A Study Of The Problem-solving Strategies For The Conical Curve In The Entrance Examinations Based On Polya's Theory

The conical curve is a core intersection of middle school mathematics knowledge,marked by synthetic content,flexible solutions and abstract thinking.It is both a hot topic of college entrance examinations but also a major point quite hard to solve.Learning the conical curve not only can cultivate students' mathematical ideas such as symbolic-graphic combination,equivalent conversion,function and equation,classification discussion,but also can deepen students' understanding of the relationship between algebra and geometry.This paper treats the problem-solving strategy of the conical curve in the college entrance examination as the research goal while adopting research methods like literature studies,statistical classification,surveys and analysis.First,The author makes a literature review of the features of the test questions about the conical curve in the college entrance examinations and of the thinking strategies to solve such test questions so as to provide a theoretical basis for the study.Then,the author summarizes the classification of the knowledge points of the conical curve in the college entrance examinations,analyzes and sums up the sources and features of the test questions,thus making preparations to solve the test questions of the college entrance examinations.A classification statistics is made of the characteristics of the questions.Based on the analysis of the characteristics of the test questions and of the problem-solving obstacles,the author comes up with the problem-solving strategies of the conical curve by introducing George Polya's "How to Solve It." Lastly,the author tries to solve the conical curve questions by applying the problem-solvingstrategies of the comical curve.The following are what the paper concludes:(1)With a statistic of the knowledge points of the conical curve of the college entrance examinations during the last five years,a background of the questions and a conclusion of the characteristics of the questions,a ground is laid for future studies.(2)Combining the specific situation of the conical curve,analyzing Polya's How to Solve It,the author proposes the steps to solve conical curve questions from the perspective of Polya's How to Solve It.Based on the characteristics of the test questions and obscles in the way of solving them,the paper puts forward four strategies to solve the questions of the conical curve: Examining the topic by definition;The inferece of nature;Operation and coversion;Verification by image.