A Survey And Research Of Factors Affecting Mathematics Application Problem-solving In High School Students

With mathematics more and more widely used, the education of mathematics application becomes even more important. An important idea of the new curriculum reform is vigorously developing students' awareness of mathematics application and improving their ability in practice. In the class, the students improve the problem solving ability mainly through solving the problem of mathematics application. However, in the long time, the basic knowledge and basic skills training is over emphasized in the high school mathematics classroom of our country, and the teaching of application problems has not yet been paid full attention. The ability of students' problem solving is still very bad. How to improve the teaching of application problems effectively is an important topic for secondary school teachers to face up.Through the investigation of 113 students from different regions we find the factors which impact students' solving the mathematics application problems are mainly as follows:Firstly, in terms of cognition mechanism the factors which impact high school students' solving the mathematics application problems lie on: context understanding , problem classification, problem representation, problem solving plan, metacognition experiencing and monitoring. These factors have a significant correlation to the achievements of solving application problems, of which problem represe ntation and context understanding play the most important role. The students with high metacognition level have better ability of solving problems than those with low metacognition level.Secondly different cognitive styles affect different types of application solutions. The students of field dependence are better at solving conventional application problems which is closely related to the mathematical knowledge, but often fail at problems which need building mathematical model. In the contrary, the students of field independence often result in faulty because of carelessness or calculation errors when solving conventional application problems. However, they can quickly categorize the problem, build mathematical model, and resolve the problem for the unconventional application problems. Furthermore the investigation indicate that there exist differences in cognitive styles between boys and girls. Boys prefer field independence than girls in the same level.In addition, the lack of solution strategy and examination evaluation are another important factors which impact the solution of application problems. The College Entrance Examination has different emphasis in different regions which leads to great difference among students in the strategy training. But over all, in today's math class too little time is spent in teaching of application problems, and students generally lack the corresponding solving strategy.In the final of the paper, some suggestions related to the teaching are proposed based on the conclusions of this study.