Do we have a sense for irrational numbers?
Author(s) / Creator(s)
Obersteiner, Andreas
Hofreiter, Veronika
Abstract / Description
Number sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational numbers, such as the cube root of 41. In a computerized experiment, we asked mathematically skilled adults to repeatedly choose the larger of two irrational numbers as quickly as possible. Participants were highly accurate on problems in which reasoning about the exact or approximate value of the irrational numbers’ whole number components (e.g., 3 and 41 in the cube root of 41) yielded the correct response. However, they performed at random chance level when these strategies were invalid and the problem required reasoning about the irrational number magnitudes as a whole. Response times suggested that participants hardly even tried to assess magnitudes of the irrational numbers as a whole, and if they did, were largely unsuccessful. We conclude that even mathematically skilled adults struggle with quickly assessing magnitudes of irrational numbers in their symbolic notation. Without practice, number sense seems to be restricted to rational numbers.
Keyword(s)
number sense magnitude representation number comparison natural number bias numerical distance effectPersistent Identifier
Date of first publication
2017-02-10
Journal title
Journal of Numerical Cognition
Volume
2
Issue
3
Page numbers
170–189
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Obersteiner, A., & Hofreiter, V. (2017). Do we have a sense for irrational numbers? Journal of Numerical Cognition, 2(3), 170–189. https://doi.org/10.5964/jnc.v2i3.43
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Author(s) / Creator(s)Obersteiner, Andreas
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Author(s) / Creator(s)Hofreiter, Veronika
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PsychArchives acquisition timestamp2018-11-21T11:42:41Z
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Made available on2018-11-21T11:42:41Z
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Date of first publication2017-02-10
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Abstract / DescriptionNumber sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational numbers, such as the cube root of 41. In a computerized experiment, we asked mathematically skilled adults to repeatedly choose the larger of two irrational numbers as quickly as possible. Participants were highly accurate on problems in which reasoning about the exact or approximate value of the irrational numbers’ whole number components (e.g., 3 and 41 in the cube root of 41) yielded the correct response. However, they performed at random chance level when these strategies were invalid and the problem required reasoning about the irrational number magnitudes as a whole. Response times suggested that participants hardly even tried to assess magnitudes of the irrational numbers as a whole, and if they did, were largely unsuccessful. We conclude that even mathematically skilled adults struggle with quickly assessing magnitudes of irrational numbers in their symbolic notation. Without practice, number sense seems to be restricted to rational numbers.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationObersteiner, A., & Hofreiter, V. (2017). Do we have a sense for irrational numbers? Journal of Numerical Cognition, 2(3), 170–189. https://doi.org/10.5964/jnc.v2i3.43en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/1242
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.1434
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Language of contenteng
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PublisherPsychOpen GOLD
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Is version ofhttps://doi.org/10.5964/jnc.v2i3.43
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Keyword(s)number senseen_US
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Keyword(s)magnitude representationen_US
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Keyword(s)number comparisonen_US
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Keyword(s)natural number biasen_US
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Keyword(s)numerical distance effecten_US
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Dewey Decimal Classification number(s)150
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TitleDo we have a sense for irrational numbers?en_US
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DRO typearticle
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Issue3
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Journal titleJournal of Numerical Cognition
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Page numbers170–189
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Volume2
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Visible tag(s)Version of Record