The SNARC (spatial-numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsignificant. Possible reasons for this nonsignificance could be that in previous studies (a) very small samples were used, (b) there were too few repetitions producing too little power and, consequently, reliabilities that were too small to reach conventional significance levels for the descriptive skill differences in the SNARC, and (c) general mathematical ability was assessed by the field of study of students, while individual arithmetic skills were not examined. Therefore we used a much bigger sample, a lot more repetitions, and direct assessment of arithmetic skills to explore relations between the SNARC effect and arithmetic skills. Nevertheless, a difference in SNARC effect between arithmetically skilled and nonskilled participants was not obtained. Bayesian analysis showed positive evidence of a true null effect, not just a power problem. Hence we conclude that the idea that arithmetically skilled and nonskilled participants generally differ in the SNARC effect is not warranted by our data.Keywords: Spatial-numerical association of response codes; Numerical cognition; Number and space.The SNARC effect (spatial-numerical association of response codes; Dehaene, Bossini, & Giraux, 1993;Fias, Brysbaert, Geypens, & d'Ydewalle, 1996;Nuerk, Wood, & Willmes, 2005) is regarded as evidence for an amodal number-space association (but see Gevers et al., 2010). When participants are judging parity of presented numbers in a speeded bimanual setting, they respond faster Correspondence should be addressed to Krzysztof Cipora, Institute of Psychology, Jagiellonian University, Kraków, Al. Mickiewicza 3, 31-120 Kraków, Poland. E-mail: krzysztof.cipora@gmail.comWe wish to thank Marc Brysbaert and two reviewers for numerous helpful comments on a previous version of the manuscript. In particular, we are grateful to Marc Brysbaert for putting our attention to Masson's Bayesian analysis methods, which improved the manuscript a lot and made our null results "positive evidence" for a true null SNARC slope difference between skilled and unskilled participants. We also thank Dorota Z˙elechowska and Dominika Czajak for their help in data collection and Franziska Burger for checking and correcting English spelling, expression, and grammar. H.-C. Nuerk's research on spatial-numerical cognition was supported by the German Research Foundation (DFG) by means of a project within the Research Group (Forschergruppe) Analyse und Förderung effektiver Lehr-Lern-Prozesse (FOR 738/2/TP02).

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.

Math anxiety has an important impact on mathematical development and performance. However, although math anxiety is supposed to be a transcultural trait, assessment instruments are scarce and are validated mainly for Western cultures so far. Therefore, we aimed at examining the transcultural generality of math anxiety by a thorough investigation of the validity of math anxiety assessment in Eastern Europe. We investigated the validity and reliability of a Polish adaptation of the Abbreviated Math Anxiety Scale (AMAS), known to have very good psychometric characteristics in its original, American-English version as well as in its Italian and Iranian adaptations. We also observed high reliability, both for internal consistency and test-retest stability of the AMAS in the Polish sample. The results also show very good construct, convergent and discriminant validity: The factorial structure in Polish adult participants (n = 857) was very similar to the one previously found in other samples; AMAS scores correlated moderately in expected directions with state and trait anxiety, self-assessed math achievement and skill as well temperamental traits of emotional reactivity, briskness, endurance, and perseverance. Average scores obtained by participants as well as gender differences and correlations with external measures were also similar across cultures. Beyond the cultural comparison, we used path model analyses to show that math anxiety relates to math grades and self-competence when controlling for trait anxiety. The current study shows transcultural validity of math anxiety assessment with the AMAS.

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.

The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this review, we present a taxonomy of SNAs and outline which of them are related to arithmetic skills. Recent research suggests that not all SNAs are related to arithmetic skills; for instance, the spatial-numerical association of response codes (SNARC) is not or at least less related to arithmetic skills than SNAs assessed in the number line estimation task. In general, we conclude that the relationship between SNAs and arithmetic skills are rather weak or caused by mediating variables. Nevertheless, interventions based on relations between space and numbers can be beneficial for arithmetic skills because space is a powerful tool to understand arithmetic concepts.

The aim of cognitive psychology is to obtain insights into human cognition in general. For this purpose, group-studies are typically conducted on representative samples so that the results can be generalized to the population. Using this approach, individual differences in such group-level cognitive phenomena are typically neglected and not much is known about their prevalence at the individual level. Such information is nevertheless important for claims about the universality of phenomena, as in theory, significant effects at the group-level can in principle be driven by a minority of participants. Here we used a uniform analysis of 18 existing data sets revealing a well-replicated phenomenon in numerical cognition: the SNARC (Spatial-Numerical Association of Response Codes) effect, in order to investigate the prevalence of the effect at the individual level. Three methods of analyzing the presence of the effect at the individual level were utilized: one psychometric and two bootstrapping methods. The results show that the group-level SNARC effect is driven by a minority of individuals (≤ 45%) who reveal the effect. This finding demonstrate an important theoretical issue: whether group-level effects really reflect general principles of cognition. We discuss advantages and drawbacks of the present methods and their usefulness for investigating the prevalence of other cognitive phenomena. We posit that testing the presence of robust group-level cognitive effects at the individual level as well as ensuring their reliable measurement is an important step towards integrating two traditionally separate approaches of scientific psychology proposed back in 50’ by Cronbach: experimental and correlational.

A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the (default) FC habits are over time and how flexible they can be. To investigate these questions, 380 Polish participants completed a questionnaire on their FC routines, the stability of these routines, and the context of FC usage, preceded by the request to count on their fingers from 1 to 10. Next, the test–retest stability of FC habits was examined in 84 participants 2 months following the first session. To the best of our knowledge, such a study design has been adopted for the first time. The results indicate that default FC routines of the majority of participants (75%) are relatively stable over time. At the same time, FC routines can flexibly adapt according to the situation (e.g., when holding an object). As regards prevalence, almost all participants, in line with previous findings on Western individuals, declared starting from the closed palm and extending consecutive fingers. Furthermore, we observed relations between FC preferences and handedness (more left-handers start from the left hand) and that actual finger use is still widespread in healthy adults for a variety of activities (the most prevalent uses of FC are listing elements, presenting arguments and plans, and calendar calculations). In sum, the results show the practical relevance of FC in adulthood, the relative stability of preferences over time along with flexible adaptation to a current situation, as well as an association of FC routines with handedness. Taken together our results suggest that FC is the phenomenon, which is moderated or mediated by multiple embodied factors.

The Abbreviated Math Anxiety Scale (AMAS) is one of the most popular instruments measuring math anxiety (MA). It has been validated across several linguistic and cultural contexts. In this study, we investigated the extent of administration method invariance of the AMAS by comparing results (average scores, reliabilities, factorial structure) obtained online with those from paper-and-pencil. We administered the online version of the AMAS to Polish students. Results indicate that psychometric properties of the AMAS do not differ between online and paper-and-pencil administration. Additionally, average scores of the AMAS did not differ considerably between administration forms, contrary to previous results showing that computerized measurement of MA leads to higher scores. Therefore, our results provide evidence for the usefulness of the AMAS as a reliable and valid MA measurement tool for online research and online screening purposes across cultures and also large similarity between administration forms outside an American-English linguistic and cultural context. Finally, we provide percentile and standard norms for the AMAS for adolescents and adults (in the latter case for both online and paper-and-pencil administration) as well as critical differences for the comparison of both subscales in an individual participant for practical diagnostic purposes.Keywords: math anxiety, Abbreviated Math Anxiety Scale, online survey, validation, norms Journal of Numerical Cognition, 2017, Vol. 3(3), 667-693, doi:10.5964/jnc.v3i3.121 Received: 2017-03-02. Accepted: 2017-08-17. Published (VoR): 2018-01-30.*Corresponding author at: Eberhard Karls Universität Tübingen, Arbeitsbereich Diagnostik und Kognitive Neuropsychologie, Fachbereich Psychologie, Schleichstraße 4 72076 Tübingen, Germany. E-mail: krzysztof.cipora@gmail.com This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License, CC BY 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Math Underachievement -Its Causes and ConsequencesPoor numeracy may even be more harmful for an individual than poor literacy (Butterworth, Varma, & Laurillard, 2011). Considerable large-scale economic consequences of math underachievement have also been reported (OECD, 2010). Therefore, the cognitive and emotional causes of impaired numeracy are of major interest both theoretically and practically. Regarding emotional aspects, math anxiety (MA) is probably the most prominent and important variable that negatively correlates with math achievement. It has been extensively investigated since the 1960's (see Dowker, Sarkar, & Looi, 2016 for review). A sizeable negative relationship between MA and math performance is evident in previous PISA (Programme for International Student Assessment) studies Journal of Numerical Cognition jnc.psychopen.eu | 2363-8761 across virtually all countries involved in th...