A Study On "Graphics And Geometry" Problem Teaching And Learning In Junior Middle School Based On Polya Theory

Junior high school "graphics and geometry" is an important content of middle school mathematics.The problem of "graphics and geometry" in junior high school is comprehensive and difficult.It not only examines the students' mastery of subject knowledge,but also examines the students' logical reasoning ability when solving problems.By solving the problem of "graphics and geometry ",we can not only broaden the vision of the problem solver,but also develop its divergent thinking,innovative exploration and practical ability.The teaching of "graphics and geometry" problem solving can not only make junior high school students master the knowledge of "graphics and geometry" systematically,but also cultivate students' ability of logical reasoning and independent problem solving,at the same time,it is also of great significance to improve the teaching ability of middle school mathematics teachers to solve problems.The article takes Polya's problem-solving theory as the core,and specifically studies the following two questions: ? What are the problems of "teaching" and "learning" in the teaching of "graphics and geometry" in junior high school? ?What are the teaching strategies of "Graphics and Geometry" in junior high school based on Polya's problem solving theory?Based on the above research questions,test papers and interview papers for "graphics and geometry" in junior middle school were prepared respectively.Four mathematics teachers in the third grades of a general middle school in Urumqi,and96 students in the ninth grade are the research samples.Investigate the current status of "teaching" of junior middle school mathematics teachers' "graphics and geometry" problem-solving teaching through classroom observation,and study the status of students' "learning" of junior middle school teachers' "graphics and geometry" problem-solving teaching through questionnaire testing and interview investigation.The survey found that both teachers and students have many problems in the "teaching" and "learning" aspects of junior middle school "graphics and geometry" problem-solving teaching.The problems found by teachers are as follows: ? Did not inspire students to guess;?Excessive inspiration;?Invalid classroom questions;?Ignore the teaching behind the motivation;? Ignore the penetration of mathematical thinking methods;? Ignore retrospect and reflection.The problems identified by students are as follows: ? Lack of solid basic knowledge;? The topic can not be explored in depth;? Poor logical derivation;?Lack of confidence in problem solving;? Lack of self-monitoring;? Lack of timely reflection and review;?Metacognitive impairment.Based on the problems found in the course of the research,and combining with the theory of solving problems in Polia,four teaching strategies of "graphics and geometry" in junior high school are put forward: ? Middle school mathematics teachers should fully understand the importance of Polia's theory of problem solving;? Encourage students to recite the "How to Solve the Problem Table" of Polia and use it consciously to solve problems;?Teachers should make full use of "problems and suggestions" in "how to solve problems" in "how to solve problems" and implement "graphics and geometry" problem solving teaching;?The teaching of "graphics and geometry" problem solving should focus on the infiltration of mathematical thinking methods.Finally,a case of problem solving teaching is designed in combination with the proposed teaching strategy.