View in EDS

Perceptual addition of continuous magnitudes in an 'artificial algebra'.

Saved in:
Bibliographic Details
Title: Perceptual addition of continuous magnitudes in an 'artificial algebra'.
Authors: Morton, Nicola J.1 (AUTHOR), Hooson-Smith, Cameron1 (AUTHOR), Stuart, Kate1 (AUTHOR), Kemp, Simon1 (AUTHOR), Grace, Randolph C.1 (AUTHOR) randolph.grace@canterbury.ac.nz
Source: Cognition. Mar2024, Vol. 244, pN.PAG-N.PAG. 1p.
Subject Terms: *Algebra, *Learning, *Explicit instruction, *Mental arithmetic, *Implicit learning, Stimulus & response (Psychology)
Abstract: Although there is substantial evidence for an innate 'number sense' that scaffolds learning about mathematics, whether the underlying representations are based on discrete or continuous perceptual magnitudes has been controversial. Yet the nature of the computations supported by these representations has been neglected in this debate. While basic computation of discrete non-symbolic quantities has been reliably demonstrated in adults, infants, and non-humans, far less consideration has been given to the capacity for computation of continuous perceptual magnitudes. Here we used a novel experimental task to ask if humans can learn to add non-symbolic, continuous magnitudes in accord with the properties of an algebraic group, by feedback and without explicit instruction. Three pairs of experiments tested perceptual addition under the group properties of commutativity (Experiments 1a-b), identity and inverses (Experiments 2a-b) and associativity (Experiments 3a-b), with both line length and brightness modalities. Transfer designs were used in which participants responded on trials with feedback based on sums of magnitudes and later were tested with novel stimulus configurations. In all experiments, correlations of average responses with magnitude sums were high on trials with feedback. Responding on transfer trials was accurate and provided strong support for addition under all of the group axioms with line length, and for all except associativity with brightness. Our results confirm that adult human subjects can implicitly add continuous quantities in a manner consistent with symbolic addition over the integers, and that an 'artificial algebra' task can be used to study implicit computation. [ABSTRACT FROM AUTHOR]
Copyright of Cognition is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Education Research Complete
FullText Text:
  Availability: 0
Header DbId: ehh
DbLabel: Education Research Complete
An: 174950411
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Perceptual addition of continuous magnitudes in an 'artificial algebra'.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Morton%2C+Nicola+J%2E%22">Morton, Nicola J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hooson-Smith%2C+Cameron%22">Hooson-Smith, Cameron</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Stuart%2C+Kate%22">Stuart, Kate</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kemp%2C+Simon%22">Kemp, Simon</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Grace%2C+Randolph+C%2E%22">Grace, Randolph C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> randolph.grace@canterbury.ac.nz</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Cognition%22">Cognition</searchLink>. Mar2024, Vol. 244, pN.PAG-N.PAG. 1p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br />*<searchLink fieldCode="DE" term="%22Learning%22">Learning</searchLink><br />*<searchLink fieldCode="DE" term="%22Explicit+instruction%22">Explicit instruction</searchLink><br />*<searchLink fieldCode="DE" term="%22Mental+arithmetic%22">Mental arithmetic</searchLink><br />*<searchLink fieldCode="DE" term="%22Implicit+learning%22">Implicit learning</searchLink><br /><searchLink fieldCode="DE" term="%22Stimulus+%26+response+%28Psychology%29%22">Stimulus & response (Psychology)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Although there is substantial evidence for an innate 'number sense' that scaffolds learning about mathematics, whether the underlying representations are based on discrete or continuous perceptual magnitudes has been controversial. Yet the nature of the computations supported by these representations has been neglected in this debate. While basic computation of discrete non-symbolic quantities has been reliably demonstrated in adults, infants, and non-humans, far less consideration has been given to the capacity for computation of continuous perceptual magnitudes. Here we used a novel experimental task to ask if humans can learn to add non-symbolic, continuous magnitudes in accord with the properties of an algebraic group, by feedback and without explicit instruction. Three pairs of experiments tested perceptual addition under the group properties of commutativity (Experiments 1a-b), identity and inverses (Experiments 2a-b) and associativity (Experiments 3a-b), with both line length and brightness modalities. Transfer designs were used in which participants responded on trials with feedback based on sums of magnitudes and later were tested with novel stimulus configurations. In all experiments, correlations of average responses with magnitude sums were high on trials with feedback. Responding on transfer trials was accurate and provided strong support for addition under all of the group axioms with line length, and for all except associativity with brightness. Our results confirm that adult human subjects can implicitly add continuous quantities in a manner consistent with symbolic addition over the integers, and that an 'artificial algebra' task can be used to study implicit computation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Cognition is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=174950411
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.cognition.2023.105710
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Learning
        Type: general
      – SubjectFull: Explicit instruction
        Type: general
      – SubjectFull: Mental arithmetic
        Type: general
      – SubjectFull: Implicit learning
        Type: general
      – SubjectFull: Stimulus & response (Psychology)
        Type: general
    Titles:
      – TitleFull: Perceptual addition of continuous magnitudes in an 'artificial algebra'.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Morton, Nicola J.
      – PersonEntity:
          Name:
            NameFull: Hooson-Smith, Cameron
      – PersonEntity:
          Name:
            NameFull: Stuart, Kate
      – PersonEntity:
          Name:
            NameFull: Kemp, Simon
      – PersonEntity:
          Name:
            NameFull: Grace, Randolph C.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Text: Mar2024
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-print
              Value: 00100277
          Numbering:
            – Type: volume
              Value: 244
          Titles:
            – TitleFull: Cognition
              Type: main
ResultId 1