A Case Study On The Construction And Application Of Mathematical Problem Solving Thinking Path For Senior High School Students

"How to solve problems" has always been a hot topic in the field of mathematics education.In the actual process of solving problems,students often have no or stagnant ideas.This paper aims to build a mathematical solution thinking path that can give full play to the advantages of mind map and Polynesian solution table to inspire students to solve problems.The research questions of this paper are as follows:(1)what is the cognition of senior high school students on problem solving?(2)How to construct the thinking path of mathematical problem solving based on Polynesian "how to solve the problem table" and mind map?(3)How to optimize the above thinking path of mathematical problem solving?The research conclusion of this paper is:(1)The situation of senior high school students' cognition of solving mathematics problems in four factors are as follows: the outstanding problem in their emotional attitude is that students have low interest in solving mathematics problems and low initiative in solving mathematics problems;students' mastery of knowledge in the knowledge structure is still weak;the prominent problem in their sense of experience problems is that students are not very active in reflection and lack of beauty in mathematics problems The outstanding problems in thinking ability are the application ability of common thinking methods and the perception ability of details.On the whole,the thinking ability of high school students is lower than other factors.(2)In this paper,the author constructs a problem-solving thinking path combining Polynesian problem-solving table and mind map.Based on the problems existing in senior high school students' current problem solving,the author puts forward the necessity of building the thinking path of mathematical problem solving in this paper.Finally,from the three aspects of reflection thinking,problem schema and goal consciousness,the author constructs the thinking path of mathematical problem solving based on mind map and Polynesian "how to solve" table.The whole process includes two steps: one is to determine the central theme and correspondingproblems,that is,the starting point of thinking and the direction of thinking divergence;the other is to determine the specific association process of thinking.(1)According to the problems reflected by the subjects,the author puts forward six optimization measures.In addition,some measures are added to the specific operation process,and the specific operation process of the optimized thinking path of mathematical problem-solving has four changes compared with the original one: one is to add a variety of representations;the other is that "is the relationship between known data,conditions and unknown quantities closer?" change to "is it closer to the unknown quantities?" The third is to increase whether the known information needs to be considered comprehensively;the fourth is to associate the auxiliary questions from the three aspects of known data,conditions and unknown quantity.