Unit-decade Compatibility Effect Research Articles

Laterality in simple multiplication: Assessing hemispheric specialization of arithmetic fact retrieval in a visual hemifield paradigm.

The prominent view in numerical cognition is that highly overlearned arithmetic facts are verbally mediated and unilaterally processed in a left-hemispheric network, including language areas. However, this view has recently been challenged. Here, we evaluated the hemispheric specialization of verbal arithmetic fact retrieval and number magnitude processing using two verification tasks (i.e., multiplication and number magnitude comparison) in a divided hemifield paradigm in healthy participants (n = 35). In the number comparison task, we replicated bilateral processing advantages for the unit-decade compatibility effect. Magnitude processing was facilitated after bilateral compared with a unilateral presentation. In the multiplication task, lateralized presentation to the left hemisphere yielded processing advantages in arithmetic fact retrieval when the required interhemispheric transitions from the input, processing, and output stages were considered. Crucially, we observed a systematic processing advantage in left visual hemifield stimuli presentation (i.e., initial right-hemisphere processing). Our findings corroborate the assumption that arithmetic fact retrieval is subserved by left-lateralized verbal/linguistic processing. Thereby, they suggest a distinction between unilateral left-hemispheric linguistic processing of arithmetic fact retrieval and bilateral number magnitude processing. Interestingly, however, our data present right-hemispheric processing advantages in identifying early processed visual symbolic numerical stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Differential processing of "small" and "large" multidigit numbers.

Little is known about the mental representation of large multidigit numbers that are usually beyond our personal experience. The present study explored the processing mechanisms of these numbers in a series of experiments, using the numerical comparison task. Experiment 1 included within and between-scale comparisons of multidigit numbers varying in their left digits (e.g., 8,000,000), with one group comparing small numbers (tens, hundreds, and thousands) and the other large ones (millions, billions, and trillions). In Experiment 2, comparisons of small (tens, hundreds) and large (millions, billions) multidigit numbers that varied in their left and right digits (e.g., 8,000,003) were presented in separate blocks. Experiment 3 presented small and large multidigit numbers (from tens to trillions) that varied in their left digits in the same block. We found novel compatibility effects between the left digit and scale components, as well as between the left digit, right digit, and scale components, and extended the previously reported unit-decade compatibility effect to larger scales. We also obtained global and scale distance effects for all scales in most conditions. Both compatibility and distance effects showed context dependency in large, but not small, multidigit numbers. Overall, these results demonstrate that small and large multidigit numbers are processed differently. We discuss these differences and propose a processing model that accounts for them. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Cognitive control in number processing: new evidence from number compatibility effects in task-switching.

A growing body of research suggests that basic numerical abilities such as number magnitude processing are influenced by cognitive control processes. So far, evidence for number processing being affected by cognitive control processes stems primarily from observed adaptations of numerical effects to stimulus set characteristics (e.g. order or ratio of specific stimulus types). Complementing previous research on adaptation to stimulus set characteristics as an index of influences of cognitive control, the present study employed a task-switching paradigm to examine how cognitive control processes influence number processing. Participants were presented with a two-digit number and had to either judge its parity or compare its magnitude to a standard depending on a preceding cue. We expected numerical congruency effects (i.e. the unit-decade compatibility effect for magnitude comparisons and the parity congruity effect for parity judgements) to be larger in switch trials, as persisting activation of the task set of the preceding trial should increase interference. In contrast to our expectations, both numerical congruity effects were reduced following task switches as compared to repetitions. This interaction of task-switching with numerical congruency effects suggests an influence of cognitive control on basic number processing in form of persisting inhibition of previously abandoned task sets, so that these exert less influence on current number processing demands.

Reactive and proactive cognitive control as underlying processes of number processing in children

Cognitive control is crucial to resolve conflict in tasks such as the flanker task. Reactive control is used when conflict is rare, whereas proactive control is more efficient in situations where conflict is frequent. Macizo and Herrera (Psychological Research, 2013, Vol. 77, pp. 651–658) found that these two control processes can also underlie two-digit number comparison in adults. Specifically, they observed that the unit–decade compatibility effect decreased in a block containing many conflict trials as compared with a block containing few conflict trials (i.e., a list-wide proportion congruency effect). In the current study, we assessed whether this finding also applies to children (7-, 9-, and 11-year-olds). Participants performed a flanker task and a two-digit number comparison task. In both tasks, the proportion of conflict was manipulated (80% vs. 20%). Results from the flanker task showed a typical list-wide proportion congruency effect in reaction times in all participating age groups. In the number comparison task, we observed list-wide proportion congruency effects in both reaction times and error rates, which did not interact with age. Our findings support the assumption that children as young as 7 years can effectively use proactive and reactive control strategies. We showed that this effect is not limited to standardized artificial laboratory tasks, such as the flanker task, but also underlies more daily life tasks, such as the processing of Arabic numbers.

The processing of prices across numerical formats

We evaluated whether the format in which prices are presented determines the processing of their magnitude. A price comparison task was used in which two-digit prices with Arabic digits, written number words and auditory number words were presented in the euro currency. Prices were number-monetary category (NMC) compatible (49 euros - 36 cents) when the number and monetary category of one price were larger than those of the other (49 > 36, euros > cents); or NMC incompatible (49 cents - 36 euros) when the number of one price was larger but the monetary category smaller than those of the other (49 > 36, cents < euros). In addition, there were unit-decade (UD) compatible prices when the decade and unit of one price were larger than those of the other (49 euros - 36 cents, 4 > 3, 9 > 6); and UD incompatible prices when the decade of one price was larger but the unit smaller than those of the other (46 euros - 39 cents, 4 > 3, 6 < 9). The results showed NMC compatibility effects in all numerical formats. However, the UD compatibility effect was not found in any numerical format. The results are discussed within the hybrid model of multisymbolic magnitude processing.

The missing link: Global-local processing relates to number-magnitude processing in women.

Number processing and visual hierarchical processing (global-local processing) have much in common. However, the shared aspects of number processing and global-local processing have not been investigated so far. Most visual stimuli are hierarchical with global structures made up of local parts. Processing of global and local aspects occurs in parallel and the global advantage effect indicates faster reactions to global than local aspects. Likewise, multidigit numbers can be represented holistically (whole number magnitudes) or in a decomposed fashion (single digit magnitudes). During comparison of 2-digit numbers, the unit-decade compatibility effect indicates slower responses when the larger number contains the smaller unit digit and has been suggested as a measure of how strongly participants rely on decomposed number representations. However, this interpretation of the compatibility effect is still controversial and a link between global-local processing and the individual tendency to rely on decomposed representations of multidigit numbers remains to be established. To that end we assessed whether the compatibility effect during number comparison was related to various measures of global advantage. To answer this question we drew upon existing data from participants who had completed both, the number comparison task and 2 global-local tasks. Results show that the compatibility effect is indeed negatively related to several measures of global advantage in women, with no evidence for such a relationship in men. These results demonstrate that global-local processing transcends into the numerical domain but also suggest that the compatibility effect reflects different mechanisms in men and women. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Eye-movements during number comparison: Associations to sex and sex hormones

Multi-digit numbers are of a hierarchical nature with whole number magnitudes depending on digit magnitudes. Processing of multi-digit numbers can occur in a holistic or decomposed fashion. The unit-decade compatibility effect during number comparison is often used as a measure of decomposed processing. It refers to the fact that performance is reduced when the larger number contains the smaller unit digit (e.g. 73 vs. 26). It has been demonstrated that women show a larger compatibility effect than men, which is in accordance with their general tendency towards focusing on stimulus details during processing of visual hierarchical stimuli (local processing style). Such a local processing style has been related to higher progesterone and lower testosterone levels. One method to study individual processing styles is eye-tracking. The aim of the present study was to examine whether sex and sex hormones (estradiol, progesterone, testosterone) relate to eye movement behavior in the number comparison task. Unlike previous studies we found no evidence for sex differences in the behavioral compatibility effect. Nevertheless, women look more often and longer at individual digits and show a stronger compatibility effect in fixation durations compared to men, while men show more saccades between numbers than women. Estradiol and progesterone were related to fewer fixations and shorter fixation durations and more saccades between numbers in men, but not in women. Furthermore, the compatibility effect in the number of fixations and fixation durations was negatively related to testosterone in women. In summary, this is the first study to demonstrate sex differences and sex hormone influences on eye gaze behavior during number comparison.

The power to adapt: How sense of power predicts number processing.

When people solve numerical tasks, they are able to adapt their responses to characteristics of the task. This suggests that number processing is under cognitive control. Yet, such prior research on cognitive control in numerical cognition largely focused on the role of task stimuli-neglecting the role of predictors that are not directly linked to cognitive and numerical capacities. Do people who sense control in other domains (such as their interpersonal relationships) employ cognitive control differently when processing numbers? As a first step to examine this, we investigated how a person's sense of power (as a predictor known to facilitate cognitive control in other domains) predicts number processing. People sensing relatively high (rather than low) power in their everyday lives usually exert more cognitive control, which enables them to better adapt to a given task setting. Building upon this, we predicted that sense of power facilitates number processing-but, only when the task setting provides valid decision-relevant information that people can adapt to. As indicator of adaptation to the task setting, we assessed the unit-decade compatibility effect. Indeed, sense of power predicted a smaller compatibility effect (better adaptation) when valid information was available; in contrast, sense of power tended to predict a larger compatibility effect when only ambiguous information was available. These findings highlight that cognitive control in number processing not only depends on stimuli, but can also depend on broader individual factors, such as people's sensed control in interpersonal situations. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Direct evidence for linguistic influences in two-digit number processing.

Language-specific differences in number words influence number processing even in nonverbal numerical tasks. For instance, the unit-decade compatibility effect in two-digit number magnitude comparison (compatible number pairs [42_57: 4 < 5 and 2 < 7] are responded to faster than incompatible pairs [47_62: 4 < 6 but 7 > 2]) was shown to be influenced by the inversion of number words (e.g., in German the number word for 42 is zweiundvierzig [literally: two-and-forty]). In two studies, we used articulatory suppression to investigate whether previously observed cross-linguistic differences in two-digit number processing are indeed driven by differences in number word formation. In a two-digit number comparison task, German- and English-speaking participants had to identify the larger of two numbers presented in Arabic digits. In Study 1, participants performed the same task twice, with and without articulatory suppression. In Study 2, the percentage of within-decade filler items (36_39) was manipulated additionally. As expected, in both studies between-groups differences in the compatibility effect disappeared under articulatory suppression irrespective of the percentage of fillers included. Furthermore, paralleling results of previous studies including 33% or less filler items, we found that the compatibility effect was larger in German compared with English speakers in the 20% filler condition. However, this pattern was reversed in the 50% filler condition in both studies. Thus, results provide first direct evidence for influences of verbal number word formation on symbolic number processing. Moreover, these new findings suggest that linguistic influences and those of cognitive control processes associated with characteristics of the stimulus set interact in symbolic number processing. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Sex Differences in Number Magnitude Processing Strategies Are Mediated by Spatial Navigation Strategies: Evidence From the Unit-Decade Compatibility Effect.

The hybrid model of number magnitude processing suggests that multi-digit numbers are simultaneously processed holistically (whole number magnitudes) and in a decomposed manner (digit magnitudes). Thus, individual tendencies and situational factors may affect which type of processing becomes dominant in a certain individual in a given situation. The unit-decade compatibility effect has been described as indicative of stronger decomposed number processing. This effect occurs during the comparison of two-digit numbers. Compatible items in which the larger number contains the larger unit digit are easier to solve than incompatible items in which the larger number contains the smaller unit digit. We have previously described women show a larger compatibility effect than men. Furthermore, the compatibility effect is modulated by situational factors like the vertical spacing of the presented numbers. However, it has not been addressed whether situational factors and sex affect the unit-decade compatibility effect interactively. We have also demonstrated that the unit-decade compatibility effects relates to global-local processing, which in turn also affects spatial processing strategies. However, a link between spatial processing strategies and the unit-decade compatibility effect has not yet been established. In the present study we investigate, whether sex differences in the unit-decade compatibility effect (i) depend on the vertical spacing between numbers, (ii) are mediated via sex hormone levels of participants, and (iii) relate to sex differences in spatial processing strategies. 42 men and 41 women completed a two-digit number comparison task as well as a spatial navigation task. The number comparison task modulates compatibility and vertical spacing in a 2 × 2 design. The results confirm a larger compatibility effect in women compared to men and with dense compared to sparse spacing. However, no interactive effect was observed, suggesting that these factors modulate number magnitude processing independently. The progesterone/testosterone ratio was related to the compatibility effect, but did not mediate the sex difference in the compatibility effect. Furthermore, spatial processing strategies were related to the compatibility effect and did mediate the sex difference in the compatibility effect. Participants with a stronger focus on landmarks in the spatial navigation task showed a larger compatibility effect.

Task instructions modulate unit-decade binding in two-digit number representation.

Previous studies have found decomposed processes, as well as holistic processes, in the representation of two-digit numbers. The present study investigated the influence of task instruction on such processes. Participants completed both magnitude and parity tasks in one of three instructional conditions, where they were asked to either consider two-digit numbers as a whole or to focus on one specific digit. In two experiments, we found that when participants were asked to consider the two digits as an integrated number, they always exhibited a unit-decade compatibility effect, indicating a failure of selective attention on the digit relevant to the given task. However, the mere presence of the neighboring digit is not a sufficient condition for the compatibility effect: when participants were explicitly asked to process a specific digit, their success/failure to selectively ignore the irrelevant digit depended on task requirements. Further, computer mouse tracking indicated that the locus of the compatibility effect was related to late response-related processing. The results signify the deep involvement of top-down processes in unit-decade binding for two-digit number representation.

Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study.

Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants' first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing-apart from age, which increases the decade distance effect-they generally influence performance on a two-digit number comparison task.

Spacing and Presentation Modes Affect the Unit-Decade Compatibility Effect During Number Comparison.

. The unit-decade compatibility effect has challenged the model of holistic number magnitude processing, suggesting decomposed processing of multi-digit numbers. Recent evidence confirms that decomposed processing of decade and unit magnitudes occurs in parallel. However, the mode of presentation of multi-digit numbers may affect the processing mode (holistic vs. decomposed, parallel vs. sequential). We therefore investigated in two studies, whether presentation mode (vertical, horizontal, or consecutive) or the distance between two vertically presented numbers affects the unit-decade compatibility effect during number comparison. We found that the compatibility effect did not differ significantly between vertical and horizontal presentation, adding to previous results on perceptual generality, but was nonsignificant with consecutive presentation. However, the compatibility effect was significantly smaller, if numbers are spaced further apart. Thus, stimulus size and distance between numbers affect the processing of multi-digit numbers and should be reported in future studies.

Toward a model framework of generalized parallel componential processing of multi-symbol numbers.

In this article, we propose and evaluate a new model framework of parallel componential multi-symbol number processing, generalizing the idea of parallel componential processing of multi-digit numbers to the case of negative numbers by considering the polarity signs similar to single digits. In a first step, we evaluated this account by defining and investigating a sign-decade compatibility effect for the comparison of positive and negative numbers, which extends the unit-decade compatibility effect in 2-digit number processing. Then, we evaluated whether the model is capable of accounting for previous findings in negative number processing. In a magnitude comparison task, in which participants had to single out the larger of 2 integers, we observed a reliable sign-decade compatibility effect with prolonged reaction times for incompatible (e.g., -97 vs. +53; in which the number with the larger decade digit has the smaller, i.e., negative polarity sign) as compared with sign-decade compatible number pairs (e.g., -53 vs. +97). Moreover, an analysis of participants' eye fixation behavior corroborated our model of parallel componential processing of multi-symbol numbers. These results are discussed in light of concurrent theoretical notions about negative number processing. On the basis of the present results, we propose a generalized integrated model framework of parallel componential multi-symbol processing.

Fluency in two reading systems and the processing of two-digit numbers

Research question: We evaluated whether the processing of two-digit numbers was determined by the direction of reading in the two languages of bilingual individuals. Methodology: A group of Arabic (L1)/Spanish (L2) proficient bilinguals performed a comparison task with Arabic digits, Arabic number words and Spanish number words while the unit–decade compatibility effect was evaluated. Data: Participants showed a regular compatibility effect with Arabic digits. However, no compatibility effect was observed when they performed the task with verbal numbers, regardless of whether numbers were presented in Arabic or in Spanish. Conclusion: The similar pattern of results across the bilinguals’ two languages suggests that the direction of the reading (right-to-left in Arabic and left-to-right in Spanish) did not influence the processing of verbal numbers. Originality: This is the first study in which the unit–decade compatibility effect has been explored with Arabic/Spanish bilinguals. Significance: The main point to highlight from this study is that bilinguals are not influenced by the reading direction of their languages when they process two-digit verbal numbers.

Cognitive control in number magnitude processing: evidence from eye-tracking

The unit-decade compatibility effect describes longer response times and higher error rates for incompatible (e.g., 37_52) than compatible (e.g., 42_57) number comparisons. Recent research indicated that the effect depends on the percentage of same-decade filler items. In the present study, we further examined this relationship by recording participants' eye-fixation behaviour. In four conditions, participants had to compare item sets with different filler item types (i.e., same-decade and same-unit filler items) and different numbers of same-decade filler items (i.e., 25, 50, and 75%). We found a weaker unit-decade compatibility effect with most fixations on tens in the condition with same-unit filler items. Moreover, the compatibility effect increased with the percentage of same-decade filler items which was accompanied by less fixations on tens and more fixations on units. Thus, our study provides first eye-tracking evidence for the influence of cognitive control in number processing.

Understanding decimal proportions: Discrete representations, parallel access, and privileged processing of zero

Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions – rational numbers between 0 and 1 expressed in the place-value symbol system. The results demonstrate that proportions are represented as discrete structures and processed in parallel. There was a semantic interference effect: When understanding a proportion expression (e.g., “0.29”), both the correct proportion referent (e.g., 0.29) and the incorrect natural number referent (e.g., 29) corresponding to the visually similar natural number expression (e.g., “29”) are accessed in parallel, and when these referents lead to conflicting judgments, performance slows. There was also a syntactic interference effect, generalizing the unit-decade compatibility effect for natural numbers: When comparing two proportions, their tenths and hundredths components are processed in parallel, and when the different components lead to conflicting judgments, performance slows. The results also reveal that zero decimals – proportions ending in zero – serve multiple cognitive functions, including eliminating semantic interference and speeding processing. The current research also extends the distance, semantic congruence, and SNARC effects from natural numbers to decimal proportions. These findings inform how people understand the place-value symbol system, and the mental implementation of mathematical symbol systems more generally.

Object-based neglect in number processing

Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and - if so - how object-based neglect influences number processing.To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing.Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system.In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients.

The processing of Arabic numbers is under cognitive control

In this study, we evaluated whether the processing of two-digit Arabic numbers is subject to cognitive control. Participants performed a number comparison task with unit-decade compatible trials (36-47) and unit-decade incompatible number pairs (37-46). The unit-decade compatibility (incompatible minus compatible trials) was considered an index of conflict situation in numerical processing. To examine whether participants adapted to numerical conflict, we manipulated the percentage of incompatible trials relative to the percentage of compatible trials (20, 50, 80% incompatible trials). The unit-decade compatibility effect was modulated by the amount of incompatible trials: the compatibility effect decreased progressively as the percentage of incompatible trials increased. This result indicated that participants adapted to numerical conflict. The findings are discussed in terms of cognitive control. Implications for models of two-digit number processing are also addressed.

A unitary or multiple representations of numerical magnitude? - the case of structure in symbolic and non-symbolic quantities.

Currently, there is a controversial debate on whether there is an abstract representation of number magnitude, multiple different ones, or multiple different ones that project onto a unitary representation. The current study aimed at evaluating this issue by means of a magnitude comparison task involving Arabic numbers and structured as well as unstructured non-symbolic patterns of squares. In particular, we were interested whether a specific numerical effect, the unit-decade compatibility effect reflecting decomposed processing of tens and units complying with the place-value structure of the Arabic number system, is affected by input notation. Indeed, a reliable unit-decade compatibility effect was observed in the symbolic-digital notation condition but was absent for unstructured non-symbolic notation. However, for structured non-symbolic notation a – albeit negative – compatibility effect was observed as well. Theses results are hard to reconcile with the notion of an abstract representation of number magnitude. Instead, our data support the existence of multiple representations of numerical magnitude. In addition, the current data indicate that it may not be a question of symbolic vs. non-symbolic notation only but also an issue of the structuring of the input notation. While unstructured non-symbolic quantities seemed to be processed holistically we found evidence suggesting at least partially decomposed processing not only for symbolic Arabic numbers but also for structured non-symbolic quantities.