Abstract: The acquisition of symbolic numbers is a milestone in the development of children's numerical cognition,as it marks the transition from the stage where children only possess primary,non-verbal numerical abilities to the stage where they can comprehend culturally-acquired symbolic number systems through conceptual learning.Children typically start to learn symbolic numbers (including the cardinality and the successor function of symbolic numbers) since 3 or 4 years of age.Although the developmental trajectory of learning about symbolic numbers has been depicted,it remains unclear how the learning occurs.In particular,it has been highly debated about the cognitive foundation for the conceptual acquisition of symbolic numbers.Researchers now have focused on examining whether children's learning of symbolic numbers is built on primary non-verbal numerical abilities that are presented since early infancy.As non-verbal numerical abilities are supported by at least two distinct cognitive systems,including the Approximate Number System (ANS) and the Object Tracking System (OTS),researchers have investigated if the acquisition of symbolic numbers relies on these systems.Specifically,there have been four different hypotheses on the cognitive foundation for learning symbolic numbers.The ANS hypothesis suggests that ANS is the cognitive foundation,while the OTS hypothesis proposes that OTS is responsible.The Dual-system hypothesis suggests that both ANS and OTS are required for the acquisition of symbolic numbers.On the other hand,the independence hypothesis suggests that neither of the two systems is the cognitive foundation.Both positive evidence and challenges for each of these hypotheses were discussed in the present review.It should be noticed that the empirical findings from previous studies cannot strictly test the four hypotheses due to limitations in experimental design.Some experimental designs were suggested to test these hypotheses and further reveal the cognitive foundation for children's acquisition of symbolic numbers.

Key words: symbolic numbers, cardinality, successor function, the Approximate Number System, the Object Tracking System