Research On The Teaching Of Comprehensive Problem Solving In Junior High School Mathematics

The knowledge span of mathematics comprehensive questions is large and the form of questions is flexible.It mainly investigates the ability of students to solve complex problems directly by applying mathematics.At the same time,comprehensive questions help students deepen the understanding of knowledge,improve knowledge structure,develop logical thinking,and cultivate students' ability to analyze and solve problems.Therefore,comprehensive questions are a kind of very valuable questions.However,students will encounter many obstacles in solving comprehensive problems,and teachers need to improve the effectiveness of solving comprehensive problems.Based on this,the research problems of this paper are as follows:(1)What are the obstacles for students to solve the comprehensive mathematical problems? What problems do these obstacles reflect?(2)How can teachers adjust teaching according to students' obstacles?(3)In the process of teaching,how to use Polya's "how to solve problems" to guide the teaching of comprehensive problems?This paper uses the method of literature research to understand the foreign research on problem-solving teaching and the domestic research on problem-solving teaching of mathematics comprehensive problems.At the same time,it analyzes the idea and steps of problem-solving in Polya's "how to solve problem table".Guided by Piaget's "constructivism" and Ausubel's "cognitive structure transfer theory",it forms the theoretical basis of this paper.In order to investigate the obstacles of junior high school students in solving comprehensive problems,the author chooses test paper and interview method to investigate the ninth grade students.Through the investigation,research and analysis of the students' problem-solving situation of geometry comprehensive problems,the author summarizes the obstacles and the causes of obstacles in solving geometry comprehensive problems,and puts forward the targeted teaching strategies.At the same time,the teaching plan is designed to explain how the teaching of comprehensive problem solving based on Polya's "how to solve problem table" can help students break through the difficulties of comprehensive problem solving.The conclusions are as follows:(1)The obstacles that students encounter in solving geometric comprehensive problems are: self-regulation,problem representation,knowledge,strategy,operation and retrospection.(2)In view of the above obstacles,the causes of the obstacles are analyzed.The reasons for the formation of self-regulation barriers are: Students' lack of interest and confidence;teachers' negative attitude towards wrong questions.The reasons for the formation of problem representation disorder are as follows: the way of problem representation is novel;students forget relevant knowledge.The reasons for the formation of knowledge-based barriers are as follows: students do not have a thorough grasp of the essence of concepts,properties and theorems;teachers have less heuristic problems in the process of teaching new lessons;teachers also do not pay attention to the cultivation of students' problem-solving habits in the teaching process.The reasons for the formation of strategic barriers: students can not use problem-solving strategies to solve problems;students do not have a deep understanding of mathematical thinking methods.The reasons for the formation of operational barriers are: students do not pay attention to problem-solving norms;weak computing ability;teachers do not pay attention to students' exercise and training in this aspect in the teaching process.The reason for the formation of retrospective and reflective barriers: students lack the habit of retrospective and reflective.(3)According to the obstacles and the causes of the obstacles,this paper puts forward some teaching strategies.The teaching strategies of self-regulation obstacles:respect students' differences,set up feasible goals,build confidence;correctly treat the obstacles in the process of solving problems.The teaching strategies of problem representation obstacles are as follows: paying attention to the analysis of problem stem,mining hidden conditions,and cultivating students' ability of transforming problems into symbolic language.The teaching strategies of knowledge barriers: pay attention to the essence of concept,nature,theorem teaching;help students improve the knowledge network.Teaching strategies of strategic obstacles: infiltrating mathematical thinking methods in the process of mathematical "discovery";helping students accumulate basic models.The teaching strategies of operational barriers are: standardizing students' problem-solving steps;strengthening students' computational ability.The teaching strategies of review and reflection are as follows: strengthening the test link;paying attention to the divergent teaching of multiple solutions to one problem;paying attention to the variant teaching.