Abstract
Operational momentum was originally defined as a bias toward underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of “recycled” mechanisms of spatial attention, including “representational momentum” – a tendency to overestimate future position of a moving object, which compensates for the moving object’s shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants’ task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply “moving attention along the mental number-line” as a direct counterpart of attention directed at a moving object.
Highlights
The term “operational momentum” refers to two biases found in mental arithmetic
The pattern of results as a whole seems to conflict with the tested model, in which operational momentum is the exact counterpart of representational momentum or even utilizes the same specific attentional mechanisms
We have shown that direction and speed of motion are powerful factors modifying internal attention directed toward numbers, it does not appear that the perception of real movement directly impacts (“accelerates” or “slows down”) the imaginary movement of attention along the mental number line
Summary
The term “operational momentum” refers to two biases (probably closely linked) found in mental arithmetic. People show a tendency toward associating subtraction with the left side of their attentional space and addition with the right. Perceived Motion and Mental Arithmetic side (“directional operational momentum”) These two biases were shown to coincide (Knops et al, 2009b) and have been typically regarded as two manifestations of the same process: moving internal attention along the “mental number line” (a spatially organized mental representation of number). Operational Momentum as a Spatial-Directional Bias in Mental Arithmetic In one of his seminal works, Stanislas Dehaene (2005) suggested that processing numerical magnitudes, such as in simple arithmetic, may employ “recycled” neural mechanisms of spatial attention operating on the mental representations of numbers, which is probably intrinsically spatially organized in the form of a “mental number line.”. It is worth noting that careful analyses by Cipora et al (2018) and Toomarian and Hubbard (2018) showed several other factors that may affect spatial-numerical associations
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