TY - JOUR
T1 - 1 + 2 is more than 2 + 1
T2 - Violations of commutativity and identity axioms in mental arithmetic
AU - Shaki, Samuel
AU - Sery, Noa
AU - Fischer, Martin H.
N1 - Publisher Copyright:
© 2014 Taylor and Francis.
PY - 2015/5/19
Y1 - 2015/5/19
N2 - 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.
AB - 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.
KW - Mental number line
KW - Operand order effect
KW - Operational momentum
KW - SNARC
KW - Situated cognition
UR - http://www.scopus.com/inward/record.url?scp=84928938464&partnerID=8YFLogxK
U2 - 10.1080/20445911.2014.973414
DO - 10.1080/20445911.2014.973414
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AN - SCOPUS:84928938464
SN - 2044-5911
VL - 27
SP - 471
EP - 477
JO - Journal of Cognitive Psychology
JF - Journal of Cognitive Psychology
IS - 4
ER -