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The Give a number task is used to characterize the initial symbolic number knowledge of preschoolers. The task is intended to identify critical phases of number processing development. Here, a modified version of the task was used with which it is possible to describe additional properties of number development. Measuring 3- and 4-year-old children it was found that in subset-knowers, the performance typically did not drop suddenly after a specific number, instead, the correct response rate decreased gradually. This result suggests that the widely used titration method together with the noise of the measurement may be imprecise. It was also found that, in contrast with the mainstream supposition, there are 5-, 6-, 7- and 8-knowers, revealing subset-knowers understanding numbers larger than 4. This result may question the role of the object tracking system in the initial symbolic number learning. Based on these results we propose that a modified version of the Give a number task should be used to measure preschoolers’ initial symbolic number knowledge, because the version predominantly applied in the literature cannot capture some critical features of the number knowledge development and it can miscategorize some of the children.