The Research On The Common Mathematical Errors By The Middle Students

Mathematical errors are common in the Mathematics learning. As long as there is mathematics learning, there will be a mathematical error. In the process of mathematical teaching, teachers and students are always dealing with the errors every day. How to correct the mathematical errors effectively? This is not only the problem encountered by teachers, but also a major study field in the mathematical teaching theory. Therefore, this research is both of important theoretical significance, and of important practical significance. It is of more important significance to the effective mathematical teaching and the training on the proper mathematical thinking for students.This paper selected and dicussed serval common errors that were seldom studied. These errors included: negative transfer, logical errors, conceptual errors and strategic mistakes. Negative transfer was discussed mainly from the perspective of cognitive psychology, including the transfer from the top downward, the transfer from bottom upward and the parallel negative transfer. The study of logical error was focused on the errors caused by the lack of implied conditions. The conceptual errors was further discussed on the interference of the daily concepts, the confusion by the close concepts,the misunderstanding of the essence of a concept, the errors in the development and the connection. The strategic error was studied from model muddle, the lack of basic methods, and the lack of goal awareness.Under the guidance of the Cognitive Theory, and the Construction Theory etc, the mathematical errors were analyzed deeply in order to find a new way to correct them. To this end, the stress of this study was put on the meta-cognitive training, the teaching with mathematical thoughts, and the preparations against mathematical errors.