Eye movements as an indicator of the strategies recruited to solve arithmetic problems: the case of subtraction by additions

Theoretical Background: Mental arithmetic is a challenging exercise. To resolve this difficulty, it has been assumed that the cognitive system relies both on memory retrieval and procedural strategies. Hence, the answer of small problems (e.g., 3+2) can be retrieved directly from memory whereas large problems (e.g., 62-17) typically require calculation procedures. A large body of evidence suggest that these procedural strategies involve attention shifts reminiscent of increments (or decrements) along a mental continuum. Attention is shifted rightward/upward or leftward/downward when participants solve additions and subtractions, respectively. While attentional shifts in both the vertical and horizontal axes co-exist, it is unknown whether the two axes are rooted into identical cognitive mechanisms and mental representations. Methods: To investigate the role of horizontal and vertical attentional shifts in mental arithmetic, we monitored horizontal and vertical eye movements, as a proxy for attentional shifts, using an eye-tracker. Adult participants, while looking at a blank screen, had to solve orally subtractions presented auditorily that are either typically solved directly (e.g., 78 - 32 = ?) or solved with a strategy consisting in transforming a subtraction into an addition (e.g., 71 - 68 = ? à 68 + ? = 71). Results: Gaze patterns reveal a dissociation between horizontal and vertical shifts. Horizontal shifts reflected the strategy that was employed to solve the problem as “subtraction by addition” elicited horizontal shifts more to the right than “direct subtractions”. Vertical eye movements were driven by the absolute magnitude of the answers as small answers were associated to more downward shifts. Discussion: Altogether, this suggests attentional shifts are part of the solving procedure but that shifts along horizontal and vertical axes reflect distinct cognitive mechanisms. The study provides direct evidence that spatial attention shifts are functionally related to the strategies used during mental arithmetic and that adult calculators preferentially use the horizontal dimension for implementing such strategies. The vertical axis is merely associated to the magnitude of the answer, irrespective of how it is accessed.

Affiliations

UCLouvainSSH/IPSY - Psychological Sciences Research Institute

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Masson, N., Geers, L., Christine Schiltz, Andres, M., & Pesenti, M. (2024). Eye movements as an indicator of the strategies recruited to solve arithmetic problems: the case of subtraction by additions. Relations between space, language, and numbers, Tubingen,Germany. https://hdl.handle.net/2078.5/236947