A Study Of The Difficulties And Countermeasures In The Problem Solving Of Three-dimensional Geometry In Senior High School

The new curriculum standard requests explicitly that"mathematics teaching should focus onproblem solving, pay attention to the application of mathematics, focus on mathematicalcommunication, pay attention to mathematics thinking method, and also to cultivate thestudents’ emotional attitude and self-confidence."Math is not a direct study of the real things orphenomena, but focus on the product of abstract thought. The cultivation of mathematicalthinking ability is one of the central task of mathematics teaching, problem solving is good for it.In fact,it is obvious that problem solving is the core of mathematics teaching. Indeed, themathematical community hold the common view that problem is to mathematics what heart is tohuman beings, problem solving is the core of both mathematics teaching and mathematicslearning. There are two aspects for problem solving: the first one is to find a problem and to putforward the problem; the second is to solve the problem; the latter indicates that mathematicsteaching applied specifically in middle school is problem solving.As is known Solid Geometry is an important part of the high school mathematics.Solidgeometry lets students know the world, can develop their geometric thinking,and cultivate theability of space imagination and logical reasoning.We note that the current high school spatialgeometry teaching is faced with some new problems and also old problems.Students can’tunderstand the concept and theorem of geometry, their reasoning ability is weak,there aredifficulties in the solid geometry problem solving.Cultivate the ideation is the main task of the the solid geometry problem solvingteaching.Some scholars divide the mathematical thinking into "conceptual thinking" and"problem solving thinking." The "problem solving thinking"is the core part of polya’s problemsolving method,in his famous series of books,Polya clearly explains "the table of problemsolving","to master mathematics is to be able to sole mathematical problem","Mathematics andguess"," how to solve the table","master mathematical means being good at problem solving","middle school mathematics teaching should focus on the training the students’ ability ofproblem solving". Of all above the theory of the table of how to solve problem is the essence ofthe book"How to solve it".The essence of the book"How to solve it" is divided into fourstages:clarifying problems,making plans,realization of plans,review.The four stages not onlyshow his general idea of the problem-solving theory,s but also formed a complete system ofteaching problem-solving.This article is based practical classroom teaching, and focuses on solving Polya’s theory of the second stage “making plans”with educational, psychologicaltheories as the theoretical foundation.With the two special models of three-dimensionalgeometry:triangular pyramids and cubes to explore the ideas of problem-solving related tothree-dimensional geometry.In this paper, based on the solid geometry problem solving teaching, we explore difficultiesand countermeasures in the problem solving of three-dimensional geometry, and explore thecultivation of mathematical thinking.In the problem solving teaching,we explore theunderstanding and application of polya’s problem solving methods; in the study of thinkingcultivating, we explore measures to cultivate the mathematical thinking.This article explores thedifficulties of high school students in the three-dimensional geometry problem solving,andinvestigates students’ thinking ability by survey volume and test volume for the students,then weexplore the solid of solving methods and measures to cultivate the mathematicalthinking.According to the teaching theory research and the results of the investigation andanalysis, this paper designed a case to practice the teaching and training.