Research On Plane Vector Teaching Based On Polay’s Problem Solving Theory

Plane vector has the dual identity of "number" and "shape" and is widely used in mathematics,physics and real life.However,because of the abstract nature of plane vector,students have difficulties in understanding it.The Hungarian-American mathematician George Polya dedicated to mathematics education research,and the "How to Solve a Problem Table" in his book "How to Solve a Problem" is an important manifestation of his thinking on problem solving.The "How to Solve a Problem Table" divides the problem-solving process into four steps.Polya’s four-step problem solving method attaches importance to guiding students to learn mathematical thinking in the process of problem solving and to the formation of students’ good emotional attitudes,which contains concepts consistent with the requirements of the General High School Mathematics Curriculum Standards(2017 edition),so it is of theoretical significance to apply this theory to teaching.The core question of this research is: How to use the Polya’s problem solving theory to guide the teaching of plane vector? First of all,this paper adopts the literature analysis method to analyze the literature related to Polya’s problem solving theory and plane vector teaching.Based on the understanding of the current situation,the necessity and feasibility of applying the Polya’s problem solving theory to the teaching of plane vector are analyzed.Next,through the questionnaire method and interview method,this study learns about the current situation of plane vector learning and teaching.From this,problems in teaching plane vector under Polya’s problem solving theory were identifiedl to prepare for the development of effective teaching strategies.Based on this,this research combines Polya’s problem solving theory with the teaching process of plane vector,develops the teaching around the core problem and carries out classroom exploration in the form of problem solving.In this research,plane vector teaching is divided into five stages on the basis of the four steps of problem solving proposed by Polya.Not only the teaching strategies of each stage are proposed,but also the new plane vector lessons and exercises are designed by using the strategies.The teaching of plane vector based on Polya’s problem solving theory can not only enrich and develop education theory,but also provide reference for first-line teaching.The results of the survey show that,on the students’ side(1)students’ awareness of the value of plane vector is insufficient;(2)students’ understanding of knowledge in relation to physics and life needs to be improved;(3)students’ performance in the execution and reflection stages of problem solving is not good enough;(4)the application of Polya’s problem solving theory to teaching plane vector meets students’ expectations.On the teachers’ side(1)teachers’ understanding of Polya’s problem solving theory is not deep enough;(2)teachers neglect students’ active inquiry,have doubts about how to put themselves in students’ shoes,have deficiencies in guiding students’ self-monitoring,and do not give full play to the value of inductive thinking and methods in their actual teaching.According to the above findings,the following teaching strategies are proposed(1)acquiring the topic stage: constructing interesting situations,designing inquiry problems,and emphasizing mathematical abstraction;(2)understanding the topic stage: guiding deep analysis of the topic,and promoting multiple representations;(3)formulating the solution stage: emphasizing analogous contents,prompting auxiliary elements,and exposing the thinking process;(4)executing the solution stage: making use of block diagrams to sort out,and implementing implementation monitoring;(5)reflecting and reviewing stage: carrying out multiple solutions to the problem,summarizing ideas and methods,and providing variant questions.