Spatial-numerical Association Research Articles

Beyond fixed sets: boundary conditions for obtaining SNARC-like effects with continuous semantic magnitudes.

Previous research has demonstrated the presence of an effect (i.e., the spatial-numerical association of response codes or SNARC) in both numerical parity and magnitude judgment tasks in which smaller numerical magnitudes are manually responded to faster on the left side and larger numerical magnitudes on the right side. Such a result has typically been attributed to a spatially based representation of numerical magnitude in long-term memory, the format of which has recently been postulated to be positional in line with learning of a canonically ordered number sequence. As a test of this view, in the current research, participants made classification judgments involving either the size (N = 88) or the living-nonliving status (N = 114) corresponding to the names of animals/objects etc. to which no learned canonical ordering of size exists. Names were taken from a very large set of 400 animals/objects etc. and each name was presented only once in an experimental session. Responses were made using left and right manual keypresses. In this work, the relation between response time and the relative sizes of the animals/objects did not differ across the left-right side of response indicating that SNARC-like effects did not occur. As such, the results suggest that space is not an inherent aspect of the long-term representation of magnitude in the brain and that some form of positional coding of magnitude is necessary for SNARC-like effects to occur.

Walking to a number: is there affective involvement in generating the SNARC effect in numerical cognition?

The effect known as the spatial-numerical association of response codes (SNARC) documents fast reaction to small numbers with a response at the left and to large numbers with a response at the right. The common explanation appeals to a hypothetical mental number line of a left-to-right orientation with the numerical magnitudes on the line activated in an automatic fashion. To explore the possibility of emotional involvement in processing, we employed prototypical affective behaviors for responses in lieu of the usual spatial-numerical ones (i.e., of pressing lateralized keys). In the present series of experiments, the participants walked toward a number or walked away from a number (in a physical approach-avoidance setup) or said "good" or "bad" in response to a number. We recorded strong SNARC effects with affective responding. For example, it took participants longer to say "good" than "bad" to small numbers, but it took them longer to say "bad" than "good" to larger numbers. Although each particular outcome can still be accounted for by a spatial interpretation, the cumulative results are suggestive of the possibly of affective involvement in generating the effect.

High-definition turns timing-dependent: Different behavioural consequences during and following cathodal high-definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task.

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High-definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity-specific neurophysiological effects-similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial-numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. 'offline'), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. 'online'). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive-behavioural performance, which could be achieved by individualised current density in electric field modelling.

The reciprocity of spatial-numerical associations of vocal response codes depends on stimulus mode.

Individuals make faster left responses to small/er numbers and faster right responses to large/r numbers than vice versa. This "spatial-numerical association of response codes" (SNARC) effect represents evidence for an overlap between the cognitive representations of number and space. Theories of the SNARC effect differ in whether they predict bidirectional S-R associations between number and space or not. We investigated the reciprocity of S-R priming effects between number and location in three experiments with vocal responses. In Experiments 1 and 2, participants completed a number-location task, with digits as stimuli and location words as responses, and a location-number task, with physical locations as stimuli and number words as responses. In addition, we varied the S-R mapping in each task. Results revealed a strong SNARC effect in the number-location task, but no reciprocal SNARC effect in the location-number task. In Experiment 3, we replaced physical location stimuli with location words and digit stimuli with number words. Results revealed a regular and a reciprocal SNARC effect of similar size. Reciprocal SNARC effects thus seem to emerge with verbal location stimuli and vocal responses, but not with physical location stimuli and vocal responses. The S-R associations underlying the SNARC effect with vocal responses thus appear bidirectional and symmetrical for some combinations of stimulus and response sets, but not for others. This has implications for theoretical accounts of the SNARC effect which need to explain how stimulus mode affects the emergence of reciprocal but not regular SNARC effects.

How do symbolic and non-symbolic spatial-numerical associations develop? Evidence from the parity judgment task and the magnitude comparison task

How do symbolic and non-symbolic spatial-numerical associations develop? Evidence from the parity judgment task and the magnitude comparison task

Effect of egocentric and allocentric reference frames on spatial-numerical associations.

From an embodied view of cognition, sensorimotor mechanisms are strongly involved in abstract processing, such as Arabic number meanings. For example, spatial cognition can influence number processing. These spatial-numerical associations (SNAs) have been deeply explored since the seminal SNAs of response code (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively). Although these SNAs along the transverse plane (left-to-right axis) have been extensively studied in cognitive sciences, no systematic assessment of other planes of the tridimensional space has been afforded. Moreover, there is no evidence of how SNAs organise themselves throughout the changes in spatial body-reference frames (egocentric and allocentric). Hence, this study aimed to explore how SNAs organise themselves along the transverse and sagittal planes when egocentric and allocentric changes are processed during body displacements in the environment. In the first experiment, the results revealed that, when the participants used an egocentric reference, SNAs were observed only along the sagittal plane. In a second experiment that used an allocentric reference, the reversed pattern of results was observed: SNAs were present only along the transverse plane of the body. Overall, these findings suggest that, depending on the spatial reference frames of the body, SNAs are strongly flexible.

Temporal speed prevails on interval duration in the SNARC-like effect for tempo.

The Spatial-Numerical Association of Response Codes (SNARC) effect is evidence of an association between number magnitude and response position, with faster left-key responses to small numbers and faster right-key responses to large numbers. Similarly, recent studies revealed a SNARC-like effect for tempo, defined as the speed of an auditory sequence, with faster left-key responses to slow tempo and faster right-key responses to fast tempo. In order to address some methodological issues of previous studies, in the present study we designed an experiment to investigate the occurrence of a SNARC-like effect for tempo, employing a novel procedure in which only two auditory beats in sequence with a very short interstimulus interval were used. In the "temporal speed" condition, participants were required to judge the temporal speed (slow or fast) of the sequence. In the "interval duration" condition, participants were required to judge the duration of the interval between the two beats (short or long). The results revealed a consistent SNARC-like effect in both conditions, with faster left-hand responses to slow tempo and faster right-hand responses to fast tempo. Interestingly, the consistency of the results across the two conditions indicates that the direction of the SNARC-like effect was influenced by temporal speed even when participants were explicitly required to focus on interval duration. Overall, the current study extends previous findings by employing a new paradigm that addresses potential confounding factors and strengthens evidence for the SNARC-like effect for tempo.

The spatial representation of loudness in a timbre discrimination task.

When participants decide whether a presented tone is loud or soft they react faster to loud tones with a top-sided response key in comparison to a bottom-sided response key and vice versa for soft tones. This effect is comparable to the well-established horizontal Spatial-Numerical Association of Response Codes (SNARC) effect and is often referred to as Spatial-Musical Association of Response Codes (SMARC) effect for loudness. The SMARC effect for loudness is typically explained by the assumption of a spatial representation or by the polarity correspondence principle. Crucially, both theories differ in the prediction of the SMARC effect when loudness is task-irrelevant. Therefore, we investigated whether the SMARC effect still occurs in a timbre discrimination task: Participants (N = 36) heard a single tone and classified its timbre with vertically arranged response keys. Additionally, the tone's loudness level varied in six levels. In case of a spatial representation, the SMARC effect should still occur while in case of polarity corresponding principle, the effect should be absent. Results showed that the SMARC effect was still present and that the differences between top-sided and bottom-sided responses were a linear function of loudness level indicating a continuous spatial representation of loudness.

Collective nouns are conceptually plural: Evidence from the grammatical SNARC effect.

To develop theories of how comprehenders extract the message from a linguistic stream, it is critical to understand how they conceptually represent referents. The experiments reported here focus on singular collective nouns (e.g., committee, team), which introduce a single group into the discourse and test whether they nonetheless are conceptually plural (i.e., construed as consisting of multiple entities) by using the spatial-numerical association of response codes (SNARC) paradigm (Dehaene & Changeux, 1993). In this paradigm, participants are typically faster to respond to smaller numbers or numerical stimuli when making a response on their left and faster to respond to larger numbers or numerical stimuli when making a response on their right. In three experiments, participants saw German words on a computer screen and decided whether each one described a single entity or something that could be subdivided into multiple entities (Experiment 1) or whether they would use "ist" or "sind" ("is" or "are") in combination with the word if it were the subject of a sentence (Experiments 2 and 3). The mapping of responses to participants' left and right hands was counterbalanced. Experiment 1 failed to show a grammatical SNARC effect. Experiments 2 and 3 showed a grammatical SNARC effect that extended to collective noun phrases. The results of these experiments suggest that collective noun phrases are instantiated as conceptually plural in comprehenders' minds. We discuss the differential task effects and the implications of these data on theories of language comprehension. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

It's SNARC o' clock: manipulating the salience of the context in a conceptual replication of Bächtold et al.'s (1998) clockfacestudy.

The Spatial-Numerical Association of Response Codes (SNARC) effect consists in faster left-/right-key responses to small/large numbers. (Bächtold et al., Neuropsychologia 36:731-735, 1998) reported the reversal of this effect after eliciting the context of a clockface-where small numbers are represented on the right and large numbers on the left. The present study investigates how the salience of a particular spatial-numerical context, which reflects the level of activation of the context in working memory, can alter Spatial Numerical Associations (SNAs). Four experiments presented the clockface as context and gradually increased its salience using different tasks. In the first two experiments (low salience), the context was presented at the beginning of the experiment and its retrieval was not required to perform the tasks (i.e., random number generation in Experiment 1, magnitude classification and parity judgement in Experiment 2). Results revealed regular left-to-right SNAs, unaffected by the context. In Experiment 3 (medium salience), participants performed magnitude classification and parity judgement (primary task), and a Go/No-go (secondary task) which required the retrieval of the context. Neither the SNARC effect nor a reversed-SNARC emerged, suggesting that performance was affected by the context. Finally, in Experiment 4 (high salience), the primary task required participants to classify numbers based on their position on the clockface. Results revealed a reversed SNARC, as in (Bächtold et al., Neuropsychologia 36:731-735, 1998). In conclusion, SNARC is disrupted when the context is retrieved in a secondary task, but its reversal is observed only when the context is relevant for the primary task.

Similarities of SNARC, cognitive Simon, and visuomotor Simon effects in terms of response time distributions, hand-stimulus proximity, and temporal dynamics.

The spatial-numerical association of response codes (SNARC) and Simon effects are attributed to the same type of conflict according to dimensional overlap (DO) theory: the congruency of task-irrelevant spatial information and the selected response (e.g., left or right). However, previous studies have yielded inconsistent results regarding the relationship between the two effects, with some studies reporting an interaction while others did not. This discrepancy may be attributed to the use of different types of Simon effects (visuomotor and cognitive Simon effects) in these studies, as the spatial codes associated with these two types of Simon effects are distinct (exogenous and endogenous, respectively). The aim of this study was to address these inconsistencies and gain a better understanding of the similarities and differences in spatial representations generated by spatial location, semantic information, and numerical information. We attempted to classify the relationships among the SNARC and Simon effects. Specifically, the visuomotor Simon, cognitive Simon, and SNARC effects were compared from three perspectives: the response time (RT) distribution, hand-stimulus proximity, and temporal dynamics (with the drift diffusion model; DDM). Regarding RTs, the results showed that the visuomotor Simon effect decreased with increased values of RT bins, while the cognitive Simon and SNARC effects increased. Additionally, the visuomotor Simon effect was the only effect influenced by hand-stimulus proximity, with a stronger effect observed in the hand-proximal condition than in the hand-distal condition. Regarding the DDM results, only the visuomotor Simon effect exhibited a higher drift rate and longer non-decision time in the incompatible condition than in the compatible condition. Conversely, both the SNARC and cognitive Simon effects exhibited an inverse pattern regarding the drift rate and no significant difference in non-decision time between the two conditions. These findings suggest that the SNARC effect is more similar to the cognitive Simon effect than the visuomotor Simon effect, indicating that the endogenous spatial-numerical representation of the SNARC effect might share an underlying processing mechanism with the endogenous spatial-semantic representation of the cognitive Simon effect but not with the exogenous location representation of the visuomotor Simon effect. Our results further demonstrate that the origin of spatial information could impact the classification of conflicts and supplement DO theory.

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as “motion along a path” and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

What the Attentional-SNARC and its (null) replications can and cannot tell us

In response to a point raised by Fischer et al. (2020), we discuss the theoretical implications of both the original Attentional SNARC (Att-SNARC) and its recent failed multi-laboratory replication. In our view, the theoretical importance of the original Att-SNARC can be summarized in two points: (1) there is a conceptual link between numbers and space, which can be observed as Spatial-Numerical Associations, and (2) Spatial-Numerical Associations are involuntary and automatic. We conclude that convergent evidence from other paradigms saves the first point from being challenged in light of the failed replication; but, on the other hand, empirical evidence for the second point no longer holds.

Spatial-numerical associations of manual response codes are strongly asymmetrical

The spatial-numerical association of response codes (SNARC) effect denotes the observation that humans respond faster and more accurately with a left-side response to smaller numbers and a right-side response to larger numbers, as compared to the opposite mapping. Existing accounts, such as the mental number line hypothesis or the polarity correspondence principle, differ in whether they assume symmetrical associations between numerical and spatial stimulus and response codes or not. In two experiments, we investigated the reciprocity of the SNARC effect in manual choice-response tasks with two conditions. In the number-location task, participants pressed a left or right key to a number stimulus (dots in Experiment 1, digits in Experiment 2). In the location-number task, participants made one or two consecutive keypresses with one hand to a left- or right-side stimulus. Both tasks were performed with a compatible (one-left, two-right; left-one, right-two) and an incompatible (one-right, two-left; left-two, right-one) mapping. In both experiments, results showed a strong compatibility effect in the number-location task, reflecting the typical SNARC effect. In contrast, in both experiments, there was no mapping effect in the location-number task when outliers were excluded. However, when outliers were not excluded, small reciprocal SNARC effects occurred in Experiment 2. Together, the findings suggest that priming of spatial responses by numerical stimuli is much stronger than priming of numerical responses by spatial stimuli. The results are consistent with some accounts of the SNARC effect (e.g., the mental number line hypothesis), but not with others (e.g., the polarity correspondence principle).

How to not induce SNAs: The insufficiency of directional force.

People respond faster to smaller numbers in their left space and to larger numbers in their right space. Here we argue that movements in space contribute to the formation of spatial-numerical associations (SNAs). We studied the impact of continuous isometric forces along the horizontal or vertical cardinal axes on SNAs while participants performed random number production and arithmetic verification tasks. Our results suggest that such isometric directional force do not suffice to induce SNAs.

Cognitive inhibition abilities explain inter-individual variability in gender-space associations.

There is a great deal of research describing the close association that exists between numerical and spatial representations, illustrating the SNARC (Spatial-Numerical Association of Response Code) effect. This effect signals the spatial mental representation of small numbers to the left and larger numbers to the right, coinciding with the direction of reading and writing. Subsequent research has found a similar spatial representation for other stimuli (e.g., size of objects and animals, and words associated with time). Some of these spatially represented stimuli are social in nature, even suggesting a spatial mental organization of stimuli based on gender (e.g., the upper part of a vertical axis for males and the lower part for females). The aim of the present study was threefold (1) to replicate and extend results on the existence of a mental gender line (as a function of response hand: female-left hand and male-right hand) when responding simply to gender of stimuli; (2) to explore the influence of inhibitory control; and, (3) to determine whether gender-space associations depend on the explicit or implicit nature of a gender task. Three experiments were designed to pursue these objectives. In Experiment 1, female, male and neutral faces and names were displayed, and the participants were asked to identify their gender. Experiment 2, which also included a Stroop task, followed the same procedure as Experiment 1, but displayed objects that could be designated as female or male and others not related to any gender. Finally, in Experiment 3, in which participants were asked to respond to the direction of an arrow, object gender was not relevant to the task. Consistent with previous research and confirming our hypotheses, the results showed a spatial mental representation of the stimuli based on gender in all three experiments, regardless of whether the stimulus was consciously perceived. Moreover, inhibitory ability showed a relationship with the gender-space line effect. The contributions and implications of this study are discussed, as are possible limitations and future lines of research.

EXPRESS: Influence of Different Spatial Representations on the SNARC Effect for Letters: Electrophysiological Evidence.

Studies have previously demonstrated that different spatial representations may affect the spatial-numerical association of response codes (SNARC) effect for numbers; however, limited studies have assessed the SNARC effect for letters. In this study, event-related potentials (ERPs) were used to measure the influence of two spatial representation modes (ruler and clock) on the SNARC effect. The ruler produced a SNARC-like effect; i.e., the left hand reacted faster than the right to the letters that appear before N in the alphabet; the right hand reacted faster than the left to the letters after N, whereas the clock produced a reverse SNARC effect. In addition, the ERP data showed that the SNARC-like effect for letters in both representations induced significant activation in the frontal and parietal regions, indicating that the same brain areas are involved in processing letters and numbers in terms of spatial dimensions. This study further identified the conditions for the SNARC effect and proved that the SNARC effect is attributed to the simultaneous participation of brain regions for sequence and spatial information processing.

Associations and indirect effects between LEGO® construction and mathematics performance.

There is a known association between LEGO® construction ability and mathematics achievement, yet the mechanisms which drive this association are largely unknown. This study investigated the spatial mechanisms underlying this association, and whether this differs for concrete versus digital construction. Between January 2020 and July 2021, children aged 7-9 years (N = 358, 189 female, ethnicity not recorded) completed spatial and mathematics tasks, and either a concrete or digital Lego construction task. Mediation analyses examining direct and indirect pathways (through spatial skills) between Lego construction ability and mathematics explained 8.4% to 26.6% of variance in mathematics scores. Exploratory moderated mediation analyses revealed that only the indirect path through mental rotation differed between Lego conditions. Findings are discussed in relation to theories of spatial-numerical associations and the potential of Lego training for mathematics improvement.

Stronger spatial bias induced more by numbers in mind than numbers in eye: Evidence from event-related potentials

The relationship between number and space is an important issue in numerical cognition. The spatial-numerical association of response codes (SNARC) effect is a classic example of the association between numbers and spaces. It refers to the phenomenon whereby left-handed responses occur faster to small number and right-handed responses occur faster to large number. The current study explored the shared and distinct neural correlates of the SNARC effect considering numbers in eye and numbers in mind, by using event-related potentials (ERPs) technology. In each trial of the task, participants were asked to press freely one of two keys as a response to a number presented visually (numbers in eye) or via imagination (numbers in mind). The behavioral results indicated that the free-choice key presses were affected by the magnitudes of the numbers either in eye or in mind. Electrophysiological results observed that the SNARC effect appeared only in the 110–140 ms time window for numbers in eye. In contrast, for numbers in mind, the SNARC effect appeared during a longer time window (110–330 ms). These results suggest that both, numbers in eye and numbers in mind, can induce spatial bias at the early stimulus-representation stage, but the time duration of the spatial bias is longer for numbers in mind than numbers in eye. This may reflect a closer connection between numbers in mind and mental number line.

Mirror numbers activate quantity representations, but show no SNARC effect: A working memory explanation.

The Spatial-Numerical Association of Response Code (SNARC) effect refers to the finding that people respond to small numbers faster with the left hand and to large numbers faster with the right hand. This effect is often explained by hypothesizing that the mental representation of quantities has a spatial component: left to right in ascending order (Mental Number Line). Here we assess the relation between quantity and spatial representation by investigating mirror numbers. Although mirror numbers denote quantity, they are not generally encountered in a left-to-right spatial organization. In Experiments 1 and 2, we assessed whether numerical distance and SNARC effects were present for both mirror and normal numbers when participants were required to process semantic information in a magnitude classification task. In Experiment 3, we assessed whether the SNARC effect was present for both mirror and normal numbers when participants were not required to process semantic information in a mirror judgment task. Results show that participants access the quantity of both normal and mirror numbers, but only normal numbers are spatially organized from left to right. In addition, we show that the physical similarity between numbers successfully predicted the performance of participants. We concluded that the Working Memory account of the SNARC effect best explains our data. (PsycInfo Database Record (c) 2023 APA, all rights reserved).