A Study of "Extension Cognition" in Primary Mathematics Education

There is no doubt about the importance of mathematics in primary education, and its biggest problem is the cognitive uncertainty of teaching and learning in mathematics education. The purpose of this paper is to establish a cognitive model for solving uncertain problems in mathematics teaching -- "extension cognition" model. Based on the extension cognitive model, this paper discusses how to recognize mathematics teaching from mathematics teaching and how to learn mathematics learning from mathematics learning, thus embodiments the extension thought of metacognitive mathematics education. The experimental results show that children have differences in the "extension cognition" of mathematics learning, small differences in divergent cognition and related cognition, and large differences in implicative cognition and conjugated cognition. And this difference in "extension cognition" is determined by many factors, such as children's learning environment, learning thinking habits, parents' behavior thinking mode and so on. Therefore, the key to narrow the differences in primary mathematics education is to improve children's mathematical "extension cognition" ability.