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Development of Preschoolers' Understanding of Zero.

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.

SUBMITTER: Krajcsi A

PROVIDER: S-EPMC8353124 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:IntroductionEffective implementation of a research Program requires an actionable plan to guide execution. To assess the actionability and success of that plan, both scientific and implementation elements must be taken into account. The aim of this study is to assess the 'Zero Childhood Cancer Personalised Medicine Program' (the Zero Program), an Australian first-ever and most comprehensive personalised medicine programme for children with high-risk or relapsed cancer, in terms of its structure, process and implementational effect.Methods and analysisWe will assess Program delivery mechanisms. The development of the implementation and evaluation strategy will concentrate on the work of the Zero Program as a complex whole. This includes the structure of collaborative links across stakeholder groups involved in Program development and delivery, changes to collaborative relationships over time and the impact of group working on Program outcomes. We are applying a mixed-methods design including: a rapid ethnography (observations of stakeholder interactions and informal conversations), Program professionals' completion of a rapid health implementation proforma and a social network analysis. Formative evaluations of the implementation science effects, applying feedback techniques, for example, Formative Evaluation Feedback Loops and the Zero Program professionals' feedback, will determine where Program tailoring may be needed. A repeat of the social network analysis downstream will examine network changes over time, followed by an expert panel using the expert recommendations for implementing change to assess the integration of implementation strategies into the Program structure. A summative evaluation of the Program will bring the research elements together, leading to comprehensive data triangulation and determining the sustainability and implementational effects of Program delivery.Ethics and disseminationEthical approval for this study has been granted by Hunter New England Research Ethics Committee, New South Wales, Australia (approval ref: 2019/ETH12025). Knowledge translation will be achieved through publications, reports and conference presentations to healthcare professionals, patients, families and researchers.Trial registrationNCT03336931; Pre-results.

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Development of Preschoolers' Understanding of Zero.

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