Nicolas Masson

Attentional bias induced by solving simple and complex addition and subtraction problems

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.

Selective Interference of Finger Movements on Basic Addition and Subtraction Problem Solving

Fingers offer a practical tool to represent and manipulate numbers during the acquisition of arithmetic knowledge, usually with a greater involvement in addition and subtraction than in multiplication. In adults, brain-imaging studies show that mental arithmetic increases activity in areas known for their contribution to finger movements. It is unclear, however, if this truly reflects functional interactions between the processes and/or representations controlling finger movements and those involved in mental arithmetic, or a mere anatomical proximity. In this study we assessed whether finger movements interfere with basic arithmetic problem solving, and whether this interference is specific for the operations that benefit the most from finger-based calculation strategies in childhood. In Experiment 1, we asked participants to solve addition, subtraction, and multiplication problems either with their hands at rest or while moving their right-hand fingers sequentially. The results showed that finger movements induced a selective time cost in solving addition and subtraction but not multiplication problems. In Experiment 2, we asked participants to solve the same problems while performing a sequence of foot movements. The results showed that foot movements produced a nonspecific interference with all three operations. Taken together, these findings demonstrate the specific role of finger-related processes in solving addition and subtraction problems, suggesting that finger movements and mental arithmetic are functionally related.

Spatial bias in symbolic and non-symbolic numerical comparison in neglect

When asked to bisect mentally numerical intervals, neglect patients show a displacement of the numerical midpoint similar to the one observed in physical line bisection. This spatial-numerical bias has been taken as evidence of the spatial nature of numerical magnitude representations. However, to date, neuropsychological studies in neglect patients have only used symbolic numerical material. Here, we compare the results of patients with right-hemisphere damage with and without unilateral left neglect and age-matched healthy control participants in two numerical comparison tasks using symbolic and non-symbolic materials, in order to determine whether the representation of non-symbolic numerosities was altered or not by the presence of neglect. When asked to judge if an Arabic digit or a sequence of flashed dots was smaller or larger than a reference value (i.e., 5), the responses of neglect patients to smaller magnitudes (i.e., 4) were impaired. Moreover, only neglect patients presented an asymmetrical distance effect (i.e., an enhanced effect only for stimuli of smaller numerical magnitude than the reference). These results provide the first direct evidence of a spatial bias in non-symbolic numerosity in neglect patients, and support the existence of common processing mechanisms and/or a representational system for symbolic and non-symbolic inputs.

Interference of lateralized distractors on arithmetic problem solving : a functional role for attention shifts in mental calculation

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.

Impact of optokinetic stimulation on mental arithmetic.

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.

Time course of overt attentional shifts in mental arithmetic: Evidence from gaze metrics

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.

Shifts of spatial attention underlie numerical comparison and mental arithmetic: Evidence from a patient with right unilateral neglect.

Objectives: Recent findings suggest that mental arithmetic involves shifting attention on a mental continuum in which numbers would be ordered from left to right, from small to large numbers, with addition and subtraction causing rightward or leftward shifts, respectively. Neuropsychological data showing that brain-damaged patients with left neglect experience difficulties in solving subtraction but not addition problems support this hypothesis. However, the reverse dissociation is needed to establish the causal role of spatial attention in mental arithmetic. Method: R.H., a 65-year-old left-brain-damaged patient exhibiting right unilateral visuospatial and representational neglect, was tested with various numerical tasks including numerical comparison, arithmetic problem-solving, and numerical interval bisection. Results: In numerical comparison, R.H. showed a selective response latency increase when judging numbers larger than the references whereas his performance was normal for numbers smaller than the references. In the arithmetic task, R.H. was impaired in solving addition but not subtraction problems. In contrast, performance in number bisection shows a deviation toward larger numbers. Conclusion: These results establish a double dissociation between subtraction and addition solving in patients with left versus right neglect and demonstrate clear evidence that attentional mechanisms are crucial for mental arithmetic. We suggest that attention shifts are involved whenever a number is represented relative to another on a mental continuum, be it during numerical comparison or arithmetic problem-solving. R.H.’s performance in numerical interval bisection indicates that this task involves processes that are distinct from those involved in number comparison and mental arithmetic.