Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition?

Effects of attentional shifts along the vertical axis on number processing: An eye-tracking study with optokinetic stimulation

Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, upward attentional displacement decreased the Magnitude effect (slower responses for large numbers) and increased the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a complex interaction between parity, magnitude, and OKS, indicating that downward attentional displacement slowed down responses for large odd numbers. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of small numbers as compared to large ones; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance, and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.

Early is left and up: Saccadic responses reveal horizontal and vertical spatial associations of serial order in working memory

Maintaining serial order in working memory is crucial for cognition. Recent theories propose that serial information is achieved by positional coding of items on a spatial frame of reference. In line with this, an early-left and late-right spatial-positional association of response code (SPoARC) effect has been established. Various theoretical accounts have been put forward to explain the SPoARC effect (the mental whiteboard hypothesis, conceptual metaphor theory, polarity correspondence, or the indirect spatial-numerical association effect). Crucially, while all these accounts predict a left-to-right orientation of the SPoARC effect, they make different predictions regarding the direction of a possible vertical SPoARC effect. In this study, we therefore investigated SPoARC effects along the horizontal and vertical spatial dimension by means of saccadic responses. We replicated the left-to-right horizontal SPoARC effect and established for the first time an up-to-down vertical SPoARC effect. The direction of the vertical SPoARC effect was in contrast to that predicted by metaphor theory, polarity correspondence, or by the indirect spatial-numerical association effect. Rather, our results support the mental whiteboard-hypothesis, according to which positions can be flexibly coded on an internal space depending on the task demands. We also found that the strengths of the horizontal and vertical SPoARC effects were correlated, showing that some people are more prone than others to use spatial references for position coding. Our results therefore suggest that context templates used for position marking are not necessarily spatial in nature but depend on individual strategy preferences.

Wide Bezel Televisions Decrease Immersive Experiences

This study explored how telepresence could be affected by stimuli from reality that distracts people while they are watching television. The sample comprised of 36 undergraduate and graduate students from a university in South Korea (age range: 18–38 years, M = 22.61, and SD = 4.12). A between-subjects experimental design was employed with two types of viewing equipment (a television screen vs. a television screen with side screens that act as stimuli from reality) and two bezel widths (2 cm vs. 10 cm) to examine how each condition influenced the viewers’ perceived telepresence. The results revealed that participants’ perception of telepresence was not affected by the type of viewing equipment. However, the level of telepresence was affected by the bezel width: the thinner the bezel, the more telepresence felt by the viewers. These findings provide important insights that can guide the future designs of screen bezels for televisions and other devices in order to more effectively create immersive virtual worlds. Future studies are needed to examine the relationship between central vision and telepresence.

Response orientation modulates pitch-space relationships: the ROMPR effect

Congruency between auditory and visuospatial stimuli has been previously shown to affect responses to multisensory stimulus pairs, and congruency between stimuli and response devices may play a role in response speed and accuracy. Across two experiments, we tested whether the accuracy and speed of pitch judgments were affected by a congruent or incongruent paired visual stimulus, and whether the relationship was modulated by response orientation. In Experiment 1, participants using a vertically (transversely) oriented keyboard demonstrated a large crossmodal vertical effect, but a minimal crossmodal horizontal effect. In contrast, Experiment 2 used a horizontally oriented keyboard, while also examining whether musical training impacts pitch judgments. As in the first experiment, we found an effect of response mapping on pitch judgments; these results suggest that vertical visual stimuli are processed automatically, while the effects of horizontal visual stimuli are decisional and require a compatible response orientation. Based on these findings, we propose an effect we call the ROMPR effect: response orientation modulates pitch-space relationships. Unexpectedly, non-musicians demonstrated significant ROMPR effects while trained musicians did not. We suggest that non-musicians are more likely to use visual information when making spatial location judgments of pitch: unlike musicians, they have not been trained to rely exclusively on auditory information during pitch processing. We also discuss alternative explanations of the data: namely, that there is a need to disambiguate audiovisual congruency from visual-response congruency with modulations of experimental design.

Emotional SNARC: emotional faces affect the impact of number magnitude on gaze patterns

The Spatial-Numerical Association of Response Codes (SNARC) effect is characterised by a spatial cognitive representation of low numbers to the left side of space and high numbers to the right side of space. This effect has been found using a diversity of stimuli and experimental paradigms. However, the influence of emotional stimuli on this effect remains unclear. In this study, the SNARC effect is analysed in relation to pairs of emotional facial stimuli (happy-neutral, sad-neutral and happy-sad pairs). Gaze patterns of 151 participants were analysed when exposed to a free-viewing eye-tracking paradigm consisting of pairs of emotional faces preceded by small and large numbers. Replicating previous results, a standard SNARC effect was found independently of the emotional expressions of the faces (i.e., there was a significant linear trend of number magnitude in the frequency of first fixations of the gaze to the left side space). However, specific slope analyses revealed that the SNARC effect was influenced by the spatial position of each emotion presented in the emotional pairs. Specifically, the effect disappeared in happy-neutral trials, when the happy faces were allocated in the right position and also in happy-sad trials when two emotional stimuli were simultaneously displayed. The study revealed that the SNARC effect is sensitive to the spatial position of emotional stimuli which further adds to other known limits of the phenomenon. The limitations of the study and its implications in the area of cognition and emotion are also discussed.

Further to the right: Viewing distance modulates attentional asymmetries ('pseudoneglect') during visual exploration

Previous studies showed that the small leftward bias found in healthy humans' spatial judgments of lines ("pseudoneglect") shifts to the right with increasing distance between stimuli and observer. In this study, we investigated whether such a modulation of attentional asymmetry can also be observed in free visual exploration. Participants freely explored photographs of naturalistic scenes for 7 s in near (60 cm) and far (140 cm) space. After an initial leftward bias, followed by a compensatory rightward bias, gaze positions were significantly more leftward in near compared to far space (around 4 s from scene onset). Our results show that the modulation of attentional asymmetries by viewing distance previously reported for spatial judgments generalizes to free visual exploration, and we revealed the temporal dynamics of these asymmetries by fine-grained eye movement analysis. In contrast, an effect of viewing distance was reduced or absent when eye movements are under strong top-down control, as in systematic serial visual search (Sensitive Negelct Test). Finally, there was no effect of viewing distance in the landmark task (as also reported in a minority of other studies), suggesting that this effect may depend on specific, yet unidentified task characteristics.

Spontaneous Cognition and Epistemic Agency in the Cognitive Niche

According to Thomas Metzinger, many human cognitive processes in the waking state are spontaneous and are deprived of the experience of epistemic agency. He considers mind wandering as a paradigm example of our recurring loss of epistemic agency. I will enrich this view by extending the scope of the concept of epistemic agency to include cases of depressive rumination and creative cognition, which are additional types of spontaneous cognition. Like mind wandering, they are characterized by unique phenomenal and functional properties that give rise to varying degrees of epistemic agency. The main claim of this paper will be that the experience of being an epistemic agent within a certain time frame is a relational phenomenon that emerges from the organism’s capacity to interact with its cognitive niche. To explore this relation, I develop a new framework that integrates phenomenological considerations on epistemic agency with a functional account of the reciprocal coupling of the embodied organism with its cognitive niche. This account rests upon dynamical accounts of strong embodied and embedded cognition and recent work on cognitive niche construction. Importantly, epistemic agency and organism-niche coupling are gradual phenomena ranging from weak to strong realizations. The emerging framework will be employed to analyze mind wandering, depressive rumination, and creative cognition as well as their commonalities and differences. Mind wandering and depressive rumination are cases of weak epistemic agency and organism-niche coupling. However, there are also important phenomenological, functional, and neuronal differences. In contrast, creative cognition is a case of strong epistemic agency and organism-niche coupling. By providing a phenomenological and functional analysis of these distinct types of spontaneous cognition, we can gain a better understanding of the importance of organism-niche interaction for the realization of epistemic agency.

Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection

Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants' verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

The visual number world: A dynamic approach to study the mathematical mind

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the "visual number world"-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.

Ocular drift along the mental number line

We examined the spontaneous association between numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to number names. In Experiment 2, they made horizontal target-direct saccades following auditory number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after number presentation. Experiment 2 also measured visual-probe-directed saccades following number presentation. Reliable ocular drift congruent with a horizontal mental number line emerged during and after number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism.

Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

Introduction

Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number line estimation tasks. The current study extends these findings to a larger group of children with mathematical learning disabilities (MLD).

Method

A group of 9–11-year-old children with MLD (N = 14) was compared to a control group of children without math difficulties (N = 14). Number line estimation was measured using a 0–100 and a 0–1000 number-to-position task. A Tobii T60 eye tracker was used to measure the children’s eye movements during task performance.

Results

The behavioral data showed that the children with MLD had higher error scores on both number lines than the children in the control group. The eye tracking data showed that the groups also differed in their estimation strategies. The children with MLD showed less adaptation of their estimation strategies to the number to be estimated.

Conclusion

This study shows that children with MLD attend to different features of the number line than children without math difficulties. Children with math difficulties are less capable of adapting their estimation strategies to the numbers to be estimated and of effectively using reference points on the number line.

Electronic supplementary material

The online version of this article (doi:10.1007/s00426-015-0736-z) contains supplementary material, which is available to authorized users.