TY  - JOUR
A1  - Shaki, Samuel
A1  - Sery, Noa
A1  - Fischer, Martin H.
T1  - 1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic
JF  - Journal of cognitive psychology
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.
KW  - Operand order effect
KW  - Situated cognition
KW  - Mental number line
KW  - SNARC
KW  - Operational momentum
Y1  - 2015
U6  - https://doi.org/10.1080/20445911.2014.973414
SN  - 2044-5911
SN  - 2044-592X
VL  - 27
IS  - 4
SP  - 471
EP  - 477
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Pinhas, Michal
A1  - Shaki, Samuel
A1  - Fischer, Martin H.
T1  - Addition goes where the big numbers are: evidence for a reversed operational momentum effect
JF  - Psychonomic bulletin & review : a journal of the Psychonomic Society
N2  - Number processing evokes spatial biases, both when dealing with single digits and in more complex mental calculations. Here we investigated whether these two biases have a common origin, by examining their flexibility. Participants pointed to the locations of arithmetic results on a visually presented line with an inverted, right-to-left number arrangement. We found directionally opposite spatial biases for mental arithmetic and for a parity task administered both before and after the arithmetic task. We discuss implications of this dissociation in our results for the task-dependent cognitive representation of numbers.
KW  - Mental arithmetic
KW  - Mental number line
KW  - Operational momentum
KW  - Pointing
KW  - SNARC
Y1  - 2015
U6  - https://doi.org/10.3758/s13423-014-0786-z
SN  - 1069-9384
SN  - 1531-5320
VL  - 22
IS  - 4
SP  - 993
EP  - 1000
PB  - Springer
CY  - New York
ER  -