How To Solve The Problem Of "How To Solve The Problem" In Junior High School Applied Mathematics

Problem solving is one of the most important content in mathematics. Math application problem has its significant role in math education. It is also weaved into the whole education system. Polya’s table of’How to solve it’ has a good use in problem solving, and it provides a useful model in solving all kinds of maths problem. So this study focuses on how to use Polya’s table of "How to solve it’ to solve math application problem in middle school.This paper first concentrates on literature review of math application problems and related concepts, which includes definitions of problem, math problem statement and math application problems. By analyzing Polya’s table of’How to solve it’, the process of problem solving can be dissected into four steps:understand the problem statement, make plans, execute plans and review. The specific tasks for each step are also a part of the analysis. The first part establishes the theoretical basis of this paper.Second, according to Polya’s table of ’How to solve it’ to design the surveys and questionnaires. The surveys and questionnaires are distributed among middle school students in order to gather information about the current trend of solving math application problems. From the survey results, we get the following preliminary conclusions:most of the students can understand the meaning of the problem and find out a right way to solve the problem. In the step of executing plans, the biggest problem is calculation and in the final step, most of the students are in lack of the sense of inspection. Students’ ability to solve the problem varies depend upon different schools. We do not notice a significant divergence based on gender difference.Third, the paper analyzes and categorizes the mistakes students made when solving the application problems, in combination with the conclusions we draw from the previous survey results. The mistakes students made can be categorized into four types:1. Understanding the problem statement, which includes disregard for the specified conditions, inappropriate presumptions, implied conditions and obscure concepts; 2. Making plans, which includes a lack of integrity and reverse thinking; 3. Executing plans:reduction of algebraic expression, computation, a lack of mathematical sense and other non-intelligence factors; 4. Review, which includes ignorance of back-checking.In the end, the paper offers strategies that will improve the students’ ability of solving application problems according to the above studies and conclusions. Similarly, the strategies are divided into four steps:1. Understanding the problem statement:improve students’ reading skills and understanding of concepts and principles; 2. Making plans:develop a habit of implementing integrity and reverse thinking to solve problems; 3. Executing plans:enhance the teaching of algebraic expression, improve students’ computation skills and mathematical sense; 4. Review: emphasize on group working and develop a habit of back-checking.