An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity—with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting.
Emily Slusser and B Sarnecka. "A picture of eight turtles: the child’s understanding of cardinality and numerosity" Journal of Experimental Child Psychology (2011): 38-51.