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Attention Drives Spatial Bias in Approximate Calculation: Evidence from ERP and fMRI
Pan Yun, Jia Liangzhi, Yang Huanyu, Zhu Jun, Wang Chengtao, Yu Fangwen, Zhang Di
Journal of Psychological Science ›› 2026, Vol. 49 ›› Issue (4) : 848-859.
PDF(3308 KB)
PDF(3308 KB)
Attention Drives Spatial Bias in Approximate Calculation: Evidence from ERP and fMRI
Approximate calculation—the ability to produce rapid, coarse numerical estimates—is a fundamental component of mathematical reasoning and reliably predicts later achievement in the field. The operational momentum effect (OME) denotes a systematic bias in approximate arithmetic whereby individuals tend to overestimate outcomes of addition and underestimate the outcomes of subtraction. The mechanism that gives rise to this effect remains unresolved. The heuristic account proposes that OME reflects a cognitive shortcut: when adding, people are biased toward amounts larger than the starting value, whereas when subtracting, they are biased toward amounts smaller than the starting value. In contrast, the attentional shift account attributes OME to a spatial displacement of attention along the mental number line (MNL): addition shifts attention to the right, while subtraction shifts it to the left. This results in overestimation for addition and underestimation for subtraction.
Previous studies have examined the behavioral origins of the OME, providing substantial support for competing accounts. However, the neural basis of the effect remains poorly understood. Complementary neuroimaging methods can address this gap: event-related potentials (ERPs) provide millisecond temporal resolution for tracking attentional shifts during approximate calculation, whereas functional magnetic resonance imaging (fMRI) offers precise spatial localization. Representational similarity analysis (RSA) furthermore enables comparison of ERP and fMRI by projecting their activity patterns into a common representational space. In the present study, we combined ERP, fMRI, and RSA to investigate behavioral performance and neural activity during addition and subtraction across directional conditions (less, neutral, more). For this purpose, sixty healthy young adults performed an arithmetic verification task, judging whether each presented addition or subtraction outcome (categorized as smaller, equal, or larger than the correct result) was correct. ERP and fMRI data were then mapped into a shared representational space, and the similarity of the neural representations at successive time points was computed. This multimodal approach aimed to elucidate the neural mechanisms underlying the OME and to determine whether the effect reflects an attentional shift along the MNL.
The results indicated that spatial attention engages approximate calculation, with larger outcomes in addition and smaller outcomes in subtraction attracting more spatial attention. Specifically, the behavioral results demonstrated that participants exhibited a tendency to accept neutral or larger outcomes in addition and neutral or smaller outcomes in subtraction, thereby indicating the presence of the OME. Furthermore, the ERP results demonstrated a significant interaction between operation and direction on the P3b component (250~350 ms), which is associated with attentional allocation. Specifically, larger outcomes in addition and smaller outcomes in subtraction elicited a larger P3b wave. The fMRI results demonstrated that larger outcomes in addition and smaller outcomes in subtraction significantly activated the right intraparietal sulcus (IPS), superior parietal lobule (SPL), and precuneus, which is related to spatial attentional shift. Furthermore, the results of the functional connectivity study indicated that the right precuneus exhibited stronger functional connectivity with the middle temporal gyrus, inferior occipital gyrus, and fusiform gyrus in the larger outcomes of addition, in comparison to the smaller outcomes. This finding suggests that the former outcomes may be allocated more attentional resources. Furthermore, the RSA results indicated that the neural representation of the OME remained consistent across various data modalities, thereby underscoring the congruence between ERP and fMRI data. This observation also reflected a transition from early visual processing to more complex cognitive processing.
Taken together, these findings indicate that the OME is a result of a spatial shift of attention along a mental number line, substantiating the attentional shift account. From a neuroscientific perspective, these results elucidate the formation mechanisms of the approximate calculation bias phenomenon and unveil the intrinsic connection between numerical cognition and spatial attention. Such insights provide a scientific foundation for efficient mathematical learning and cognitive interventions.
approximate calculation / operational momentum / attentional shift account / P3b / superior parietal lobule
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