Article Version of Record

Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency

Author(s) / Creator(s)

Vogel, Stephan E.
Haigh, Trent
Sommerauer, Gerrit
Spindler, Melanie
Brunner, Clemens
Lyons, Ian M.
Grabner, Roland H.

Abstract / Description

A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.

Keyword(s)

numerical and non-numerical order arithmetic abilities reverse distance effect canonical distance effect reliability ordinality processing symbolic numbers non-symbolic numbers arithmetic fluency

Persistent Identifier

Date of first publication

2017-12-22

Journal title

Journal of Numerical Cognition

Volume

3

Issue

2

Page numbers

288–308

Publisher

PsychOpen GOLD

Publication status

publishedVersion

Review status

peerReviewed

Is version of

Citation

Vogel, S. E., Haigh, T., Sommerauer, G., Spindler, M., Brunner, C., Lyons, I. M., & Grabner, R. H. (2017). Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency. Journal of Numerical Cognition, 3(2), 288–308. https://doi.org/10.5964/jnc.v3i2.55
  • Author(s) / Creator(s)
    Vogel, Stephan E.
  • Author(s) / Creator(s)
    Haigh, Trent
  • Author(s) / Creator(s)
    Sommerauer, Gerrit
  • Author(s) / Creator(s)
    Spindler, Melanie
  • Author(s) / Creator(s)
    Brunner, Clemens
  • Author(s) / Creator(s)
    Lyons, Ian M.
  • Author(s) / Creator(s)
    Grabner, Roland H.
  • PsychArchives acquisition timestamp
    2018-11-21T11:42:47Z
  • Made available on
    2018-11-21T11:42:47Z
  • Date of first publication
    2017-12-22
  • Abstract / Description
    A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.
    en_US
  • Publication status
    publishedVersion
  • Review status
    peerReviewed
  • Citation
    Vogel, S. E., Haigh, T., Sommerauer, G., Spindler, M., Brunner, C., Lyons, I. M., & Grabner, R. H. (2017). Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency. Journal of Numerical Cognition, 3(2), 288–308. https://doi.org/10.5964/jnc.v3i2.55
    en_US
  • ISSN
    2363-8761
  • Persistent Identifier
    https://hdl.handle.net/20.500.12034/1264
  • Persistent Identifier
    https://doi.org/10.23668/psycharchives.1456
  • Language of content
    eng
  • Publisher
    PsychOpen GOLD
  • Is version of
    https://doi.org/10.5964/jnc.v3i2.55
  • Keyword(s)
    numerical and non-numerical order
    en_US
  • Keyword(s)
    arithmetic abilities
    en_US
  • Keyword(s)
    reverse distance effect
    en_US
  • Keyword(s)
    canonical distance effect
    en_US
  • Keyword(s)
    reliability
    en_US
  • Keyword(s)
    ordinality processing
    en_US
  • Keyword(s)
    symbolic numbers
    en_US
  • Keyword(s)
    non-symbolic numbers
    en_US
  • Keyword(s)
    arithmetic fluency
    en_US
  • Dewey Decimal Classification number(s)
    150
  • Title
    Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency
    en_US
  • DRO type
    article
  • Issue
    2
  • Journal title
    Journal of Numerical Cognition
  • Page numbers
    288–308
  • Volume
    3
  • Visible tag(s)
    Version of Record