Relationship and quantity:different perspectives on fraction understanding

Fraction is an important and difficult part of the mathematics teaching in primary schools. There are many abundant and explicit studies on fraction teaching and cognition in China and abroad. Comparing these research, the concept of fraction can be macroscopically divided into the concept of Relationship and the concept of quantity. The difficulties of fraction cognition are from three aspects. Firstly, each relationship concept has abstraction and the transformation between relationships has complexity. Secondly, the concept of quantity has relativity, denseness and infinity. Thirdly, there should be the teaching isomorphism based on Concepts of relationship. and quantity. Therefore, in the process of teaching, we need to improve the structure of the relationship of fraction and find the connection between the concept of relationship and the concept of quantity, which can effectively break the barriers of fraction learning and construct the structure of fraction teaching as a whole.