Abstract
While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers’ understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word “zero” refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle. Some also know that these sets are labeled as “zero.” However, preschoolers are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta-knowledge. To account for these results, we propose that preschoolers may understand numbers as the properties of items or objects in a set. In this view, zero is not regarded as a number because an empty set does not include any items, and missing items cannot have any properties, therefore, they cannot have the number property either. This model can explain why zero is handled correctly in numerical tasks even though it is not regarded as a number.
Highlights
Children start to understand the use of symbolic exact numbers at around the age of three (Wynn, 1990, 1992)
Note again that the present work focuses on the processing of symbolic stimuli because (a) investigating non-symbolic zero involves many unresolved methodological issues, (b) in recent years, several works have revealed essential differences between symbolic and non-symbolic number processing (e.g., Noël and Rousselle, 2011; Bulthé et al, 2015; Krajcsi et al, 2016, 2020; Schneider et al, 2017), and such differences put into question whether symbolic stimuli are processed by an evolutionarily old, imprecise number representation, and (c) CP-knowledge points beyond approximate number handling (Carey and Barner, 2019
Syntactic processes behind transcoding are only relevant in multi-power
Summary
Children start to understand the use of symbolic exact numbers at around the age of three (Wynn, 1990, 1992). In infants, numerical information is handled by either the imprecise Approximate Number System (Feigenson et al, 2004; Piazza, 2010) or the visual attention related Object Tracking System (Feigenson et al, 2004). It is not straightforward whether either of these systems can handle zero (see more details on how these models may or may not account for zero processing in Supplementary Material)
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