Working Paper Article Version 2 This version is not peer-reviewed

# Preschoolers’ Development of Understanding Zero

Version 1 : Received: 24 August 2017 / Approved: 25 August 2017 / Online: 25 August 2017 (12:28:23 CEST)
Version 2 : Received: 16 July 2020 / Approved: 16 July 2020 / Online: 16 July 2020 (12:35:17 CEST)

A peer-reviewed article of this Preprint also exists.

Krajcsi, A.; Kojouharova, P.; Lengyel, G. Development of Preschoolers’ Understanding of Zero. Frontiers in Psychology 2021, 12, doi:10.3389/fpsyg.2021.583734. Krajcsi, A.; Kojouharova, P.; Lengyel, G. Development of Preschoolers’ Understanding of Zero. Frontiers in Psychology 2021, 12, doi:10.3389/fpsyg.2021.583734.

## Abstract

While the knowledge about the development of understanding positive integers is rapidly growing, the development of understanding zero is not well-known. Here we tested several components of preschoolers’ understanding zero: whether they can use empty sets in numerical tasks, whether they can use empty sets soon after they understand the cardinality principle, whether they know what the word “zero” refers to, and whether they categorize zero as a number. The results show that preschoolers can handle empty sets in numerical tasks as soon as they understand the cardinality principle or even earlier, and some of them know that these sets are labeled as “zero.” However, they 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 might understand numbers as the properties of items or objects in a set. In this view, zero cannot be a number, because an empty set does not include any items, and the missing items cannot have any property, excluding also the number property. This model might explain why zero is handled correctly in numerical tasks, while it is not regarded to be a number.

## Supplementary and Associated Material

https://www.thenumberworks.org/zero_in_preschoolers.html: Summary of the work on the lab web page

## Keywords

numerical cognition; zero; number status of zero; items based number representation

## Subject

Social Sciences, Psychology

Comment 1
Commenter: Attila Krajcsi
Commenter's Conflict of Interests: Author
Comment: Revised version of the manuscript
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