Task instructions determine the visuospatial and verbal–spatial nature of number–space associations

Evidence for number–space associations comes from the spatial–numerical association of response codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand, respectively. Two different proposals are commonly discussed concerning the cognitive origin of the SNARC effect: the visuospatial account and the verbal–spatial account. Recent studies have provided evidence for the relative dominance of verbal–spatial over visuospatial coding mechanisms, when both mechanisms were directly contrasted in a magnitude comparison task. However, in these studies, participants were potentially biased towards verbal–spatial number processing by task instructions based on verbal–spatial labels. To overcome this confound and to investigate whether verbal–spatial coding mechanisms are predominantly activated irrespective of task instructions, we completed the previously used paradigm by adding a spatial instruction condition. In line with earlier findings, we could confirm the predominance of verbal–spatial number coding under verbal task instructions. However, in the spatial instruction condition, both verbal–spatial and visuospatial mechanisms were activated to an equal extent. Hence, these findings clearly indicate that the cognitive origin of number–space associations does not always predominantly rely on verbal–spatial processing mechanisms, but that the spatial code associated with numbers is context dependent.     

Coding strategies in number space: Memory requirements influence spatial–numerical associations

The tendency to respond faster with the left hand to relatively small numbers and faster with the right hand to relatively large numbers (spatial numerical association of response codes, SNARC effect) has been interpreted as an automatic association of spatial and numerical information. We investigated in two experiments the impact of task-irrelevant memory representations on this effect. Participants memorized three Arabic digits describing a left-to-right ascending number sequence (e.g., 3–4–5), a descending sequence (e.g., 5–4–3), or a disordered sequence (e.g., 5–3–4) and indicated afterwards the parity status of a centrally presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the reaction times, the SNARC effect in the parity task was mediated by the coding requirements of the memory tasks. That is, a SNARC effect was only present after memorizing ascending or disordered number sequences but disappeared after processing descending sequences. Interestingly, the effects of the second task were only present if all sequences within one experimental block had the same type of order. Taken together, our findings are inconsistent with the idea that spatial–numerical associations are the result of an automatic and obligatory cognitive process but do suggest that coding strategies might be responsible for the cognitive link between numbers and space.     

Language statistics explain the spatial–numerical association of response codes

The spatial–numerical association of response codes (SNARC) has shown that parity judgments with participants’ left hands yield faster response times (RTs) for smaller numbers than for larger numbers, with the opposite result for right-hand responses. These findings have been explained by participants perceptually simulating magnitude on a mental number line. In three RT experiments, we showed that the SNARC effect can also be explained by language statistics. Participants made parity judgments of number words (Exp. 1) and Arabic numerals (Exp. 2). Linguistic frequencies of the number words and numbers mirrored the SNARC effect, explaining aspects of processing that a perceptual simulation account could not. In Experiment 3, we investigated whether high- and low-frequency nonnumerical words would also elicit a SNARC-like effect. Again, RTs were faster for high-frequency words for left-hand responses, with the opposite result for right-hand responses. These results demonstrate that what has only been attributed to perceptual simulation should also be attributed to language statistics.     

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 Fischer, M. H., Riello, M., Giordano, B. L., &; Rusconi, E. (2013). Singing numbers?…?in cognitive space--a dual-task study of the link between pitch, space, and numbers. Topics in Cognitive Science, 5(2), 354–366. Retrieved from http://doi.org/10.1111/tops.12017[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). 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 impact of inhibition capacities and age on number–space associations

Numerical and spatial representations are tightly linked, i.e., when doing a binary classification judgment on Arabic digits, participants are faster to respond with their left/right hand to small/large numbers, respectively (Spatial-Numerical Association of Response Codes, SNARC effect, Dehaene et al. in J Exp Psychol Gen 122:371–396, 1993). To understand the underlying mechanisms of the well-established SNARC effect, it seems essential to explore the considerable inter-individual variability characterizing it. The present study assesses the respective roles of inhibition, age, working memory (WM) and response speed. Whereas these non-numerical factors have been proposed as potentially important factors to explain individual differences in SNARC effects, none (except response speed) has so far been explored directly. Confirming our hypotheses, the results show that the SNARC effect was stronger in participants that had weaker inhibition abilities (as assessed by the Stroop task), were relatively older and had longer response times. Interestingly, whereas a significant part of the age influence was mediated by cognitive inhibition, age also directly impacted the SNARC effect. Similarly, cognitive inhibition abilities explained inter-individual variability in number–space associations over and above the factors age, WM capacity and response speed. Taken together our results provide new insights into the nature of number–space associations by describing how these are influenced by the non-numerical factors age and inhibition.     

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).     

Measuring spatial–numerical associations: evidence for a purely conceptual link

Previous work on spatial–numerical association (SNAs) included either spatially distributed stimuli or responses. This raises the possibility that the inferred spatial nature of number concepts was a methodological artifact. We present results from a novel task that involves two categories (spatially oriented objects and number magnitudes) and dissociates spatial classification from number classification. The results reveal SNAs without inferential limitations of previous work and point to a working memory mechanism that transfers spatial coding across categories.     

Influences of multiple spatial stimulus and response codes on orthogonal stimulus—response compatibility

When up-down stimuli are mapped to left-right responses, an up-right/down-left mapping advantage is found that is modified by response eccentricity and hand posture. These effects can be attributed to correspondence of asymmetric stimulus and response codes formed relative to multiple reference frames. We examined the influence of stimulus-set location on these orthogonal stimulus-response compatibility (SRC) effects. In Experiment 1, the stimulus set appeared in the upper or lower display positions. A spatial code for stimulus-set location was formed, producing Simon-type response eccentricity and hand posture effects, but this code had no influence on the coding of the relevant stimuli. In Experiment 2, the stimulus set appeared in the left, center, or right positions relative to the response location, which also varied, to dissociate the effects of response location, relative to the stimulus display and body midline. The former factor influenced the orthogonal SRC effect for both unimanual switch movements and bimanual keypresses, and the latter factor influenced the effect for only unimanual switch movements. Stimulus-set location causes orthogonal Simon-type effects when varied along the stimulus dimension and provides a referent for response coding when varied along the response dimension.     

How to cook a SNARC: Number placement in text rapidly changes spatial–numerical associations

Most theoreticians believe that reading habits explain why Western adults associate small numbers with left space and large numbers with right space (the SNARC effect). We challenge this belief by documenting, in both English and Hebrew, that SNARC changes during reading: small and large numbers in our texts appeared near the left or right ends of the lines, positioned either spatially congruent or incongruent with reading habits. In English, the congruent group showed reliable SNARC before and after reading and the incongruent group’s SNARC was significantly reduced. In Hebrew the incongruent reading condition even induced a reverse SNARC. These results show that SNARC is a fleeting aspect of number representation that captures multiple spatial associations.     

Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds

Human adults’ numerical representation is spatially oriented; consequently, participants are faster to respond to small/large numerals with their left/right hand, respectively, when doing a binary classification judgment on numbers, known as the SNARC (spatial–numerical association of response codes) effect. Studies on the emergence and development of the SNARC effect remain scarce. The current study introduces an innovative new paradigm based on a simple color judgment of Arabic digits. Using this task, we found a SNARC effect in children as young as 5.5 years. In contrast, when preschool children needed to perform a magnitude judgment task necessitating exact number knowledge, the SNARC effect started to emerge only at 5.8 years. Moreover, the emergence of a magnitude SNARC but not a color SNARC was linked to proficiency with Arabic digits. Our results suggest that access to a spatially oriented approximate magnitude representation from symbolic digits emerges early in ontogenetic development. Exact magnitude judgments, on the other hand, rely on experience with Arabic digits and, thus, necessitate formal or informal schooling to give access to a spatially oriented numerical representation.     

Beyond the mental number line: A neural network model of number–space interactions

It is commonly assumed that there is an interaction between the representations of number and space (e.g., Dehaene et al., 1993, Walsh, 2003), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but that instead spatial and numerical representations are separate. However, cultural factors establish ties between them. By extending earlier models (Gevers et al., 2006, Verguts et al., 2005) based on this hypothesis, the authors present computer simulations showing that a model incorporating this idea can account for data from a series of studies. These results suggest that number–space interactions are emergent properties resulting from the interaction between different brain areas.     

Finger counting habit and spatial–numerical association in children and adults

Sensory-motor experiences are known to build up concrete and abstract concepts during the lifespan. The present study aimed to test how finger counting habits (right-hand vs. left-hand starters) could influence the spatial–numerical representation in number-to-position (explicit) and digit-string bisection (implicit) tasks. The subjects were Italian primary school children (N = 184, from the first to the fifth year) and adults (N = 42). No general preference for right- or left-starting in the finger counting was found. In the explicit task, right- or left-starting did not affect performance. In the implicit task, the right-hand starters shifted from the left to the right space when bisecting small and large numbers respectively, while the left-hand starters shifted from the right to the left space with higher leftward bias for large numbers. The finger configuration in Italian children and adults influences the spatial–numerical representation, but only when implicit number processing is required by the task.     

Action–perception coupling in pianists: Learned mappings or spatial musical association of response codes (SMARC) effect?

The principle of common coding suggests that a joint representation is formed when actions are repeatedly paired with a specific perceptual event. Musicians are occupationally specialized with regard to the coupling between actions and their auditory effects. In the present study, we employed a novel paradigm to demonstrate automatic action–effect associations in pianists. Pianists and nonmusicians pressed keys according to aurally presented number sequences. Numbers were presented at pitches that were neutral, congruent, or incongruent with respect to pitches that would normally be produced by such actions. Response time differences were seen between congruent and incongruent sequences in pianists alone. A second experiment was conducted to determine whether these effects could be attributed to the existence of previously documented spatial/pitch compatibility effects. In a “stretched” version of the task, the pitch distance over which the numbers were presented was enlarged to a range that could not be produced by the hand span used in Experiment 1. The finding of a larger response time difference between congruent and incongruent trials in the original, standard, version compared with the stretched version, in pianists, but not in nonmusicians, indicates that the effects obtained are, at least partially, attributable to learned action effects.     

Effects of visual cue and response assignment on spatial stimulus coding in stimulus–response compatibility

Tlauka and McKenna (2000 Tlauka, M. and McKenna, F. P. 2000. Hierarchical knowledge influences stimulus–response compatibility effects. Quarterly Journal of Experimental Psychology, 53A: 85–103.  [Google Scholar]) reported a reversal of the traditional stimulus–response compatibility (SRC) effect (faster responding to a stimulus presented on the same side than to one on the opposite side) when the stimulus appearing on one side of a display is a member of a superordinate unit that is largely on the opposite side. We investigated the effects of a visual cue that explicitly shows a superordinate unit, and of assignment of multiple stimuli within each superordinate unit to one response, on the SRC effect based on superordinate unit position. Three experiments revealed that stimulus–response assignment is critical, while the visual cue plays a minor role, in eliciting the SRC effect based on the superordinate unit position. Findings suggest bidirectional interaction between perception and action and simultaneous spatial stimulus coding according to multiple frames of reference, with contribution of each coding to the SRC effect flexibly varying with task situations.     

The influence of the response–stimulus interval on implicit and explicit learning of stimulus sequence

Three experiments investigated the influence of the response-stimulus interval (RSI) on implicit and explicit learning of stimulus sequences. Participants responded to numerals presented in predetermined positions with alternating long and short RSIs. Half of the participants were instructed explicitly to learn the position sequence. In the transfer phase of Experiments 1 and 2, changing RSI patterns reduced the expression of incidental and intentional learning of position sequence. In Experiment 3 the position sequence was transformed, except that sub-sequences demarcated by long RSIs remained unchanged; this greatly reduced the expression of intentional learning, and slightly reduced that of incidental learning. These results indicate that in implicit learning, stimulus sequences are learned under the constraints of RSIs, whereas in explicit learning, learning independent of RSIs, as well as learning constrained by RSIs, occurs.     

Preferring alphabet–keyboard compatibility: Congruency between spatial codes shapes the affective connotation of letters

When letters are encountered, two spatial stimulus codes resulting from their positions within the alphabet and on the computer keyboard are activated mentally. If these two spatial codes match, letter processing is more efficient. The present study tested whether the processing fluency gain resulting from alphabet–keyboard compatibility also enhances affective evaluations of letters. In Experiment 1, participants preferred alphabet–keyboard compatible over incompatible letters in a forced-choice preference rating. Similarly, in Experiment 2, liking ratings for alphabet–keyboard compatible letters were higher compared to incompatible letters. Moreover, in Experiment 3, preference ratings of non-words were positively correlated with the relative number of alphabet–keyboard compatible letters within these letter strings. These findings suggest that alphabet–keyboard compatibility shapes the affective connotation of letters. Moreover, this processing fluency–valence association is activated at the level of letters as well as whole letter strings.     

Stimulus–classification and stimulus–action associations: Effects of repetition learning and durability

It has been shown that acquired stimulus–response bindings result from at least two types of associations from the stimulus to the task (stimulus–task or stimulus–classification; S–C) and from the stimulus to the motor response (stimulus–response or stimulus–action; S–A). These types of associations have been shown to independently affect behaviour. This finding suggests that they are processed in different pathways or different parts of a pathway at the neural level. Here we test a hypothesis that such associations may be differentially affected by repetition learning and that such effects may be detected by measuring their durability against overwriting. We show that both S–C and S–A associations are in fact strengthened when learning is boosted by increasing repetitions of the primes. However, the results further suggest that associations between stimuli and actions have less durable effects on behaviour and that the durability of S–C and S–A associations is independent of repetition learning. This is an important finding for the understanding of the underlying mechanisms of associative learning and particularly raises the question of which processes may affect flexibility of learning.     

Reaction time measures in deception research: Comparing the effects of irrelevant and relevant stimulus–response compatibility

Evidence regarding the validity of reaction time (RT) measures in deception research is mixed. One possible reason for this inconsistency is that structurally different RT paradigms have been used. The aim of this study was to experimentally investigate whether structural differences between RT tasks are related to how effective those tasks are for capturing deception. We achieved this aim by comparing the effectiveness of relevant and irrelevant stimulus–response compatibility (SRC) tasks. We also investigated whether an intended but not yet completed mock crime could be assessed with both tasks. Results showed (1) a larger compatibility effect in the relevant SRC task compared to the irrelevant SRC task, (2) for both the completed and the intended crime. These results were replicated in a second experiment in which a semantic feature (instead of color) was used as critical response feature in the irrelevant SRC task. The findings support the idea that a structural analysis of deception tasks helps to identify RT measures that produce robust group effects, and that strong compatibility effects for both enacted crimes as well as merely intended crimes can be found with RT measures that are based on the manipulation of relevant SRC.     

Approximate number sense,symbolic number processing,or number–space mappings: What underlies mathematics achievement?

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children’s performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well children compared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.