How to rapidly construct a spatial–numerical representation in preliterate children (at least temporarily)

Spatial processing of numbers has emerged as one of the basic properties of humans’ mathematical thinking. However, how and when number–space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading and writing. However, some early forms of a number–space link have been observed in preschool children who cannot yet read and write. As literacy experience is evidently not necessary for number–space effects, we are searching for other potential sources of this association. Here we propose and test a hypothesis that the number–space link can be quickly constructed in preschool children's cognition on the basis of spatially oriented visuo‐motor activities. We trained 3‐ and 4‐year‐old children with a non‐numerical spatial movement task (left‐to‐right or right‐to‐left), where via touch screen children had to move a frog across a pond. After the training, children had to perform a numerosity comparison task. After left‐to‐right training, we observed a SNARC‐like effect (reactions to smaller numbers were faster on the left side, and reactions to larger numbers on the right side), and after right‐to‐left training a reverse effect. These results are the first to show a causal link between visuo‐motor activities and number–space associations in children before they learn to read and write. We argue that simple activities, such as manual games, dominant in a given society, might shape number–space associations in children in a way similar to lifelong reading training.     

Moving attention along the mental number line in preschool age: Study of the operational momentum in 3‐ to 5‐year‐old children's non‐symbolic arithmetic

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3–5 years old were tested with non‐symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give‐a‐number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial‐directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial‐directional and magnitude OM. This undermines the canonical version of the number line‐based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial‐numerical associations in numerical development are proposed.     

New visuospatial associations by training verbospatial mappings in the first language

We investigated whether verbospatial and visuospatial information share a common representation. We demonstrate that when the associations from spatial words to spatial responses are altered, so that the word left becomes associated with a right response and the word right with a left response, the associations from the spatial locations left and right to the spatial responses also change. This effect was only observed for first-language spatial words (Dutch) and not for second-language spatial words (French), and it did not increase when these languages were combined. The findings argue for shared spatial representations for different types of spatial input.     

Direction counts: a comparative study of spatially directional counting biases in cultures with different reading directions

Western adults associate small numbers with left space and large numbers with right space. Where does this pervasive spatial–numerical association come from? In this study, we first recorded directional counting preferences in adults with different reading experiences (left to right, right to left, mixed, and illiterate) and observed a clear relationship between reading and counting directions. We then recorded directional counting preferences in preschoolers and elementary school children from three of these reading cultures (left to right, right to left, and mixed). Culture-specific counting biases existed before reading acquisition in children as young as 3 years and were subsequently modified by early reading experience. Together, our results suggest that both directional counting and scanning activities contribute to number–space associations.     

Agency and the Annunciation

Prior research has revealed that when healthy participants, who are not artists, are asked to draw a person who is performing an action, they are more likely to position the agent on the left and the person or object receiving this action, the patient, on the right. Thus, the goal of this study was to learn whether in works of art, such as those portraying the Annunciation of the angel Gabriel to the Blessed Virgin Mary, artists would be more likely to place the angel, who is the agent, on the left of Mary, who is the patient. We found that in our sample of 604 paintings of the Annunciation by different artists that the agent Gabriel is significantly more frequently portrayed to left of Mary. Whereas this result supports the left-agent, right-patient hypothesis, the reason for this spatial bias is not entirely known, but may be related to several factors such as the learned left to right direction of reading/writing in European languages, left-versus right-sided emotional facial expressive asymmetries, a left-sided spatial attentional bias and a spatial motor-action preference of upper extremity for making abductive (left to right) movements when using the right upper extremity. Additionally, biblical explanations and theological principles may have influenced the organization of this scene.     

Evidence for two types of spatial representations: hemispheric specialization for categorical and coordinate relations

Analyses of human object recognition abilities led to the hypothesis that 2 kinds of spatial relation representations are used in human vision. Evidence for the distinction between abstract categorical spatial relation representations and specific coordinate spatial relation representations was provided in 4 experiments. These results indicate that Ss make categorical judgments--on/off, left/right, and above/below--faster when stimuli are initially presented to the left cerebral hemisphere, whereas they make evaluations of distance--in relation to 2 mm, 3 mm, or 1 in. (2.54 cm)--faster when stimuli are initially presented to the right cerebral hemisphere. In addition, there was evidence that categorical representations developed with practice.     

数字-空间联结的内在机制：基于工作记忆的视角

已有研究证实数字-空间联结是普遍存在的现象，但关于这种联结的解释仍存在争论。当前对数字-空间联结主要有两种解释。其中，心理数字线假设数字的心理表征是一条从左到右方向的水平线，而工作记忆假设认为数字-空间联结是任务执行期间暂时的工作记忆表征。本文通过分析心理数字线不能解释的数字-空间联结现象及局限性，来探讨工作记忆解释的适用性，并通过工作记忆的核心观点来解释数字-空间联结现象，以期更好地揭示数字-空间联结的内在机制。但关于工作记忆解释仍有亟待解决的问题，还需实证研究探讨。     

Cross-cultural differences in mental representations of time: evidence from an implicit nonlinguistic task

Across cultures people construct spatial representations of time. However, the particular spatial layouts created to represent time may differ across cultures. This paper examines whether people automatically access and use culturally specific spatial representations when reasoning about time. In Experiment 1, we asked Hebrew and English speakers to arrange pictures depicting temporal sequences of natural events, and to point to the hypothesized location of events relative to a reference point. In both tasks, English speakers (who read left to right) arranged temporal sequences to progress from left to right, whereas Hebrew speakers (who read right to left) arranged them from right to left, replicating previous work. In Experiments 2 and 3, we asked the participants to make rapid temporal order judgments about pairs of pictures presented one after the other (i.e., to decide whether the second picture showed a conceptually earlier or later time-point of an event than the first picture). Participants made responses using two adjacent keyboard keys. English speakers were faster to make "earlier" judgments when the "earlier" response needed to be made with the left response key than with the right response key. Hebrew speakers showed exactly the reverse pattern. Asking participants to use a space-time mapping inconsistent with the one suggested by writing direction in their language created interference, suggesting that participants were automatically creating writing-direction consistent spatial representations in the course of their normal temporal reasoning. It appears that people automatically access culturally specific spatial representations when making temporal judgments even in nonlinguistic tasks.     

The spatial representation of numerical and non-numerical ordered sequences: Insights from a random generation task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.     

Preschoolers prior formal mathematics education engage numerical magnitude representation rather than counting principles in symbolic ±1 arithmetic: Evidence from the operational momentum effect

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This study is the first to demonstrate OM in symbolic arithmetic in preschoolers. It was modeled on Haman and Lipowska's (2021) non-symbolic arithmetic task, using Arabic numerals instead of visual sets. Seventy-seven children (4–7 years old) who know Arabic numerals and counting principles (CP), but without prior school math education, solved addition and subtraction problems presented as videos with one as the second operand. In principle, such problems may be difficult when involving a non-symbolic approximate number processing system, whereas in symbolic format they can be solved based solely on the successor/predecessor functions and knowledge of numerical orders, without reference to representation of numerical magnitudes. Nevertheless, participants made systematic errors, in particular, overestimating results of addition in line with the typical OM tendency. Moreover, subtraction and addition induced longer response times when primed with left- and right-directed movement, respectively, which corresponds to the reversed spatial form of OM. These results largely replicate those of non-symbolic task and show that children at early stages of mastering symbolic arithmetic may rely on numerical magnitude processing and spatial-numerical associations rather than newly-mastered CP and the concept of an exact number.     

Time,space, and memory for order

Information about the order of items in a sequence can be conveyed either spatially or temporally. In the present investigation, we examined whether these different modes of presentation map onto compatible mental representations of serial order. We examined this issue in three immediate serial-recall experiments, in which participants recalled lists of letters in the temporal order in which they had appeared. Each letter in a to-be-remembered sequence was presented in a unique spatial position, with the order of these spatial positions progressing from either left to right or right to left. In this way, the visually presented lists contained both temporal and spatial order information. Recall of the temporal order information was more accurate with congruent spatial order information—that is, when the letters progressed from left to right, following the typical reading direction of English—than when the spatial order information was incongruent. These results suggest compatible representations of serial order when sequences are conveyed spatially and temporally.     

Increased spatial salience in the social Simon task: A response-coding account of spatial compatibility effects

A spatial compatibility effect (SCE) is typically observed in forced two-choice tasks in which a spatially defined response (e.g., pressing a left vs. a right key) has to be executed to a nonspatial feature of a stimulus (e.g., discriminating red from green) that is additionally connoted by a spatial feature (e.g., the stimulus points to the left or the right). Responses are faster and more accurate when the response side and the spatial stimulus feature are compatible than when they are incompatible. Previous research has demonstrated that SCEs are diminished when stimuli from only one response category are responded to in individual go/no-go tasks, whereas SCEs reemerge when two participants work jointly on two complementary, individual go/no-go tasks in a joint go/no-go task setting. This social Simon effect has been considered evidence for shared task representations. We show that SCEs emerge in individual go/no-go tasks when the spatial dimension is made more salient, whereas SCEs are eliminated in joint go/no-go tasks when the spatial dimension is made less salient. These findings are consistent with an account of social Simon effects in terms of spatial response coding, whereas they are inconsistent with an account of shared task representations. The relevance of social factors for spatial response coding is discussed.     

Pseudoneglect for the bisection of mental number lines

Patients with unilateral neglect of the left side bisect physical lines to the right whereas individuals with an intact brain bisect lines slightly to the left (pseudoneglect). Similarly, for mental number lines, which are arranged in a left-to-right ascending sequence, neglect patients bisect to the right. This study determined whether individuals with an intact brain show pseudoneglect for mental number lines. In Experiment 1, participants were presented with visual number triplets (e.g., 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Despite changing the spatial configuration of the stimuli, or their temporal order, the numerical length on the left was consistently overestimated. The fact that the bias was unaffected by physical stimulus changes demonstrates that the bias is based on a mental representation. The leftward bias was also observed for sets of negative numbers (Experiment 2)--demonstrating not only that the number line extends into negative space but also that the bias is not the result of an arithmetic distortion caused by logarithmic scaling. The leftward bias could be caused by a rounding-down effect. Using numbers that were prone to large or small rounding-down errors, Experiment 3 showed no effect of rounding down. The task demands were changed in Experiment 4 so that participants determined whether the inner number was the true arithmetic centre or not. Participants mistook inner numbers shifted to the left to be the true numerical centre--reflecting leftward overestimation. The task was applied to 3 patients with right parietal damage with severe, moderate, or no spatial neglect (Experiment 5). A rightward bias was observed, which depended on the severity of neglect symptoms. Together, the data demonstrate a reliable and robust leftward bias for mental number line bisection, which reverses in clinical neglect. The bias mirrors pseudoneglect for physical lines and most likely reflects an expansion of the space occupied by lower numbers on the left side of the line and a contraction of space for higher numbers located on the right.     

Pseudoneglect for the bisection of mental number lines

Patients with unilateral neglect of the left side bisect physical lines to the right whereas individuals with an intact brain bisect lines slightly to the left (pseudoneglect). Similarly, for mental number lines, which are arranged in a left-to-right ascending sequence, neglect patients bisect to the right. This study determined whether individuals with an intact brain show pseudoneglect for mental number lines. In Experiment 1, participants were presented with visual number triplets (e.g., 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Despite changing the spatial configuration of the stimuli, or their temporal order, the numerical length on the left was consistently overestimated. The fact that the bias was unaffected by physical stimulus changes demonstrates that the bias is based on a mental representation. The leftward bias was also observed for sets of negative numbers (Experiment 2)—demonstrating not only that the number line extends into negative space but also that the bias is not the result of an arithmetic distortion caused by logarithmic scaling. The leftward bias could be caused by a rounding-down effect. Using numbers that were prone to large or small rounding-down errors, Experiment 3 showed no effect of rounding down. The task demands were changed in Experiment 4 so that participants determined whether the inner number was the true arithmetic centre or not. Participants mistook inner numbers shifted to the left to be the true numerical centre—reflecting leftward overestimation. The task was applied to 3 patients with right parietal damage with severe, moderate, or no spatial neglect (Experiment 5). A rightward bias was observed, which depended on the severity of neglect symptoms. Together, the data demonstrate a reliable and robust leftward bias for mental number line bisection, which reverses in clinical neglect. The bias mirrors pseudoneglect for physical lines and most likely reflects an expansion of the space occupied by lower numbers on the left side of the line and a contraction of space for higher numbers located on the right.     

Reading habits for both words and numbers contribute to the SNARC effect

This study compared the spatial representation of numbers in three groups of adults: Canadians, who read both English words and Arabic numbers from left to right; Palestinians, who read Arabic words and Arabic-Indic numbers from right to left; and Israelis, who read Hebrew words from right to left but Arabic numbers from left to right. Canadians associated small numbers with left and large numbers with right space (the SNARC effect), Palestinians showed the reverse association, and Israelis had no reliable spatial association for numbers. These results suggest that reading habits for both words and numbers contribute to the spatial representation of numbers.     

Spatial Simon effects with nonspatial responses

Recent studies have shown that spatial Simon effects can be modulated by short-term associations that are set up as a result of task instructions. I examined whether spatial Simon effects can also be produced by short-term associations even when the responses are unrelated to spatial position. Participants were to say “cale” or “cole” on the basis of the direction of arrows (i.e., left or right), the meaning of words (i.e.,left orright), and the color of squares presented left or right of the screen center. Responses to squares were faster when the correct response was associated with the same position as the irrelevant position of the square (e.g., say “cale” to a square on the left when “cale” was assigned to the wordleft and the left arrow). This new type of stimulus-response compatibility effect provides the first evidence for short-term associations that involve mode-independent representations.     

From left to right: Processing acronyms referring to names of political parties activates spatial associations

In line with previous studies, showing that abstract concepts like “power” or “god” implicitly activate spatial associations, in the present study we hypothesized that spatial associations are coactivated during the processing of acronyms referring to names of political parties as well. In four studies, it was found that the reading of these acronyms was accompanied by the implicit activation of spatial left–right associations. That is, participants responded faster to left-wing parties by means of a left-hand button press and vice versa for right-wing parties (Experiments 1 to 3), and participants responded faster when a political acronym was presented at the side of the screen corresponding to the political orientation of the acronym (Experiment 4). Interestingly, a correlation was observed between the effect size for left-wing parties and participants' political preferences, suggesting that the reaction time effects reflect the perceived distance of a party to one's own political orientation. Together these findings indicate that spatial representations activated in response to political acronyms do not simply reflect lexical–semantic associations or spatial metaphors, but representations of parties' political orientation relative to one's own sociopolitical position.     

Duration and numerical estimation in right brain‐damaged patients with and without neglect: Lack of support for a mental time line

Previous studies have shown that left neglect patients are impaired when they have to orient their attention leftward relative to a standard in numerical comparison tasks. This finding has been accounted for by the idea that numerical magnitudes are represented along a spatial continuum oriented from left to right with small magnitudes on the left and large magnitudes on the right. Similarly, it has been proposed that duration could be represented along a mental time line that shares the properties of the number continuum. By comparing directly duration and numerosity processing, this study investigates whether or not the performance of neglect patients supports the hypothesis of a mental time line. Twenty‐two right brain‐damaged patients (11 with and 11 without left neglect), as well as 11 age‐matched healthy controls, had to judge whether a single dot presented visually lasted shorter or longer than 500 ms and whether a sequence of flashed dots was smaller or larger than 5. Digit spans were also assessed to measure verbal working memory capacities. In duration comparison, no spatial‐duration bias was found in neglect patients. Moreover, a significant correlation between verbal working memory and duration performance was observed in right brain‐damaged patients, irrespective of the presence or absence of neglect. In numerical comparison, only neglect patients showed an enhanced distance effect for numerical magnitude smaller than the standard. These results do not support the hypothesis of the existence of a mental continuum oriented from left to right for duration. We discuss an alternative account to explain the duration impairment observed in right brain‐damaged patients.     

The flexibility of association between temporal concepts and physical space in the Japanese language

Previous studies have indicated that temporal concepts such as the past and future are associated with horizontal (left–right) space. This association has been interpreted as reflecting left‐to‐right writing systems. The Japanese language, however, is written both horizontally and vertically and, when texts are presented vertically, the sequence of columns runs from right to left. This study examines whether the associations between time and space are changed by the direction of the character strings using a word categorization task. Consistent with previous studies, response times and error rates indicated left‐past and right‐future associations when participants read words presented horizontally. On the other hand, response times indicated the opposite (i.e., left‐future and right‐past associations) when participants read words presented vertically. These results suggest that temporal concepts are not associated with one's body or physical space in an inflexible manner, but rather the associations can flexibly change through experience.     

Visuo-spatial representations of the alphabet in synaesthetes and non-synaesthetes

Visuo-spatial representations of the alphabet (so-called 'alphabet forms') may be as common as other types of sequence-space synaesthesia, but little is known about them or the way they relate to implicit spatial associations in the general population. In the first study, we describe the characteristics of a large sample of alphabet forms visualized by synaesthetes. They most often run from left to right and have salient features (e.g., bends, breaks) at particular points in the sequence that correspond to chunks in the 'Alphabet Song' and at the alphabet mid-point. The Alphabet Song chunking suggests that the visuo-spatial characteristics are derived, at least in part, from those of the verbal sequence learned earlier in life. However, these synaesthetes are no faster at locating points in the sequence (e.g., what comes before/after letter X?) than controls. They tend to be more spatially consistent (measured by eye tracking) and letters can act as attentional cues to left/right space in synaesthetes with alphabet forms (measured by saccades), but not in non-synaesthetes. This attentional cueing suggests dissociation between numbers (which reliably act as attentional cues in synaesthetes and non-synaesthetes) and letters (which act as attentional cues in synaesthetes only).