Abstract: The approximate number system plays an important role in the development of individual mathematical abilities, and the relationship between the two factors is affected by age. Mainly, as age increases, the degree of correlation gradually weakens, and the mechanisms change from cardinal knowledge mediation to the joint effect of multiple intermediary variables. Future research should use a more rigorous experimental design and multiple research methods to investigate the development trend, causal direction, key turning points and the underlying mechanisms of the relationship between the approximate number system and different mathematical abilities of children of all ages to better understand the role of the approximate number system in the development of individual mathematical abilities.

Key words: approximate number system, mathematical abilities, cardinal knowledge mediation hypothesis, visual form perception hypothesis, development