A functional role for oculomotor preparation in mental arithmetic evidenced by the abducted eye paradigm

Spatial coding of arithmetic operations in early learning: an eye tracking study in first-grade elementary school children

A growing body of evidence indicates that mental calculation in adults is accompanied by horizontal attention shifts along a mental continuum representing the range of plausible answers. The fast deployment of spatial attention suggests a predictive role in guiding the search for the answer. The link between arithmetic and spatial functions is theoretically justified by the need to alleviate the cognitive load of mental calculation, but the question of how this link establishes during development gives rise to opposing views emphasizing either biological or cultural factors. The role of education, in particular, remains debated in the absence of data covering the period when children learn arithmetic. In this study, we measured gaze movements, as a proxy for attentional shifts, while first-grade elementary school children solved single-digit additions and subtractions. The investigation was scheduled only a few weeks after the formal teaching of symbolic subtraction to assess the role of spatial attention in early learning. Gaze patterns revealed horizontal- but not vertical- attentional shifts, with addition shifting the gaze more rightward than subtraction. The shift was observed as soon as the first operand and the operator were presented, corroborating the view that attention is used to predictively identify the portion of the numerical continuum where the answer is likely to be located, as adult studies suggested. The finding of a similar gaze pattern in adults and six-year-old children who have just learned how to subtract single digits challenges the idea that arithmetic problem solving requires intensive practice to be linked to spatial attention.

Internal coupling: Eye behavior coupled to visual imagery

Our eyes do not only respond to visual perception but also to internal cognition involving visual imagery, which can be referred to as internal coupling. This review synthesizes evidence on internal coupling across diverse domains including episodic memory and simulation, visuospatial memory, numerical cognition, object movement, body movement, and brightness imagery. In each domain, eye movements consistently reflect distinct aspects of mental imagery typically akin to those seen in corresponding visual experiences. Several findings further suggest that internal coupling may not only coincide with but also supports internal cognition as evidenced by improved cognitive performance. Available theoretical accounts suggest that internal coupling may serve at least two functional roles in visual imagery: facilitating memory reconstruction and indicating shifts in internal attention. Moreover, recent insights into the neurobiology of internal coupling highlight substantially shared neural pathways in externally and internally directed cognition. The review concludes by identifying open questions and promising avenues for future research such as exploring moderating roles of context and individual differences in internal coupling.

Spatial attention in mental arithmetic: A literature review and meta-analysis

We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.