Investigation And Research On The Cause Of Thinking Disorder Of The Third Grade Students In Solving Geometric Maximum Value Problems

In 300 BC,the ancient Greek mathematician Euclid completed a mathematical magnum opus affecting the world——"Elements of Geometry",its birth opened the door of geometry for human beings.Geometry as an important branch of mathematics,geometry curriculum reform has been paid more and more attention by more and more countries.In the new mathematics curriculum reform,a series of measures have been taken.Great changes have taken place in teaching content with the curriculum reform.According to the requirements of the Curriculum standards,the curriculum is divided into four parts:number and algebra,figure and geometry,statistics and probability,synthesis and practice.Figure and geometry as a separate part,so as to see their importance.As a kind of comprehensive and difficult problem in graphics and geometry,junior high school students have thought obstacles in solving this kind of problem.In this study,the process of solving the geometric maximum value problem is divided into four stages,namely,clarifying the problem,drawing up the plan,executing the plan,checking and reviewing.According to the literature review,the thinking process of students at different stages in the process of solving mainly includes seven major thinking obstacles:understanding thinking disorder,choice thinking disorder,thinking method thinking disorder,set thinking disorder,structural thinking disorder,methodical thinking disorder and reflective thinking disorder.Based on this,the author first designed a student test paper and questionnaire,through the test survey reached the following conclusions:1.In the process of solving geometric maximum value problem,there is a common mathematical thinking obstacle in the third grade students.Among them,interpretive thinking disorder and structural thinking disorder have the greatest influence on students’ problem solving.2.There are differences in thinking disorders between boys and girls.Boys are more likely to have methodical thinking disorders,while girls are more likely to have structural thinking disorders.3.The frequency of students’ thinking disorder in the process of solving geometric maximum value problem is related to students’ original scores.Then,based on the investigation results of students’ thinking obstacles in solving geometric maximum value problems,the author designed an interview outline for teachers and students respectively,hoping to investigate students’ difficulties in solving geometric maximum value problems from the perspectives of both students and teachers,and analyze the inducement factors of thinking obstacles in solving geometric maximum value problems at each stage.Based on the analysis results,the author finally puts forward the corresponding teaching suggestions and students’ learning suggestions for each stage from the four stages of problem solving:1.In the stage of clarifying problems,teachers should help students to improve their ability of reviewing problems,strengthen their understanding of concepts and theorems,and change their attitude towards geometric maximum value problems.In the planning stage,teachers should pay attention to guiding students to master some basic problem-solving strategies when explaining the geometric maximum value problem,so as to adapt to all changes.In the implementation stage,teachers should pay attention to the cultivation of students’ geometric writing;In the examination and review stage,teachers should pay attention to the training of students’ computing ability and awareness of problem solving monitoring.At the same time,teachers should pay attention to typical examples,establish problem solving procedures,and skillfully use variable teaching and multiple solutions to one problem to cultivate students’ innovative thinking.2.In addition to strengthening the accumulation of basic knowledge,experience and mathematical thoughts and methods,it is more important for students to form the habit of summarizing and reflecting on such topics.