Spatial biases during mental arithmetic: evidence from eye movements on a blank screen

Abstract

While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the “mental number line”), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8–3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.

Exploring the numerical mind by eye-tracking: a special issue

“…Hartmann et al (2016, this issue) find that eye gaze position on a blank screen shifts upward and rightward when participants perform continuous additions (i.e., upward counting), supporting the idea that mental addition is conceptualized as rightward movement along the mental number line (McCrink et al, 2007;Pinhas & Fischer, 2008). By presenting addition and subtraction problems and varying the operand order, Yu et al (2016, this issue) find further support for this claim and clarify that the direction of the spatial-numerical association during mental arithmetic does not only depend on the operation (addition-right, subtraction-left), but also on the relative magnitude of operands and results (see also Hartmann, Mast, & Fischer, 2015;Loetscher, Bockisch, & Brugger, 2008). These results point to a surprisingly flexible mental number line in the context of arithmetic.…”

“…Interestingly, Hartmann et al find a different time course for horizontal than for vertical spatial-numerical associations, suggesting that they might be governed by different mechanisms (for further discussions see Fischer, 2012;Hartmann, Gashaj, Stahnke, & Mast, 2014;Hartmann et al, 2015;Winter, Matlock, Shaki, & Fischer, 2015). Myachykov et al (2016, this issue) interpret their multiphasic oculomotor resonance effect to suggest that the spatial mapping might consist of distinct processing stages.…”

Gamble on gaze: Eye movements reflect the numerical value of blackjack hands

“…Such methods leave open the possibility that the observed biases are artifacts of polarity correspondence (e.g., left-less/right-more, a type of stimulus-response compatibility; Proctor & Cho, 2006), rather than evidence of an MNL (see also Santens & Gevers, 2008). Moreover, in the case of mental arithmetic specifically, spatial biases may be driven by semantic associations between space and arithmetic operations (e.g., left-subtraction/right-addition; Hartmann, Mast, & Fischer, 2015), not by shifts of attention along the MNL toward the outcome of such operations (i.e., solution magnitude; cf. Marghetis et al, 2014).…”

“…On the basis of evidence for left-to-right orientation of number in Westerners, and that gaze patterns reflect this orientation (Hartmann et al, 2015;Loetscher, Bockisch, & Brugger, 2008;Loetscher, Bockisch, Nicholls, & Brugger, 2010), we expected that smaller-value and larger-value hands would elicit more leftward and rightward eye movements, respectively. Because vertical orientation of number has also been observed (e.g., Hartmann, Gashaj, Stahnke, & Mast, 2014;Loetscher et al, 2010;Winter & Matlock, 2013; for discussion of mixed findings, see Hartmann et al, 2014;Holmes & Lourenco, 2012), we assessed whether upward and downward eye movements also reflected the value of participants' hands.…”

“…We analyzed participants' spontaneous eye movements on a blank screen following the presentation of each card. Eye movements have been used to study diverse cognitive processes, both in the lab and in more natural settings (e.g., Hayhoe & Ballard, 2005;Loftus & Mackworth, 1978), and, importantly, have provided insight into mental associations between space and number (e.g., Bulf, de Hevia, & Cassia, 2015;Hartmann et al, 2015;Klein, Huber, Nuerk, & Moeller, 2014;Knops, Thirion, Hubbard, Michel, & Dehaene, 2009). …”