Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

Fischer, Martin H.; Shaki, Samuel

doi:10.1080/17470218.2014.927515

Cited by 213 publications

(191 citation statements)

References 141 publications

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“…So far, we focused on the most frequently investigated signatures of number-space interactions. Yet, there are other phenomena that express spatial-numerical associations (see for instance Brugger (2011) or Fischer andShaki (2014) for overviews). In the absence of empirical testing it is hard to tell whether or not serial position in WM is the determining factor in these cases as well.…”

Section: Discussionmentioning

confidence: 99%

The temporary nature of number—space interactions.

Fias¹,

Dijck²

2016

Canadian Journal of Experimental Psychology / Revue canadienne

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It is commonly accepted that the mental representation and processing of number and of space are tightly linked. This is evident from studies showing relations between math ability and visuospatial skill. Also, math instruction and education rely strongly on visuospatial tools and strategies. The dominant explanation for these number-space interactions is that the mental representation of numbers takes the form of a mental number line with numbers positioned in ascending order according to our reading habits. A long-standing debate is whether the link between numbers and space can be considered as evidence for a spatial number representation in long-term semantic memory, or whether this spatial frame is a temporary representation that emerges in working memory (WM) during task execution. Here we give an overview of our recent work that indicates that basic number processing tasks do not operate on a long-term spatial memory representation, but on a representation constructed in serial order WM, where the elements are spatially coded as a function of their ordinal position in the memorized sequence.Implications for a new theoretical framework linking serial order WM and basic number processing are discussed.

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Section: Discussionmentioning

confidence: 99%

The temporary nature of number—space interactions.

Fias¹,

Dijck²

2016

Canadian Journal of Experimental Psychology / Revue canadienne

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“…Feb. 2016). SNARC-like effects have been investigated in a wide range of numerical tasks (Fischer & Shaki, 2014), and can be observed across different effectors, including hands and feet (Schwarz & Müller, 2006) and also the eyes (e.g., Schwarz & Keus, 2004). For example, eye movements to the left side are faster after processing a small number, whereas eye movements to the right side are faster after processing a large number, when compared to the opposite pairings.…”

Section: Development and Impairments Of Number Conceptsmentioning

confidence: 99%

“…However, spatial-numerical associations can also be found for more complex numerical tasks, such as mental arithmetic (Fischer & Shaki, 2014). Therefore, it is not unexpected to see systematic eye movement patterns during such tasks.…”

Section: Development and Impairments Of Number Conceptsmentioning

confidence: 99%

“…In this field of study the currently dominant view holds that number concepts are represented on a spatially oriented ''mental number line'', with small numbers represented to the left of larger numbers (at least in Western cultures; Dehaene, Bossini, & Giraux, 1993). The ''mental number line'' gives rise to spatial-numerical associations, which can be widely observed, both in simple number classification tasks and also in more complex tasks such as mental arithmetic (Fischer & Shaki, 2014). Eye movements provide online access to the focus of spatial attention and can therefore reveal the order and duration of concept activations, information that is not available when merely collecting response times or error rates at task completion.…”

Section: Introductionmentioning

confidence: 99%

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

Hartmann

Fischer

2016

Psychological Research

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“…Mentally summing the values of successive cards, and thereby computing the total value of one's hand, is a prerequisite for making this decision wisely. Research suggests that such mental arithmetic may rely on an internal spatial representation of numerical magnitude (e.g., Knops, Viarouge, & Dehaene, 2009;Marghetis, Nuñez, & Bergen, 2014;McCrink, Dehaene, & DehaeneLambertz, 2007; for a review, see Fischer & Shaki, 2014). For example, when pointing to an arithmetic solution on a visually presented number line, participants are biased leftward on subtraction problems and rightward on addition problems (Pinhas & Fischer, 2008).…”

mentioning

confidence: 99%

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

2016

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We used a novel task-a blackjack game that naturally involves mental summation of numerical values-to investigate the role of attention in the mental number line (MNL) and to provide insight into the ecological validity of this representational format. By analyzing the spatial position of participants' spontaneous, task-irrelevant eye movements, we avoided some of the limitations of previous research on the MNL, in which the findings could be attributed to taskspecific factors such as the use of overt spatial cues. In two experiments, we found that eye movements along the horizontal axis reflected the overall numerical value of participants' hands, with smaller-value hands eliciting fixations toward the left of the screen and larger-value hands eliciting fixations toward the right. This pattern held even when controlling for the number of cards in the hand and the value of the card most recently dealt-suggesting that the effects were driven by mental summation of values, not merely by the processing of serial order or individual numbers. Vertical eye movements, in contrast, reflected hand value less reliably. In showing that spontaneous eye movements along the horizontal axis track the magnitude of internally computed sums in an ecologically relevant task, our findings provide evidence for a dynamic MNL that supports magnitude-driven shifts of attention and that may be recruited during everyday forms of numerical reasoning.

show abstract

Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

Cited by 213 publications

References 141 publications

The temporary nature of number—space interactions.

The temporary nature of number—space interactions.

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

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

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