Spatial-numerical Association Of Response Codes Effect Research Articles

Cognitive Mechanisms Underlying Directional and Non-directional Spatial-Numerical Associations across the Lifespan.

There is accumulating evidence suggesting an association of numbers with physical space. However, the origin of such spatial-numerical associations (SNAs) is still debated. In the present study we investigated the development of two SNAs in a cross-sectional study involving children, young and middle-aged adults as well as the elderly: (1) the SNARC (spatial-numerical association of response codes) effect, reflecting a directional SNA; and (2) the numerical bisection bias in a line bisection task with numerical flankers. Results revealed a consistent SNARC effect in all age groups that continuously increased with age. In contrast, a numerical bisection bias was only observed for children and elderly participants, implying an U-shaped distribution of this bias across age groups. Additionally, individual SNARC effects and numerical bisection biases did not correlate significantly. We argue that the SNARC effect seems to be influenced by longer-lasting experiences of cultural constraints such as reading and writing direction and may thus reflect embodied representations. Contrarily, the numerical bisection bias may originate from insufficient inhibition of the semantic influence of irrelevant numerical flankers, which should be more pronounced in children and elderly people due to development and decline of cognitive control, respectively. As there is an ongoing debate on the origins of SNAs in general and the SNARC effect in particular, the present results are discussed in light of these differing accounts in an integrative approach. However, taken together, the present pattern of results suggests that different cognitive mechanisms underlie the SNARC effect and the numerical bisection bias.

Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not difficult to detect a SNARC effect within a group, but it has been quite unusual to find group differences. Is the SNARC effect as it is usually estimated using regression slopes largely insensitive to group differences, and are there design parameters necessary to increase sensitivity in group comparison analyses? Using numerical simulations, we provide evidence that both sample size and the number of stimulus repetitions, as well as intra-individual variability, contribute in a substantial way to the probability of detecting an existing SNARC effect. Our results show that the adequate choice of either sample size or number of repetitions per experimental cell does not fully compensate for a poor choice of the other parameter. Moreover, repeated failures to find significant group differences in the SNARC effect can be explained by insufficient power. Fortunately, increasing the number of repetitions to about 20 and testing at least 20 participants provides in most cases sufficient sensitivity to reliably detect the SNARC effect as well as group differences. Power plots are provided, which may help to improve both the economy and sensitivity of experimental design in future SNARC experiments, or, more generally when regression slopes are estimated intra-individually.

Perceiving Musical Note Values Causes Spatial Shift of Attention in Musicians

The Spatial-Numerical Association of Response Codes (SNARC) suggests the existence 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. The attentional SNARC effect (Att-SNARC) suggests that perceiving numbers can also affect the allocation of spatial attention, causing a leftward (vs. rightward) target detection advantage after perceiving small (vs. large) numbers. Considering previous findings that revealed similar spatial association effects for both numbers and musical note values (i.e., the relative duration of notes), the aim of this study is to investigate whether presenting note values instead of numbers causes a spatial shift of attention in musicians. The results show an advantage in detecting a leftward (vs. rightward) target after perceiving small (vs. large) musical note values. The fact that musical note values cause a spatial shift of attention strongly suggests that musicians process numbers and note values in a similar manner.

Transcranial direct current stimulation (tDCS) reveals a dissociation between SNARC and MARC effects: Implication for the polarity correspondence account

The concept of stimulus response compatibility (SRC) refers to the existence of a privileged association between a specific stimulus feature and a specific response feature. Two examples of SRC are the Spatial Numerical Association of Response Codes (SNARC) and the Markedness Association of Response Codes (MARC) effects. According to the polarity correspondence principle, these two SRC effects occur because of a match between the most salient dimensions of stimulus and response. Specifically, the SNARC effect would be caused by a match between right-sided responses and large numbers, while a match between right-sided responses and even numbers would give rise to the MARC effect. The aim of the present study was to test the validity of the polarity correspondence principle in explaining these two SRC effects. To this end, we applied transcranial direct current stimulation (tDCS) over left and right posterior parietal cortex (PPC), which is thought to be the neural basis of salience processing, during a parity judgement task. Results showed that cathodal tDCS over the PPC significantly reduced the MARC effect but did not affect the SNARC effect, suggesting a dissociation between the two effects. That is, the MARC would rely on a salience processing mechanism, whereas the SNARC would not. Despite this interpretation is in need of further experimental confirmations (i.e., testing different tasks or using different tDCS montages), our results suggest that the polarity correspondence principle can be a plausible explanation only for the MARC effect but not for the SNARC effect.

Mathematical abilities in elementary school: Do they relate to number–space associations?

Considering the importance of mathematics in Western societies, it is crucial to understand the cognitive processes involved in the acquisition of more complex mathematical skills. The current study, therefore, investigated how the quality of number–space mappings on the mental number line, as indexed by the parity SNARC (spatial–numerical association of response codes) effect, relates to mathematical performances in third- and fourth-grade elementary school children. Mathematical competencies were determined using the “Heidelberger Rechentest,” a standardized German math test assessing both arithmetical and visuospatial math components. Stronger parity SNARC effects significantly related to better arithmetical but not visuospatial math abilities, albeit only in the relatively younger children. These findings highlight the importance of spatial–numerical interactions for arithmetical (as opposed to visuospatial) math skills at the fairly early stages of mathematical development. Differential relations might be explained by the reliance on problem-solving strategies involving number–space mappings only for arithmetic tasks mainly in younger children.

It does exist! A left-to-right spatial-numerical association of response codes (SNARC) effect among native Hebrew speakers.

Several studies, starting with Dehaene, Bossini, and Giraux (1993), have reported that, in parity-judgment tasks, the difference in response latencies generated by the right and left hand are negatively correlated with number magnitudes. This SNARC (spatial-numerical association of response codes) effect is in line with the notion that the "mental number line" extends from left to right. The SNARC effect has been found mainly in native speakers of Germanic/Romanic languages; it has been suggested that the SNARC effect may derive from the experience of reading from left to right. To date, there is no evidence that the SNARC (or reverse SNARC) effect exists in parity judgments in native speakers of Hebrew readers. Here we provide the first demonstration of a horizontal, left-to-right SNARC effect in native speakers of Hebrew performing the parity task. Although we found no SNARC effect using the standard parity task, a reliable SNARC effect was found when we succeeded in reducing the MARC (markedness association of response codes) effect. We succeeded in reducing the MARC effect by implementing the parity task in 2 sessions, on 2 different days, each time using a different mapping of the parity-to-response side. (PsycINFO Database Record

The SNARC Effect in Number Memorization and Retrieval. What is the Impact of Congruency, Magnitude and the Exact Position of Numbers in Short-Term Memory Processing?

Mental representations of numbers are spatially organized along a Mental Number Line (MNL). One widely proven manifestation of this relationship is the Spatial Numerical Association of Response Codes (SNARC) effect. It refers to the phenomenon of faster responses to numbers when there is congruency between the reaction side and the number position on the MNL . Although long-term memory is considered to house the MNL, short-term memory (STM) load may also modulate responses to numbers and the SN ARCRC effect. Our question, however, was not how STM content modulates the SNARC effect observed in responses to digits, but rather how the MNLNL representation affects the number retrieval from ST M. Each trial began with four digits presented horizontally in a spatial sequence (prime stimuli), which were then replaced by one of the priming digits as a single target. The task required participants to recall the exact location of the target. The SN ARCRC effect occurred only in the retrieval of left-sided digits, most likely because of the generally better processing of right-sided ones, as well as in reaction to digits presented more laterally. Moreover, memory processing was more efficient with low-magnitude numbers, which may suggest that they trigger attention shifting. We conclude that the MNL affects not only the responses to numbers obtained in typical SNARC-induction tasks, such as number detection, parity judgment or magnitude comparison, but also memorization and retrieval of them. Importantly, this effect seems to be dependent on the exact position of a digit in STM.

The SNARC effect in two dimensions: Evidence for a frontoparallel mental number plane

The existence of an association between numbers and space is known for a long time. The most prominent demonstration of this relationship is the spatial numerical association of response codes (SNARC) effect, describing the fact that participants’ reaction times are shorter with the left hand for small numbers and with the right hand for large numbers, when being asked to judge the parity of a number (Dehaene et al., J. Exp. Psychol., 122, 371–396, 1993). The SNARC effect is commonly seen as support for the concept of a mental number line, i.e. a mentally conceived line where small numbers are represented more on the left and large numbers are represented more on the right. The SNARC effect has been demonstrated for all three cardinal axes and recently a transverse SNARC plane has been reported (Chen et al., Exp. Brain Res., 233(5), 1519–1528, 2015). Here, by employing saccadic responses induced by auditory or visual stimuli, we measured the SNARC effect within the same subjects along the horizontal (HM) and vertical meridian (VM) and along the two interspersed diagonals. We found a SNARC effect along HM and VM, which allowed predicting the occurrence of a SNARC effect along the two diagonals by means of linear regression. Importantly, significant differences in SNARC strength were found between modalities. Our results suggest the existence of a frontoparallel mental number plane, where small numbers are represented left and down, while large numbers are represented right and up. Together with the recently described transverse mental number plane our findings provide further evidence for the existence of a three-dimensional mental number space.

The effect of working memory load on the SNARC effect: Maybe tasks have a word to say.

We investigated the effect of working memory load on the SNARC (spatial-numerical association of response codes) effect under different number judgment tasks (parity judgment and magnitude comparison), using a novel dual task. Instead of exerting load over the whole block of number judgment trials, in this dual task, number judgment trials were inserted into each interstimulus interval of an n-back task, which served as the working memory load. We varied both load type (verbal and spatial) and amount (1-load, 2-load, and 3-load). The results indicated that the SNARC effect disappeared even under the 1-load condition for a parity judgment, regardless of the type of load. However, during the magnitude comparison task, the SNARC effect increased with increasing load amounts under spatial load conditions; under verbal load conditions, the SNARC effect decreased with increasing amounts of load, and disappeared during the 3-load task. The difference between the parity and magnitude tasks was not attributable to the interval stimuli or task switching. These findings confirm that different spatial-numerical associations for comparing numerical magnitudes and judgments of parity have different needs with respect to working memory resources.

Dancing with the SNARC: Measuring spatial-numerical associations on a digital dance mat.

According to the concept of embodied numerosity, bodily experiences influence the way in which we process numerical magnitude. The development of this influence could be anchored in the spatial ordering of numbers along a mental number line representation, which is measured by effects of spatial-numerical associations. The aim of this study was to investigate whether horizontally oriented full-body movement and visual presentation of a number line both contribute to spatial-numerical associations in children. We presented fourth-graders with 2 magnitude comparison tasks that differed in the relevance of magnitude information. In both tasks, we varied the amount of bodily movement in different response conditions (responding verbally, with a foot tap, or by jumping) and the visual presentation (items were presented with or without a number line). From the data, we calculated 2 spatial-numerical effects and expected to find the strongest effects if a full-body response was combined with a number line presentation. The 2 effects were differentially influenced by response modalities, but not presentation. The SNARC (= Spatial Numerical Association of Response Codes) effect was present in all conditions and was not influenced by our manipulations. In contrast, a new relative numerical congruity effect was influenced by the variations in responses in accordance with our hypotheses. The relative numerical congruity effect results suggest that responses involving bodily movement increase activation of spatial-numerical associations compared to verbal responses. These results are the first to demonstrate such an influence in a full-body approach in elementary schoolchildren. (PsycINFO Database Record

Spatial reference frames and SNARC

ABSTRACTIn this work, the role that spatial reference frames play in determining the spatial-numerical association of response codes (SNARC) effect is examined. Participants were instructed to generate an image of the numbers 1–9 oriented spatially in either a horizontal, vertical, or proximo-distal manner. Responses to a magnitude comparison task were then provided manually using keys located either to the left and right or at the bottom and top of a computer keyboard. For conditions in which the orientation of the generated image and the response locations were orthogonally misaligned, SNARC effects were not evident. It is argued that such results imply that alignment of the spatial reference frames associated with the responses and with the representation of numerical magnitude is a necessary condition for the elicitation of the SNARC effect.

Counteracting Implicit Conflicts by Electrical Inhibition of the Prefrontal Cortex.

Cognitive conflicts and distractions by task-irrelevant information often counteract effective and goal-directed behaviors. In some cases, conflicting information can even emerge implicitly, without an overt distractor, by the automatic activation of mental representations. For instance, during number processing, magnitude information automatically elicits spatial associations resembling a mental number line. This spatial-numerical association of response codes (SNARC) effect can modulate cognitive-behavioral performance but is also highly flexible and context-dependent, which points toward a critical involvement of working memory functions. Transcranial direct current stimulation to the PFC, in turn, has been effective in modulating working memory-related cognitive performance. In a series of experiments, we here demonstrate that decreasing activity of the left PFC by cathodal transcranial direct current stimulation consistently and specifically eliminates implicit cognitive conflicts based on the SNARC effect, but explicit conflicts based on visuospatial distraction remain unaffected. This dissociation is polarity-specific and appears unrelated to functional magnitude processing as classified by regular numerical distance effects. These data demonstrate a causal involvement of the left PFC in implicit cognitive conflicts based on the automatic activation of spatial-numerical processing. Corroborating the critical interaction of brain stimulation and neurocognitive functions, our findings suggest that distraction from goal-directed behavior by automatic activation of implicit, task-irrelevant information can be blocked by the inhibition of prefrontal activity.

How Math Anxiety Relates to Number-Space Associations.

Given the considerable prevalence of math anxiety, it is important to identify the factors contributing to it in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of more complex arithmetic skills. Recent evidence, however, suggests that deficits in basic numerical processing and spatial skills also constitute potential risk factors of math anxiety. Given these observations, we determined whether math anxiety also depends on the quality of spatial-numerical associations. Behavioral evidence for a tight link between numerical and spatial representations is given by the SNARC (spatial-numerical association of response codes) effect, characterized by faster left-/right-sided responses for small/large digits respectively in binary classification tasks. We compared the strength of the SNARC effect between high and low math anxious individuals using the classical parity judgment task in addition to evaluating their spatial skills, arithmetic performance, working memory and inhibitory control. Greater math anxiety was significantly associated with stronger spatio-numerical interactions. This finding adds to the recent evidence supporting a link between math anxiety and basic numerical abilities and strengthens the idea that certain characteristics of low-level number processing such as stronger number–space associations constitute a potential risk factor of math anxiety.

Separate mechanisms for magnitude and order processing in the spatial-numerical association of response codes (SNARC) effect: The strange case of musical note values.

The spatial-numerical association of response codes (SNARC) effect is considered an evidence of the association between numbers and space, with faster left key-press responses to small numbers and faster right key-press responses to large numbers. We examined whether visually presented note values produce a SNARC-like effect. Differently from numbers, note values are represented as a decreasing left-to-right progression, allowing us to disambiguate the contribution of order and magnitude in determining the direction of the effect. Musicians with formal education performed a note value comparison in Experiment 1 (direct task), a line orientation judgment in Experiment 2 (indirect task), and a detection task in Experiment 3 (indirect task). When note values were task relevant (direct task), participants responded faster to large note values with the left key-press, and vice versa. Conversely, when note values were task irrelevant (indirect tasks), the direction of this association was reversed. This evidence suggests the existence of separate mechanisms underlying the SNARC effect. Namely, an Order-Related Mechanism (ORM) and a Magnitude-Related Mechanism (MRM) that are revealed by different task demands. Indeed, according to a new model we proposed, ordinal and magnitude related information appears to be preferentially involved in direct and indirect tasks, respectively. (PsycINFO Database Record

SNARC (spatial-numerical association of response codes) meets SPARC (spatial-pitch association of response codes): Automaticity and interdependency in compatibility effects.

Concepts, including the mental number line, or addressing pitch as high and low, suggest that the spatial-numerical and spatial-pitch association of response codes (SNARC and SPARC) effects are domain-specific and thus independent. Alternatively, there may be dependencies between these effects, because they share common automatic or controlled decision mechanisms. In two experiments, participants were presented with spoken numbers in different pitches; their numerical value, pitch, and response compatibility were varied systematically. This allowed us to study SNARC and SPARC effects in a factorial design (see also Fischer, Riello, Giordano, & Rusconi, 2013 ). Participants judged the stimuli on numerical magnitude, pitch, or parity (odd-even). In all tasks, the SNARC and SPARC effects had superadditive interactions. These were interpreted as both effects sharing a common mechanism. The task variation probes the mechanism: In the magnitude judgement task, numerical magnitude was explicit, whereas pitch was implicit; in the pitch judgement task, it was vice versa. In the parity judgement task, both dimensions were implicit. Regardless of whether they were implicit or explicit, both SNARC and SPARC effects occurred in all tasks. We concluded that by not requiring focal attention the common mechanism operates automatically.

The Instructional Dependency of SNARC Effects Reveals Flexibility of the Space-Magnitude Association of Nonsymbolic and Symbolic Magnitudes.

The Spatial-Numerical Association of Response Codes (SNARC) effect refers to the phenomenon that small versus large numbers are responded to faster in the left versus right side of space, respectively. Using a pairwise comparison task, Shaki etal. found that task instruction influences the pattern of SNARC effects of certain types of magnitudes which are less rigid in their space-magnitude association .The present study examined the generalizability of this instruction effect using pairwise comparison of nonsymbolic and symbolic stimuli within a wide range of magnitudes. We contrasted performance between trials in which subjects were instructed to select the stimulus representing the smaller versus larger magnitude within each pair. We found an instruction-dependent pattern of SNARC effects for both nonsymbolic and symbolic magnitudes. Specifically, we observed a SNARC effect for the "Select Smaller" instruction, but a reverse SNARC effect for the "Select Larger" instruction. Considered together with previous studies, our findings suggest that nonsymbolic magnitudes and relatively large symbolic magnitudes have greater flexibility in their space-magnitude association.

The underlying number–space mapping among kindergarteners and its relation with early numerical abilities

People map numbers onto space. The well-replicated SNARC (spatial–numerical association of response codes) effect indicates that people have a left-sided bias when responding to small numbers and a right-sided bias when responding to large numbers. This study examined whether such spatial codes were tagged to the ordinal or magnitude information of numbers among kindergarteners and whether it was related to early numerical abilities. Based on the traditional magnitude judgment task, we developed two variant tasks—namely the month judgment task and dot judgment task—to elicit ordinal and magnitude processing of numbers, respectively. Results showed that kindergarteners oriented small numbers toward the left side and large numbers toward the right side when processing the ordinal information of numbers in the month judgment task but not when processing the magnitude information in the number judgment task and dot judgment task, suggesting that the left-to-right spatial bias was probably tagged to the ordinal but not magnitude property of numbers. Moreover, the strength of the SNARC effect was not related to early numerical abilities. These findings have important implications for the early spatial representation of numbers and its role in numerical performance among kindergarteners.

Spatial-Numerical and Ordinal Positional Associations Coexist in Parallel.

There is evidence for a systematic association of numbers and space. A prominent finding supporting this notion is the spatial-numerical association of response codes (SNARC) effect describing relatively faster responses to smaller numbers using a left-hand key and to larger numbers using a right-hand key. However, the assumption of the SNARC effect reflecting spatial-numerical associations was challenged recently. A working memory account was proposed suggesting that not numbers per se but their position in a memorized sequence is associated with space. Yet, there is also first evidence suggesting that this ordinal position and the SNARC effect may not be mutually exclusive. In the present study, we further examined the relationship between the ordinal position and the SNARC effect. We manipulated the number of items in the memorized ordered sequence and the number range employed. Results revealed both a significant ordinal position effect, but also a significant SNARC effect, substantiating the view that both effects are not mutually exclusive but may co-exist. Furthermore, we found that the SNARC effect was reduced when numbers ranging from 1 to 10 versus numbers ranging from 1 to 9 were employed. Thus, our results question a pure working memory account for the SNARC effect. Additionally, they highlight the critical role of the number range employed in research about the SNARC effect.

Bad-good constraints on a polarity correspondence account for the spatial-numerical association of response codes (SNARC) and markedness association of response codes (MARC) effects.

Performance in numerical classification tasks involving either parity or magnitude judgements is quicker when small numbers are mapped onto a left-sided response and large numbers onto a right-sided response than for the opposite mapping (i.e., the spatial-numerical association of response codes or SNARC effect). Recent research by Gevers et al. [Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number-space interactions. Journal of Experimental Psychology: General, 139, 180-190] suggests that this effect also arises for vocal "left" and "right" responding, indicating that verbal-spatial coding has a role to play in determining it. Another presumably verbal-based, spatial-numerical mapping phenomenon is the linguistic markedness association of response codes (MARC) effect whereby responding in parity tasks is quicker when odd numbers are mapped onto left-sided responses and even numbers onto right-sided responses. A recent account of both the SNARC and MARC effects is based on the polarity correspondence principle [Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132, 416-442]. This account assumes that stimulus and response alternatives are coded along any number of dimensions in terms of - and + polarities with quicker responding when the polarity codes for the stimulus and the response correspond. In the present study, even-odd parity judgements were made using either "left" and "right" or "bad" and "good" vocal responses. Results indicated that a SNARC effect was indeed present for the former type of vocal responding, providing further evidence for the sufficiency of the verbal-spatial coding account for this effect. However, the decided lack of an analogous SNARC-like effect in the results for the latter type of vocal responding provides an important constraint on the presumed generality of the polarity correspondence account. On the other hand, the presence of robust MARC effects for "bad" and "good" but not "left" and "right" vocal responses is consistent with the view that such effects are due to conceptual associations between semantic codes for odd-even and bad-good (but not necessarily left-right).

Using Key Distance to Clarify a Theory on the SNARC

The most prominent explanation for the spatial numerical association of response codes (SNARC) effect is the direct mapping account (DMA). The DMA assumes that (a) numbers are represented on a mental number line, (b) this mental number line is mapped to external space, and (c) the better the mapping location corresponds to the response location, the faster the response. The DMA leaves open whether a variation of response locations can (ceteris paribus) influence the location to which numbers are mapped in external space. In order to investigate this question, we varied response key distance during a standard parity judgment and a magnitude judgment task. We found that even drastic manipulations of response key distance did not modulate the SNARC effect. Power and meta-analyses show that this null effect is not due to insufficient statistical power or a poor experimental setup. Thus, our results indicate that, in order for the DMA to explain the SNARC effect, it must assume that the mapping from the mental number line to external space is anchored to response location. For future research, our results suggest that it is not necessary to control the horizontal separation of the response keys in basic SNARC experiments.