Operational Momentum Affects Eye Fixation Behaviour

The operational momentum effect (OM) indicates an association of mental addition with a rightward spatial bias, whereas subtraction is associated with a leftward bias. To evaluate the assumed attentional origin of the OM effect, we evaluated not only participants’ relative estimation error in a task requiring them to locate addition and subtraction results on a given number line but also their eye-fixation behaviour. Furthermore, to investigate the situatedness of spatial–numerical associations, the orientation of the number line (left-to-right vs. right-to left) was manipulated. OM biases in participants’ explicit number line estimations and more implicit eye-fixation behaviour are integrated into a two-process hypothesis of the OM effect suggesting a first rough spatial anticipation followed by an evaluation/correction process. This account not only is capable of accounting for the results observed for participants’ relative estimation error but is also corroborated by the eye-fixation results. Importantly, the fact that all effects were found independent of the orientation of the number line indicates that spatial–numerical associations such as the OM effect may not be hard-wired associations of spatial and numerical representations but rather reflect influences of situatedness on numerical cognition.

Eye fixation behaviour in the number bisection task: evidence for temporal specificity

Together with magnitude representations, knowledge about multiplicativity and parity contributes to numerical problem solving. In the present study, we used eye tracking to document how and when multiplicativity and parity are recruited in the number bisection task. Fourteen healthy adults evaluated whether the central number of a triplet (e.g., 21_24_27) corresponds to the arithmetic integer mean of the interval defined by the two outer numbers. We observed multiplicativity to specifically affect gaze duration on numbers, indicating that the information of multiplicative relatedness is activated at early processing stages. In contrast, parity only affected total reading time, suggesting involvement in later processing stages. We conclude that different representational features of numbers are available and integrated at different processing stages within the same task and outline a processing model for these temporal dynamics of numerical cognition.

Factors related to the magnitude of T2* MR signal changes during functional imaging

Our aim was to determine whether age, sex, the degree of weakness, anticonvulsants, the histology of the underlying lesion(s), the presence of oedema or the distance of the lesion from the motor region have an impact on the blood oxygenation level-dependent (BOLD) signal strength and therefore on the validity of functional MRI (fMRI). We studied 98 patients with masses near the central region imaged for surgical planning at 1.5 tesla, employing a BOLD sequence during a motor task. We calculated percentage signal change in the primary motor cortex between rest and activation and carried out multiple linear regression to examine the impact of the above factors on signal strength. Using a stepwise analysis strategy, the distance of the lesion from the motor region had the strongest influence (r=0.653, P<0.001). The factor with largest uncorrelated additional impact on signal change was the presence of oedema. Both predictors together formed a highly significant multiple r=0.739 ( P<0.001). No other predictive factor was identified (all P>0.20). Disturbances of cerebral blood flow and metabolism induced by the tumour were presumed to be the causes of a decrease in signal in the adjacent cortex.

Decade breaks in the mental number line? Putting the tens and units back in different bins

Most models of number recognition agree that among other number representations there is a central semantic magnitude representation which may be conceptualized as a logarithmically compressed mental number line. Whether or not this number line is decomposed into different representations for tens and units is, however, controversial. We investigated this issue in German participants in a magnitude comparison (selection) task in which the larger of two visually presented Arabic two-digit numbers had to be selected. Most importantly, we varied unit-decade-compatibility: a number pair was defined as compatible if the decade magnitude comparison and the unit magnitude comparison of the two numbers would lead to the same response (e.g. 52 and 67) and as incompatible if this was not the case (e.g. 47 and 62). While controlling for overall numerical distance, size and other variables, we consistently found compatibility effects. A control experiment showed that this compatibility effect was not due to perceptual presentation characteristics. We conclude that the idea of one single number line representation that does not additionally assume different magnitude representations for tens and units is not sufficient to account for the data. Finally, we discuss why decade effects were not found in other experimental settings.