TY  - JOUR
A1  - Fischer, Martin H.
A1  - Shaki, Samuel
T1  - Number concepts: abstract and embodied
JF  - Philosophical transactions of the Royal Society of London : B, Biological sciences
N2  - Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind.
KW  - embodied cognition
KW  - mental arithmetic
KW  - mental number line
KW  - numerical cognition
KW  - SNARC effect
Y1  - 2018
U6  - https://doi.org/10.1098/rstb.2017.0125
SN  - 0962-8436
SN  - 1471-2970
VL  - 373
IS  - 1752
PB  - Royal Society
CY  - London
ER  - 
TY  - JOUR
A1  - Fischer, Martin H.
A1  - Shaki, Samuel
T1  - Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic
JF  - Frontiers in psychology
N2  - Even simple mental arithmetic is fraught with cognitive biases. For example, adding repeated numbers (so-called tie problems, e.g., 2 + 2) not only has a speed and accuracy advantage over adding different numbers (e.g., 1 + 3) but may also lead to under-representation of the result relative to a standard value (Charras et al., 2012, 2014). Does the tie advantage merely reflect easier encoding or retrieval compared to non-ties, or also a distorted result representation? To answer this question, 47 healthy adults performed two tasks, both of which indicated under-representation of tie results: In a result-to-position pointing task (Experiment 1) we measured the spatial mapping of numbers and found a left-bias for tie compared to non-tie problems. In a result-to-line-length production task (Experiment 2) we measured the underlying magnitude representation directly and obtained shorter lines for tie-compared to non-tie problems. These observations suggest that the processing benefit of tie problems comes at the cost of representational reduction of result meaning. This conclusion is discussed in the context of a recent model of arithmetic heuristics and biases.
KW  - AHAB
KW  - cognitive bias
KW  - mental arithmetic
KW  - numerical cognition
KW  - operational momentum
KW  - SNARC
KW  - tie problems
Y1  - 2018
U6  - https://doi.org/10.3389/fpsyg.2018.02453
SN  - 1664-1078
VL  - 9
PB  - Frontiers Research Foundation
CY  - Lausanne
ER  - 
TY  - JOUR
A1  - Fischer, Martin H.
A1  - Miklashevsky, Alex A.
A1  - Shaki, Samuel
T1  - Commentary : The Developmental Trajectory of the Operational Momentum Effect
JF  - Frontiers in Psychology
KW  - embodied cognition
KW  - operational momentum
KW  - SNARC effect
KW  - mental arithmetic
KW  - numerical cognition
Y1  - 2018
U6  - https://doi.org/10.3389/fpsyg.2018.02259
SN  - 1664-1078
N1  - A Commentary on The Developmental Trajectory of the Operational Momentum Effect by Pinheiro-Chagas, P., Didino, D., Haase, V. G., Wood, G., and Knops, A. (2018). Front. Psychol. 9:1062 doi: 10.3389/fpsyg.2018.01062
VL  - 9
PB  - Frontiers Research Foundation
CY  - Lausanne
ER  -