Cognitive Process Of Understanding Mathematical Concepts

Understanding of mathematical cognition is important in the process of mathematics learning a part, for the study of mathematical knowledge to understand the total effect. The current understanding of mathematical cognition research has focused on cognitive understanding of mathematics content, level, feature, etc., and for the specific process of understanding mathematical cognition research is still relatively small, and only partial results are more general. Based on previous research, with the current high school students learn mathematical concepts, in-depth study of the middle school students to understand the psychological process of cognitive concepts, and thus the concept of the current middle school mathematics teaching is explored.In this paper, the main methods are: oral report,interview and experimental method.The order: first to understand the current research on mathematics are reviewed by review of the current understanding of mathematics and the lack of focus of the study, and then used in this article introduces the major research methods - oral report Method. Then the previous understanding of the views of cognitive understanding of mathematical concepts is given the definition of a mathematical concept analysis and theoretical knowledge related to the teaching of mathematical concepts put forward their own ideas. Third, the use of oral reports and interviews form the Combination of the investigation, after the survey data collection and analysis of the students summed up the cognitive understanding of mathematical concepts and characteristics of internal processes, and gives the students understand the mathematical concept of cognitive Internal mental process model. Fourthly, according to middle school students to understand the characteristics of the concept of cognitive and psychological mechanisms made a number of teaching recommendations, and in later experiments proved the effectiveness of teaching suggestions put forward.The main conclusions of this study: First, the students understanding of mathematical concepts to understand the positive initiative, continuity, order, and immediacy; II, understanding of mathematical concepts students understand the internal process is a mathematical concept based on the new Features two-way operation in the minds of the process, the first direction of operation is the mathematical concept into a new cognitive structure, the nature of links established with the relevant knowledge to form a coding system; second direction of operation is called a variety of students consciously Related to old knowledge to new mathematical concepts deduced, straighten out the link between the old and new knowledge to form extensive contacts between the old and new knowledge and the nature of the contact.