The Application Of Polya's Problem-solving Ideas In The Teaching Of High School Mathematics Application Questions

Applied mathematics is a bridge between mathematics and real life, to improve the students' mathematical literacy, plays an important role in cultivating students'communicative consciousness. In mathematics teaching, can cultivate students'thinking and ability to solve problems with the knowledge of mathematical analysis and can improve the students' ability of innovation, for the future to adapt to social life and promote social development and lay a solid foundation. In the college entrance examination every year there is a mathematical application problem, which is based on the geometry of the background of the majority of mathematical problems,to investigate the ability of students to analyze and solve problems and quality. In the college entrance examination for many years, the score of the students is not too satisfactory, as the first line of the high school teachers need to conduct in-depth study of such issues.Based on the above consideration, this paper takes Polya's thought of solving problem as the main guiding ideology, behavior, questionnaire, case tracking research and interviews and other research methods through literature research, through theoretical study and practical exploration. First, through literature research methods of problem-solving thinking theory of mathematics teaching and Polya sums up;secondly, to understand the actual situation of the students through the questionnaire survey, and through interviews to further understand students in mathematics to solve the problem solving ideas in the process of compliance with Polya's thought of solving problem; third. On the basis of the investigation of Polya proposed mathematical thinking problem solving model based on the model applied to the mathematical problem solving teaching practice in senior high school; finally, we selected two different basis for the students in the sample, tracking experiment,further verify the effect.The research conclusion is mainly reflected in the:(1) the investigation of the mathematics application problem solving of the senior high school students shows that: the present situation of the students' problem solving is not ideal, and it is not in line with Polya's problem-solving model from the understanding of the problem, the formulation of the plan, the implementation of the program and the review of the reflection.(2) according to the research on Polya's thought of solving problem, put forward four steps of mathematical understanding: 1 ? plan review the implementation of the plan(3) in three of the problem solving teaching practice, based on Polya's thought of solving problem, strengthen the basic concept and the basic theorem is used to train the ability to understand the focus on reading five teaching strategies in the teaching of the review to pay attention to let the students understand the teaching practice of the independent analysis and pay attention to cultivating students' operation ability and training students' reflection habits. Through the study of a school year, it is obvious that the problem solving model based on Polya's thinking of solving problems not only expands the students' ability of solving practical problems, but also improves the mathematics achievement.(4) case study show that: through the three stages of the experiment, let students sort out the wrong topic, by Polya thought of solving problem solution pattern discovery based on students in solving problems in problems where analysis of students in the course of solving the obstacles and mistakes, to carry out guidance and training to students, to help them find the general mode of solving problems, develop the students' ability of solving mathematical problems, and achieved certain results.