Numerically induced attentional biases in horizontal, vertical, and two-dimensional shapes

Previous studies have suggested that there is a left-to-right mental number line, which is based on individuals responding faster when a smaller magnitude is presented on the left visual field and a larger magnitude is presented on the right visual field. This study examined whether the Spatial-Numerical Associations could influence individuals’ responses in an inequality judgment task. Specifically, this study tested the differences in reaction time between judging inequalities with a greater than sign and inequalities with a less than sign and investigated individuals’ subjective liking and perceived fluency in judging these inequalities. Three types of stimuli were used in this study: Arabic number inequalities (numerical and symbolic magnitudes), dot array inequalities (numerical and non-symbolic magnitudes), and square inequalities (non-numerical magnitudes). Results showed that participants reacted quicker to inequalities with a greater than sign than a less than sign when responding to true inequalities in all of the three tasks and reported more subjective liking and perceived fluency in judging inequalities with a greater than sign in symbolic task. This study has implications for studies that are interested in Spatial-Numerical Associations and mathematical education.

Spatial representations of number, such as a left-to-right oriented mental number line, are well documented in Western culture. Yet, the functional significance of such a representation remains unclear. To test the prominent hypothesis that a mental number line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasks: a non-symbolic magnitude comparison task, and a symbolic “Where was the number?” (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional mental number line across numerical format. Although there were no significant correlations between children’s SNAs on the WTN task and math ability, children’s SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented mental number line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the mental number line to math performance. We conclude with a discussion of the different properties that characterize a mental number line and how these different properties may relate to mathematical ability.

The mental number line, with its left-to-right orientation of increasing numerical values, is often regarded as evidence for a unique connection between space and number. Yet left-to-right orientation has been shown to extend to other dimensions, consistent with a general magnitude system wherein different magnitudes share neural and conceptual resources. Such observations raise a fundamental, yet relatively unexplored, question about spatial-numerical associations: What is the nature of the information represented along the mental number line? Here we show that this information is not exclusive to number, simultaneously accommodating numerical and non-numerical magnitudes. Participants completed the classic SNARC (Spatial-Numerical Association of Response Codes) task while sometimes wearing wrist weights. Weighting the left wrist–thereby linking less and more weight to right and left, respectively–worked against left-to-right orientation of number, leaving no behavioral trace of the mental number line. Our findings point to the dynamic integration of magnitude dimensions, with spatial organization instantiating representational currency (i.e., more/less relations) shared across magnitudes.

Newborn chicks need no number tricks. Commentary: Number-space mapping in the newborn chick resembles humans' mental number line.

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the 'mental number line'. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the 'mental number line'. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number-space association.

Two steps to space for numbers.

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants' responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude.

Spatial-Numerical Associations (SNAs) refer to the demonstrations of spatial processing of numbers. The Mental Number Line (MNL) is a representation model describing numbers as aligning left-to-right (LR) and was suggested to account for directional biases in participants’ responses during numerical tasks. One common behavioral demonstration of this is the Spatial-Numerical Associations of Response Codes (SNARC) effect, which describes faster left-/right-hand responses to smaller/larger numbers, respectively. The MNL, and, consequently, directional SNAs, show variabilities across different cultures. Reading direction is considered to be the main factor in explaining these differences. In line with this, individuals with right-to-left (RL) reading habits show a weaker or even reverse SNARC effect. In the present study, we investigated whether SNAs are influenced not only by reading direction, but also by cultural directional preferences such as drawing lines, arranging objects, imagining objects (i.e., rightward or leftward facing), or representing events in time (i.e., mentally representing the past/future on the left/right, respectively). To test this hypothesis, we measured the cultural directional preferences and the SNARC effect across three cultures in an online setup; German, Turkish, and Iranian. LR preferences in the Cultural Directional Preferences Questionnaire were most prominent in German participants, intermediate in Turkish participants, and least prominent in Iranian participants. In line with this, the LR SNARC effect was strongest in German, intermediate in Turkish, and weakest (but not RL) in Iranian culture. These findings suggest that cultural directional preferences are involved in the emergence of adult SNAs in addition to the reading direction.

Spatial-Numerical Associations (SNAs) refer to the demonstrations of spatial processing of numbers. The Mental Number Line (MNL) is a representation model describing numbers as aligning left-to-right (LR) and was suggested to account for directional biases in participants’ responses during numerical tasks. One common behavioral demonstration of this is the Spatial-Numerical Associations of Response Codes (SNARC) effect, which describes faster left/right-hand responses to smaller/larger numbers, respectively. The MNL, and, consequently, directional SNAs, show variabilities across different cultures. Reading direction is considered to be the main factor in explaining these differences. In line with this, individuals with right-to-left (RL) reading habits show a weaker or even reverse SNARC effect. In the present study, we investigated whether SNAs are influenced not only by reading direction, but also by cultural directional preferences such as drawing lines, arranging objects, imagining objects (i.e., rightward or leftward facing), or representing events in time (i.e., mentally representing the past and the future on the left or right). To test this hypothesis, we measured the cultural directional preferences and the SNARC effect across three cultures in an online setup; German, Turkish, and Iranian. LR preferences in the Cultural Directional Preferences Questionnaire were most prominent in German participants, intermediate in Turkish participants, and least prominent in Iranian participants. In line with this, the LR SNARC effect was strongest in German, intermediate in Turkish, and weakest (but not RL) in Iranian culture. These findings suggest that cultural directional preferences are involved in the emergence of adult SNAs in addition to the reading direction.

We associate small numbers with the left and large numbers with the right side of space. Recent evidence from human newborns and non-human animals has challenged the primary role assigned to culture, in determining this spatial numerical association (SNA). Nevertheless, the effect of individual spatial biases has not been considered in previous research. Here, we tested the effect of numerical magnitude in SNA and we controlled for itablendividual biases. We trained 3-day-old chicks (Gallus gallus) on a given numerical magnitude (5). Then chicks could choose between two identical, left or right, stimuli both representing either 2, 8, or 5 elements. We computed the percentage of Left-sided Choice (LC). Numerical magnitude, but not individual lateral bias, explained LC: LC2 vs. 2>LC5 vs. 5>LC8 vs. 8. These findings suggest that SNA originates from pre-linguistic precursors, and pave the way to the investigation of the neural correlates of the number space association.

The SNARC effect does not imply a mental number line

The topographic representation of space interacts with the mental representation of number. Evidence for such number–space relations have been reported in both synaesthetic and non-synaesthetic participants. Thus far most studies have only examined related effects in sighted participants. For example, the mental number line increases in magnitude from left to right in sighted individuals (Loetscher et al., 2008, Curr. Biol.). What is unclear is whether this association arises from innate mechanisms or requires visual experience early in life to develop in this way. Here we investigated the role of visual experience for the left to right spatial numerical association using a random number generation task in congenitally blind, late blind, and blindfolded sighted participants. Participants orally generated numbers randomly whilst turning their head to the left and right. Sighted participants generated smaller numbers when they turned their head to the left than to the right, consistent with past results. In contrast, congenitally blind participants generated smaller numbers when they turned their head to the right than to the left, exhibiting the opposite effect. The results of the late blind participants showed an intermediate profile between that of the sighted and congenitally blind participants. Visual experience early in life is therefore necessary for the development of the spatial numerical association of the mental number line.

Adults take longer to judge the locations of horizontal stimuli than to judge the locations of vertical stimuli. In order to determine the source of this difficulty with the horizontal dimension, the congruity between the locations of stimuli and verbal descriptions was judged in a reaction time (RT) task. Because bilateral symmetry of the nervous system may be related to the difficulty with horizontal stimuli, this was varied by using right-handed, left-handed, and ambidextrous subjects. However, this variable produced no significant effects in the RT task. Horizontal stimuli took longer than vertical stimuli whether the verbal description was encoded before or during the RT periods, suggesting that label encoding is not the entire source of the effect. However, when the verbal labels were eliminated entirely by having subjects learn and use stimulus-letter pairs, horizontal stimuli did not take longer than vertical stimuli. This suggests that perception of the stimulus is not the cause of the difficulty. Together, the experiments indicated that comparing horizontal labels to stimuli is the largest source of the difficulty in telling right from left. Reasons why adults have such a problem were discussed.

There is substantial evidence linking numerical magnitude to the physical properties of space. The most influential support for this connection comes from the SNARC effect (spatial–numerical association of response codes), in which responses to small/large numbers are faster on the left/right side of space, respectively. The SNARC effect has been extensively replicated, and is understood as horizontal mapping of numerical magnitude. However, much less is known about how numbers are represented on the vertical and sagittal axes, and whether spatial–numerical associations on different axes emerge during childhood. To that end, we tested two groups of children, aged 5–7 years and 8 and 9 years, on a single-digit magnitude comparison task with response buttons positioned either upper/lower (vertical), left/right (horizontal) or near/far (sagittal). Our results provide evidence of spatial–numerical mapping on all three axes for both age groups that are similar in strength. This indicates that, even at an early stage of formal education, children can flexibly assign numerical magnitude to any spatial dimension. To examine the contribution of extracorporeal space and spatio-anatomical mapping to the SNARC effect across axes, these sources were pitted against each other by swapping the position of the response hands in Experiment 1b. Switching hand position did not reveal convincing evidence for SNARC effects on any axis. Results are discussed with respect to the utility of three-dimensional mental number lines, and potential avenues for future research are outlined.