A Study On The Problem-solving Strategy For The Sequence Of Number In The Entrance Examination Based On Polya's Problem-Solving Theory

As one of the important examination points of the college entrance examination,the sequence of number is an important part of the mathematics content in high school and the initial entrance of the limit concept in the university calculus in the future.In addition to the sequence of basic operations,the examination of college entrance examination is also about synthesized knowledge,include inequalities,geometry,advanced mathematics ideas and other knowledge points.This paper chooses the main national college entrance examination papers: Zhejiang,Beijing,Shanghai,Jiangsu,Shandong and the whole country to analyze the serial examination questions of the college entrance examination in the past three years,and finds that there are many kinds of propositions of the questions.According to the difference of join knowledge points,it can be divided into seven classes,Simple Calculation Problem and Proof Problem of Sequence of Numbers,"Sequence of Number + Inequality ","Sequence of Number + Geometry ","Sequence of Number + New Define ","Sequence of Number + Application","Sequence of Number + Advanced Mathematics Thought".Through combining the problem-solving method for each class,exploring the problem-solving step and designing the problem-solving flow chart,the basic characteristics of the problem-solving strategy can be found:pertinence,universality,direction and flexibility.Polya has a great reputation in the world,and his method of solving mathematics problems is unique.The thesis puts forward the solving strategies to the sequence of number problem according to the four steps of Polya's Problem Solving: clarifying the problem,drawing up the plan,carrying out the plan,reviewing:(1)Using concept of sequence of number to reason and distinguish uncertain sequence of number's type.Through function to judge the simple sequence type.Studying the new definition in the prerequisite to decide the type of new sequence.Ensuring complex sequence of number's type by associating special sequence of number;(2)Using divergent thinking to transform problem.Simplifying geometric problems with algebraic forms.Establishing sequence model to simplify application questions.Using functional thought to prove inequality of sequence of numbers.Reverse thinking proves the proposition of sequence of numbers;(3)Mastering skills to simplify difficulties."know three and seek two","extend it" and "Split each item for sum of sequence of number";(4)Verify the results and pay attention to the expansion of the sequence knowledge while testing the process.Evaluation test,leak detection and infer other things from one fact.It is hoped that the four-step problem solving strategy can be provided for students to solve the problem and prepare for the examination.