Analyze And Solve Problems Based On Cognitive Models Of Mathematical Problems Math Is Wrong

In recent years, there are a lot of research about mathematical-problem solving. Those research are much depth. Now mathematical-problem solving and error research are becoming an important research topic, in which the causes of the problem-solving and error analysis is one of the important aspects. By examining and collating the literature can be found that the field about mathematical problem solving and error has drawn a lot of meaningful results, but there are still many problems to be studied. This research will combine the theory about cognitive structure of mathematical problem solving. This research will analysis mathematical error that are Grade A in Beijing. On this basis, the research will interview the math teacher who teach math in this class. At last, this research will give some thoughts on teachers’ teaching.Through the review of related literature home and abroad, this paper gave a definition of mathematical error, that is:In the face of a mathematical problem, students through the problem representation, pattern recognition, problem-solving transfer, problem-solving monitoring four cognitive components as above, and the students with basic knowledge of mathematics, problem solving strategy, those comprise the cognitive mode together. In the cognitive mode of operation, a student does not meet the target state, which specific performance in part of the mistake or all error.This paper uses the text analysis, interviews and other research on the following three key problems:(1) Analysis of the reasons behind the typical errors from the perspective of cognitive psychology;(2) To explore the top students, average students, and poor students mathematical errors existing rules, and analysis problems and differences of the three class of students in the cognitive aspects;(3) Interaction between teachers and students teaching grope error problem solving, and perfect teaching so as to better.The main conclusions of the study:students have a mathematical error, from the analysis of cognitive structure are in the problem representation, pattern recognition, problem-solving transfer, problems-solving monitoring and basic knowledge of mathematics, problem-solving strategies etc.(1) Top students in mathematics knowledge, thinking, problem solving method is higher than the level of secondary students and poor students. For simple problems,they have little problem-solving transfer and self-monitoring. They are mainly the automatic solving and so is the secondary students.But secondary students in mathematics knowledge, methods of understanding are less than the top students. So the average student have much mathematical error. Because of poor students self-monitoring, so their error rate is very low.(2) For difficult problems, there exists obvious difference between three kinds of students. Difficult problems easily let the student carry on problem-solving transfer and self monitoring. At this time, top students in the problem representation, pattern recognition, problem-solving transfer are better than the other two types of students. At the same time, top students have self-monitoring, so they think problem carefully. Their error rate is very low and the high error rate of two other students.Through the research, this paper does some thoughts on teaching:Firstly, teachers should help students consolidate the learned knowledge, while introducing extra-curricular knowledge, that can broad student’s horizons. Secondly, increase the difficulty of mathematical problems of secondary students gradually. Thirdly, teachers should help poor students to understand the concept, principle, method accurately.