Although many US children can count sets by 4 years, it is not until 5½-6 years that they understand how counting relates to number -i.e., that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½-6-year-olds (N = 136) may leverage to acquire this "successor function": (1) mastery of productive rules governing count list generation; and (2) training with "+1" math facts. Both productive counting and "+1" math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from "+1" math facts.

No abstract