a mathematicstextbook module is relatively smaller; For how to problem-solving table functions and their properties thestudy relatively larger geometry topics, especially prove that the subject of the study is relatively smaller. Inthis paper, combined with the initial content of the high school solid geometry, analysis of the four-step"how to solve problem.", The thinking process of the students in the problem-solving process and problemsolving strategies, and expectations of the line for high school teachers teaching practice provide somehelp.The research concluded that Polya problem solving four-step analysis and problem-solving strategies:to define a problem, the problem is to understand the conditions and requirements for the issue ofcertificates and their proper characterization. Specific problem solving strategies to geometric problems: tryto draw graphics, the conditions and requirements of the permit issues identified in the graph; For the textdescription of the problem, it should be converted to symbolic expression. Consider the issue of specialcircumstances, to simplify the problem.Developing plans, we must first determine the conditions and requirements of the permit problemabout knowledge base, and secondly, to find a model for solving problems with the skills and techniquesrequired to resolve problems. Plan strategy: find the equivalent, or change the problem formulation;analogies have already solved a similar problem, or to consider the issue of the inverse proposition tochange the structure of the problem, or even add auxiliary line; conditions decomposition, considering theextreme case, and the like. Plan staging, not only has remained highly concentrated attention, but also with enough care andpatience, attention to every detail of the plan carefully check.Checking the contents of the review, your plan can be streamlined? Results can verify? Solution of theproblem can not solve a class of problems? Converse proposition holds it?etc.