The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement

•Children's arithmetic operation understanding correlated with their math achievement.•Its contribution is similar to that of numerical magnitude representation.•More effort should be devoted to investigate arithmetic operation understanding.

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning.