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1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic

  • Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally.

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Metadaten
Author details:Samuel ShakiORCiD, Noa Sery, Martin H. FischerORCiDGND
DOI:https://doi.org/10.1080/20445911.2014.973414
ISSN:2044-5911
ISSN:2044-592X
Title of parent work (English):Journal of cognitive psychology
Publisher:Routledge, Taylor & Francis Group
Place of publishing:Abingdon
Publication type:Article
Language:English
Year of first publication:2015
Publication year:2015
Release date:2017/03/27
Tag:Mental number line; Operand order effect; Operational momentum; SNARC; Situated cognition
Volume:27
Issue:4
Number of pages:7
First page:471
Last Page:477
Organizational units:Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Psychologie
Peer review:Referiert
Institution name at the time of the publication:Humanwissenschaftliche Fakultät / Institut für Psychologie
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