The how many and give-N tasks: Conceptually distinct measures of the cardinality principle

In the current study we investigated performance on the how many (how many?) and give-N tasks. We first investigated the relative performance of three-to-five-year-old children (N = 393; M = 4.75 years, SD = .75 years) on these tasks. Replicating prior work, we found that children performed worse on give-N compared to how many? and this performance gap increased as the set size increased. This performance gap remained even after controlling for children's counting skill. We next conducted a series of confirmatory factor analyses to identify the best fitting factor structure of three tasks that measure children's understanding of set sizes across both small and large sets: a subitizing measure, how many?, and give-N. We found that the best fitting factor structure contained separate factors for each task. This suggests that each measure provides task-specific variance not captured by the other cardinality measures. These results highlight the different aspects of children's understanding of cardinality.