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

Age-related effects in magnitude and place-value processing

While general cognitive skills decline during aging, numerical skills seem to be mainly preserved. Such skills are essential for an independent life up to old age, e.g., when dealing with money or time. Operating with numbers usually requires number magnitude and place-value processing. The question is whether these processes are negatively affected by aging due to the general cognitive decline or positively affected due to lifelong experience with numbers. Therefore, we investigated age-related changes in the distance and compatibility effects in single-digit, two-digit, and four-digit number comparison. On the one hand, older adults took longer for number processing and showed a smaller distance effect, indicating altered number magnitude representations. On the other hand, older adults were better in place-value processing as indicated by a smaller compatibility effect than in younger adults. We conclude that aging differentially affects basic numerical skills.

Children's comparison of different-length numbers: Managing different attributes in multidigit number processing

In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.

tDCS effects in basic symbolic number magnitude processing are not significantly lateralized

Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.

Length is not all that matters: testing the role of number identity and the ratio of fillers in comparisons of multi-digits with different digit length

Research in multi-digit number comparison usually considers stimuli with the same number of digits (e.g., 3452 vs. 7831). Surprisingly, there is almost no research on the comparison of numbers that differ in length (e.g., 995 vs. 1000), which demands a focus on the number of digits in each multi-digit, despite the fact that the role of number length has been explicitly acknowledged in componential models of multi-digit processing. Our study explores whether the comparison of pairs of natural numbers that differ in length is affected by the identity of the leftmost digit of each multi-digit, and asks what is the effect of having variable proportions of trials with pairs of numbers of the same-length in the task. Across three studies participants compared numbers in blocks with different proportions of same-length multi-digit pairs (Experiment 1 and 2: 25% vs. 50% vs. 75%; Experiment 3: 0% vs. 50%). Stimuli in the different-length condition were length-digit congruent (the number with more digits starting with a larger digit: 2384 vs. 107) or length-digit incongruent (the number with more digits starting with a smaller number: 2675 vs. 398). Response times were shorter in length-digit congruent pairs than in the incongruent pairs. Unexpectedly, this effect was only slightly modulated by the proportion of same-/different-length multi-digit pairs in the experimental set. Despite its perceptual saliency, length is not the only information considered when comparing different-length numbers. The leftmost-digit is also taken into account, with variable relevance here, depending on the characteristics of the stimuli set.

Numeracy and COVID-19: examining interrelationships between numeracy, health numeracy and behaviour

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between (i) basic numeracy, (ii) COVID-19 health numeracy, and (iii) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health-related attitudes and behaviours (e.g. follow experts' recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Running Online Behavioral Experiments Using R: Implementation of a Response-Time Decision Making Task as an R-Shiny App

Online experiments allow for fast, massive, cost-efficient data collection. However, uncontrolled conditions in online experiments can be problematic, particularly when inferences hinge on response-times (RTs) in the millisecond range. To address this challenge, we developed a mobile-friendly open-source application using R-Shiny, a popular R package. In particular, we aimed to replicate the numerical distance effect, a well-established cognitive phenomenon. In the task, 169 participants (109 with a mobile device, 60 on a desktop computer) completed 116 trials displaying two-digit target numbers and decided whether they were larger or smaller than a fixed standard number. Sessions lasted ~7-minutes. Using generalized linear mixed models estimated with Bayesian inference methods, we observed a numerical distance effect: RTs decreased with the logarithm of the absolute difference between the target and the standard. Our results support the use of R-Shiny for RT-data collection. Furthermore, our method allowed us to measure systematic shifts in recorded RTs related to different OSs, web browsers, and devices, with mobile devices inducing longer shifts than desktop devices. Our work shows that precise RT measures can be reliably obtained online across mobile and desktop devices. It further paves the ground for the design of simple experimental tasks using R, a widely popular programming framework among cognitive scientists.

Hand preference and Mathematical Learning Difficulties: New data from Greece, the United Kingdom, and Germany and two meta-analyses of the literature

Increased rates of atypical handedness are observed in neurotypical individuals who are low-performing in mathematical tasks as well as in individuals with special educational needs, such as dyslexia. This is the first investigation of handedness in individuals with Mathematical Learning Difficulties (MLD). We report three new studies (N = 134; N = 1,893; N = 153) and two sets of meta-analyses (22 studies; N = 3,667). No difference in atypical hand preference between MLD and Typically Achieving (TA) individuals was found when handedness was assessed with self-report questionnaires, but weak evidence of a difference was found when writing hand was the handedness criterion in Study 1 (p = .049). Similarly, when combining data meta-analytically, no hand preference differences were detected. We suggest that: (i) potential handedness effects require larger samples, (ii) direction of hand preference is not a sensitive enough measure of handedness in this context, or that (iii) increased rates of atypical hand preference are not associated with MLD. The latter scenario would suggest that handedness is specifically linked to language-related conditions rather than conditions related to cognitive abilities at large. Future studies need to consider hand skill and degree of hand preference in MLD.

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.

Non-symbolic representation is modulated by math anxiety and cognitive inhibition while symbolic representation not

The present study aimed to investigate whether there are basic numerical processing deficits in high math anxiety (HMA) individuals and examine the effects of cognitive inhibition on the performance of high and low math anxiety (LMA) individuals. 35 undergraduate students were recruited to perform a numerical comparison task, a numerical Stroop task, a dot comparison task, and a dot Stroop task. Results showed the following: (1) Compared with LMA group, HMA group reacted more slowly and exhibited more fixation counts in non-symbolic representation task. (2) Inhibition condition significantly increased HMA individuals' fixation durations, whereas the fixation durations of LMA individuals were similar between inhibition and non-inhibition condition. The results demonstrated that MA might temporarily occupy individuals' working memory resources. (3) In non-symbolic representation task, the effect of numerical ratio on fixation counts was larger for HMA group than that for LMA group under inhibition condition, indicating MA might arise from a basic level deficit in numerosity processing.

Functional lateralization of arithmetic processing in the intraparietal sulcus is associated with handedness

Functional lateralization is established for various cognitive functions, but was hardly ever investigated for arithmetic processing. Most neurocognitive models assume a central role of the bilateral intraparietal sulcus (IPS) in arithmetic processing and there is some evidence for more pronounced left-hemispheric activation for symbolic arithmetic. However, evidence was mainly obtained by studies in right-handers. Therefore, we conducted a functional near-infrared spectroscopy (fNIRS) study, in which IPS activation of left-handed adults was compared to right-handed adults in a symbolic approximate calculation task. The results showed that left-handers had a stronger functional right-lateralization in the IPS than right-handers. This finding has important consequences, as the bilateral IPS activation pattern for arithmetic processing seems to be shaped by functional lateralization and thus differs between left- and right-handers. We propose three possible accounts for the observed functional lateralization of arithmetic processing.

Gender stereotypes and incremental beliefs in STEM and non-STEM students in three countries: relationships with performance in cognitive tasks

Women's underrepresentation in science, technology, engineering and mathematics (STEM) has been linked, among others, to gender stereotypes and ability-related beliefs as well as gender differences in specific cognitive abilities. However, the bulk of studies focused on gender stereotypes related to mathematics. The present study, therefore, aimed to map gender stereotypes and incremental beliefs (i.e., the conviction about modifiability) with respect to a wide range of stereotypical male-favouring and female-favouring abilities. Gender stereotypes and incremental beliefs were assessed with self-report questionnaires in 132 STEM students (65 women) and 124 non-STEM students (73 women) in three European countries ranked in the top, middle, and bottom of the Global Gender Gap Report. Moreover, a mental rotation and a verbal fluency test were completed. Men endorsed male-favouring stereotypes more than women, and women endorsed female-favouring stereotypes more than men, an effect that was most pronounced in the country with the larger gender gap. Male STEM students endorsed male-favouring stereotypes more strongly than male non-STEM and female STEM students. Male non-STEM students endorsed female-favouring stereotypes less than female and male STEM students. Female STEM students reported higher incremental beliefs than female non-STEM students, especially in the country with the lowest gender gap. Men outperformed women, and STEM students outperformed non-STEM in mental rotation, while women outperformed men in verbal fluency. Male STEM students' stronger endorsement of male-favouring stereotypes might reflect genuine group differences, at least in mental rotation. While potentially such gender stereotypes can help creating a "chilly climate" where women in academic STEM degrees are expected to perform poorly, those women believed more in the possibility to change and improve in male-favouring abilities which could help them to overcome the potential negative effect of stereotyping.

Automatic place-value activation in magnitude-irrelevant parity judgement

Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed. However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question using the parity congruency effect in two-digit numbers: It describes that responding to decade-digit parity congruent numbers (e.g., 35, 46; same parity of decades and units) is faster than to decade-digit parity incongruent numbers (e.g., 25; 36; different parities of decades and units). Here we investigate the (a-) symmetry of the parity congruency effect; i.e. whether it makes a difference whether participants are assessing the parity of the unit digit or the decade digit. We elaborate, how and why such an asymmetry is related to place-value processing, because the parity of the unit digit only interferes with the parity of the decade digit, while the parity of the decade digit interferes with both the parity of the unit digit and the integrated parity of the whole two-digit number. We observed a significantly larger parity congruency effect in the decade parity decision than in the unit parity decision. This suggests that automatic place-value processing also takes place in a typical parity judgment task, in which magnitude is irrelevant. Finally, because of the cross-lingual design of the study, we can show that these results and their implications were language-independent.

Conducting Web-Based Experiments for Numerical Cognition Research

It is becoming increasingly popular and straightforward to collect data in cognitive psychology through web-based studies. In this paper, I review issues around web-based data collection for the purpose of numerical cognition research. Provided that the desired type of data can be collected through a web-browser, such online studies offer numerous advantages over traditional forms of physical lab-based data collection, such as gathering data from larger sample sizes in shorter time-windows and easier access to non-local populations. I then present results of two replication studies that employ classical paradigms in numerical cognition research: the number-size congruity paradigm and comparison to a given standard, which also included a masked priming manipulation. In both replications, reaction times and error rates were comparable to original, physical lab-based studies. Consistent with the results of original studies, a distance effect, a congruity effect, and a priming effect were observed. Data collected online thus offers a level of reliability comparable to data collected in a physical lab when it comes to questions in numerical cognition.

Sex hormones and number processing. Progesterone and testosterone relate to hemispheric asymmetries during number comparison

Like many visual stimuli, multi-digit numbers are of a hierarchical nature, with whole number magnitudes depending on individual digit magnitudes. Accordingly, multi-digit numbers can be processed in a holistic (whole number magnitudes) or decomposed manner (digit magnitudes). The compatibility effect during number comparison serves as an indicator of decomposed processing. It is characterized by impaired performance for items where the larger number contains the smaller unit-digit. We were recently able to demonstrate, that the compatibility effect indeed depends on an individual's tendency to process visual hierarchical stimuli on a global or local level. Accordingly, factors affecting global-local processing, should also affect number magnitude processing, i.e. the compatibility effect. Among these factors are hemispheric asymmetries, sex differences and sex hormones (estradiol, progesterone, testosterone). In the present study 39 men and 37 naturally cycling women in their luteal cycle phase completed a number comparison task with stimuli randomly presented to the left and right hemifield. As in previous studies, we observed a larger compatibility effect in the right hemifield (left hemisphere) than in the left hemifield (right hemisphere) and in men than in women. However, this is the first study to evaluate the effects of sex hormones on hemispheric asymmetries during number comparison. We found progesterone to relate to increased hemispheric asymmetries in men, but decreased hemispheric asymmetries in women. Additionally, testosterone was negatively related to hemispheric asymmetries in women's compatibility effect in reaction times. These results add to the growing evidence that sex hormones relate to hemispheric asymmetries in cognitive functions.

The SNARC and MARC effects measured online: Large-scale assessment methods in flexible cognitive effects

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster reactions to small/large numbers on the left-/right-hand side) is usually observed along with the linguistic Markedness of Response Codes (MARC) effect-that is, faster left-/right-hand responses to odd/even numbers. The SNARC effect is one of the most thoroughly investigated phenomena in numerical cognition. However, almost all SNARC and MARC studies to date were conducted with sample sizes smaller than 100. Here we report on a study with 1,156 participants from various linguistic and cultural backgrounds performing a typical parity judgment task. We investigated whether (1) the SNARC and MARC effects can be observed in an online setup, (2) the properties of these effects observed online are similar to those observed in laboratory setups, (3) the effects are reliable, and (4) they are valid. We found robust SNARC and MARC effects. Their magnitude and reliabilities were comparable to values previously reported in in-lab studies. Furthermore, we reproduced commonly observed validity correlations of the SNARC and MARC effects. Namely, SNARC and MARC correlated with mean reaction times and intraindividual variability in reaction times. Additionally, we found interindividual differences in the SNARC and MARC effects (e.g., finger-counting routines for the SNARC and handedness for the MARC). Large-scale testing via web-based data acquisition not only produces SNARC and MARC effects and validity correlations similar to those from small, in-lab studies, but also reveals substantial insights with regard to interindividual differences that usually cannot be revealed in the offline laboratory, due to power considerations.

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.

Clock Walking and Gender: How Circular Movements Influence Arithmetic Calculations

Starting from a rich body of evidence on the strict bidirectional relationship between numerical cognition and action processes, the present study aims at deepening the existing knowledge of the influence of body movement on arithmetic calculation. Numerous studies have shown that moving the body along the vertical or the horizontal axis could facilitate calculations such as additions and subtractions. More specifically, results showed an effect of congruence between the type of operation (additions vs. subtractions) and the direction of the movement performed (up/right or down/left). While this congruence effect is present for both additions and subtractions when the axis of action is vertical, when the axis of action is horizontal, the effect appears only for additions. The purpose of this study is to investigate the influence of circular motion, which has so far not been explored, on counting. Participants were asked to count by adding or subtracting “three,” while performing a circular motion (i.e., a clockwise or counterclockwise movement), in an active (i.e., walking) or passive mode (i.e., being pushed on a wheelchair). Results showed a congruence effect for additions calculated in the active modality and only for male participants. Implications of the results for theories of embodied cognition and for the debate on gender differences in mathematical skills are discussed in this paper.