Mauro Pesenti

Solving subtraction and addition problems is accompanied by spontaneous leftward and rightward gaze shifts, respectively. These shifts have been related to attentional processes involved in mental arithmetic, but whether these processes induce overt attentional shifts mediated by the activation of the motor programs underlying lateral eye movements or covert shifts only is still unknown. Here, we used the abducted eye paradigm to selectively disrupt activation of the oculomotor system and prevent oculomotor preparation, which affects overt but not covert attentional shifts. Participants had to mentally solve addition and subtraction problems while fixating a screen positioned either in front of them or laterally to their left or right such that they were physically unable to programme and execute saccades further into their temporal field while they still could do so in their nasal field. In comparison to the frontal condition, rightward eye abduction impaired additions (with carrying), and leftward eye abduction impaired subtractions (with borrowing) showing that at least some arithmetic problems rely on processes dedicated to overt attentional shifts. We propose that when solving arithmetic problems requires procedures such as carrying and borrowing, oculomotor mechanisms operating on a mental space transiently built in working memory are recruited to represent one numerical magnitude in relation to another (e.g. the first operand and the result).

Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward, respectively. At the neurofunctional level, the activations elicited by the solving of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here, we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition problems. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure and suggest that their functional role is to access, from the first operand, the representation of the result.

Solving arithmetic problems has been shown to induce shifts of spatial attention, subtraction problems orienting attention to the left side, and addition problems to the right side of space. At the neurofunctional level, the activations elicited by the solving of arithmetical problems resemble those elicited by horizontal eye movements. Whether overt orientation of attention (i.e., eye movements) can be linked to the solving procedure is, however, still under debate. In the present study, we used optokinetic stimulation (OKS) to trigger automatic eye movements to orient participants’ overt attention to the right or to the left of their visual field while they were solving addition or subtraction problems. The results show that, in comparison to leftward OKS and a control condition, rightward OKS facilitates the solving of addition problems that necessitate a carrying procedure. Subtraction solving was unaffected by leftward or rightward OKS. These results converge with previous findings to show that attentional shifts are functionally related to mental arithmetic processing.

Numerical magnitude and specific grasping action processing have been shown to interfere with each other because some aspects of numerical meaning may be grounded in sensorimotor transformation mechanisms linked to finger grip control. However, how specific these interactions are to grasping actions is still unknown. The present study tested the specificity of the number–grip relationship by investigating how the observation of different closing–opening stimuli that might or not refer to prehension-releasing actions was able to influence a random number generation task. Participants had to randomly produce numbers after they observed action stimuli representing either closure or aperture of the fingers, the hand or the mouth, or a colour change used as a control condition. Random number generation was influenced by the prior presentation of finger grip actions, whereby observing a closing finger grip led participants to produce small rather than large numbers, whereas observing an opening finger grip led them to produce large rather than small numbers. Hand actions had reduced or no influence on number production; mouth action influence was restricted to opening, with an overproduction of large numbers. Finally, colour changes did not influence number generation. These results show that some characteristics of observed finger, hand and mouth grip actions automatically prime number magnitude, with the strongest effect for finger grasping. The findings are discussed in terms of the functional and neural mechanisms shared between hand actions and number processing, but also between hand and mouth actions. The present study provides converging evidence that part of number semantics is grounded in sensory-motor mechanisms.

Previous studies have shown that left neglect patients are impaired when they have to orient their attention leftward relative to a standard in numerical comparison tasks. This finding has been accounted for by the idea that numerical magnitudes are represented along a spatial continuum oriented from left to right with small magnitudes on the left and large magnitudes on the right. Similarly, it has been proposed that duration could be represented along a mental time line that shares the properties of the number continuum. By comparing directly duration and numerosity processing, this study investigates whether or not the performance of neglect patients supports the hypothesis of a mental time line. Twenty‐two right brain‐damaged patients (11 with and 11 without left neglect), as well as 11 age‐matched healthy controls, had to judge whether a single dot presented visually lasted shorter or longer than 500 ms and whether a sequence of flashed dots was smaller or larger than 5. Digit spans were also assessed to measure verbal working memory capacities. In duration comparison, no spatial‐duration bias was found in neglect patients. Moreover, a significant correlation between verbal working memory and duration performance was observed in right brain‐damaged patients, irrespective of the presence or absence of neglect. In numerical comparison, only neglect patients showed an enhanced distance effect for numerical magnitude smaller than the standard. These results do not support the hypothesis of the existence of a mental continuum oriented from left to right for duration. We discuss an alternative account to explain the duration impairment observed in right brain‐damaged patients.

Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants’ performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.

The processing of numbers has been shown to induce shifts of spatial attention in simple probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. Recently, the investigation of this spatial–numerical association has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems may induce attentional displacements (to the right and to the left, respectively) along a mental number line onto which the magnitude of the numbers would range from left to right, from small to large numbers. Here we investigated such attentional shifts using a target detection task primed by arithmetic problems in healthy participants. The constituents of the addition and subtraction problems (first operand; operator; second operand) were flashed sequentially in the centre of a screen, then followed by a target on the left or the right side of the screen, which the participants had to detect. This paradigm was employed with arithmetic facts (Experiment 1) and with more complex arithmetic problems (Experiment 2) in order to assess the effects of the operation, the magnitude of the operands, the magnitude of the results, and the presence or absence of a requirement for the participants to carry or borrow numbers. The results showed that arithmetic operations induce some spatial shifts of attention, possibly through a semantic link between the operation and space.

Recent findings suggest that number processing is intimately linked to space and attention orienting processes. For example, processing numbers induces shifts of spatial attention, with small numbers causing leftward shifts and large numbers causing rightward shifts, suggesting that number magnitude might be represented on a left-to-right mental number line. However, whether inducing spatial attention shifts would in turn influence number production, and whether such influence, if observed, would be restricted to the left-to-right orientation or would extend to an up-to-down orientation in space, remains a matter of debate. The present study assessed whether observing gaze movements, known to moderate spatial attention, was able to influence a random number generation task, and how different directions of the gaze moderated this influence. Participants were asked to randomly produce a number between 1 and 10 after they observed either a horizontal or a vertical eye gaze, or after they observed color changes as a control condition. The results revealed that number production was influenced by the prior presentation of specific gaze changes. Observing leftward or downward gaze led participants to produce more small than large numbers, whereas observing gaze oriented rightward and upward or observing color changes did not influence the magnitude of the numbers produced. These results show that the characteristics of the observed gaze changes primed number magnitude, but that this only held true for some movements, and these were not restricted to the left-to-right axis.