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  - Wasner, Mirjam
A1  - Moeller, Korbinian
A1  - Fischer, Martin H.
A1  - Nuerk, Hans-Christoph
T1  - Aspects of situated cognition in embodied numerosity: the case of finger counting
JF  - Cognitive processing : international quarterly of cognitive science
N2  - Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations.
KW  - Finger counting
KW  - Situated cognition
KW  - Number processing
KW  - Finger-digit mapping
Y1  - 2014
U6  - https://doi.org/10.1007/s10339-014-0599-z
SN  - 1612-4782
SN  - 1612-4790
VL  - 15
IS  - 3
SP  - 317
EP  - 328
PB  - Springer
CY  - Heidelberg
ER  -