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The knowledge of the preceding number reveals a mature understanding of the number sequence

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journal contribution
posted on 06.03.2020, 10:09 by Francesco Sella, Daniela Lucangeli
© 2019 There is an ongoing debate concerning how numbers acquire numerical meaning. On the one hand, it has been argued that symbols acquire meaning via a mapping to external numerosities as represented by the approximate number system (ANS). On the other hand, it has been proposed that the initial mapping of small numerosities to the corresponding number words and the knowledge of the properties of counting list, especially the order relation between symbols, lead to the understanding of the exact numerical magnitude associated with numerical symbols. In the present study, we directly compared these two hypotheses in a group of preschool children who could proficiently count (most of the children were cardinal principle knowers). We used a numerosity estimation task to assess whether children have created a mapping between the ANS and the counting list (i.e., ANS-to-word mapping). Children also completed a direction task to assess their knowledge of the directional property of the counting list. That is, adding one item to a set leads to he next number word in the sequence (i.e., successor knowledge) whereas removing one item leads to the preceding number word (i.e., predecessor knowledge). Similarly, we used a visual order task to assess the knowledge that successive and preceding numbers occupy specific spatial positions on the visual number line (i.e., preceding: [?], [13], [14]; successive: [12], [13], [?]). Finally, children's performance in comparing the magnitude of number words and Arabic numbers indexed the knowledge of exact symbolic numerical magnitude. Approximately half of the children in our sample have created a mapping between the ANS and the counting list. Most of the children mastered the successor knowledge whereas few of them could master the predecessor knowledge. Children revealed a strong tendency to respond with the successive number in the counting list even when an item was removed from a set or the name of the preceding number on the number line was asked. Crucially, we found evidence that both the mastering of the predecessor knowledge and the ability to name the preceding number in the number line relate to the performance in number comparison tasks. Conversely, there was moderate/anecdotal evidence for a relation between the ANS-to-word mapping and number comparison skills. Non-rote access to the number sequence relates to knowledge of the exact magnitude associated with numerical symbols, beyond the mastering of the cardinality principle and domain-general factors.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Cognition

Volume

194

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Cognition and the definitive published version is available at https://doi.org/10.1016/j.cognition.2019.104104

Acceptance date

08/10/2019

Publication date

2019-11-04

Copyright date

2020

ISSN

0010-0277

eISSN

1873-7838

Language

en

Depositor

Dr Francesco Sella (email: F.Sella@lboro.ac.uk | regno: 5035977). h 2020

Article number

104104

Exports