Project-related Outputs
Here we list project-related papers, conference contributions, and our public activity. As we still work intensely on data collection and analysis, the list will hopefully extend soon, so stay tuned.
Peer-reviewed journal articles
Heubner, L.*, Cipora, K.*, Soltanlou, M., Schlenker, M.-L., Lipowska, K., Goebel, S. M., Domahs, F., Haman, M., & Nuerk, H.-C. (2018). A mental odd-even continuum account: Some numbers may be “more odd” than others, and some numbers may be “more even” than others. Frontiers in Psychology 9:1081. [* equal contribution]
In this paper, we demonstrate that mentally the parity of multi-digit numbers is not binary. Factors such as divisibility by 4, being part of a multiplication table, or being a square significantly influenced parity judgments of auditorily presented two-digit numbers. In this study we tested Polish-, German- and English speaking adults. Between language differences indicate that unit-decade inversion in German (e.g., 21 in German is named one-and-twenty) influences parity decision times. Furthermore, our results strongly suggest that generalizability of numerical processing models (especially those of parity processing) between languages should not be taken as granted.
Bahnmüller, J., Nuerk, H.-C., & Moeller, K. (2018). A Taxonomy Proposal for Types of Interactions of Language and Place-Value Processing in Multi-Digit Numbers. Frontiers in Psychology, 9, 1024. doi: DOI: 10.3389/fpsyg.2018.01024.
In this paper, we attempt at proposing a framework of how language influences different levels of multi-digit number processing. This paper fills in the gap in the literature, as before theoretical analyses were focused either on different levels of multi-digit number processing, or different levels of language influences on number processing.
Cipora, K., Soltanlou, M., Reips, U.-D., & Nuerk, H.-C. (2019). The SNARC and MARC effects measured online: Large-scale assessment methods in flexible cognitive effects. Behavior Research Methods, 51(4), 1676-1692. DOI: 10.3758/s13428-019-01213-5.
This study, is so far the largest SNARC (i.e., left / right hand advantage in responding to small / large magnitude numbers respectively) study published. It was prepared in 15 different languages (including German and Polish), and a total of 1056 participants was included into analysis. Apart from standard parity judgment task (considering single digit numbers) we have asked a number of demographic questions and measures several factors, which can be related to the SNARC effect (e.g., mother tongue, reading direction, finger counting routines, handedness, math and language grades, educational background). At the same time we looked at the MARC effect (i.e., left / right hand advantage when responding to odd / even numbers respectively).
The magnitude and reliabilities of the SNARC and MARC effects 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). Crucially for the objectives of this project, it was possible to compare the SNARC effect in German (N = 530) and Polish (N = 100) speakers. They did not differ regarding the SNARC and MARC effects.
Cipora, K., Soltanlou, M., Smaczny, S., Göbel, S.M., & Nuerk, H.-C. (2019). Automatic place-value activation in magnitude-irrelevant parity judgement. Psychological Research. DOI: 10.1007/s00426-019-01268-1.
In this study, in which we tested groups of English- and German-speaking adults, we show that not only magnitude but also parity is automatically processed in multi-digit numbers. Despite predictions on language modulation of this effect related to unit-decade inversion in German (e.g., 21 in German is named one-and-twenty) and lack of such inversion in English, in this study we did not find any language effects.
Cipora, K., He, Y., & Nuerk, H.-C. (2020). The Spatial Numerical Association of Response Codes effect and math skills: why related? Annals of the New York Academy of Sciences. DOI: 10.1111/nyas.14355.
In this theoretical paper, we try to answer not only a question on whether the SNARC effect (i.e., faster responses to small / large magnitude numbers on left and right hand side respectively) relates to math skills, but also why it should be related. We do so by providing a tentative model of how the SNARC effect arises, and how factors related to math skills can affect certain stages of the formation of the SNARC effect. Our framework allows explaining why some studies find the link between the SNARC effect and math skills while some other studies do not find it. Moreover, it explains why direction of the relationship (if it exists) differs between adults and children.
Huber, S., Nuerk, H.-C., Reips, U.-D., & Soltanlou, M. (2019). Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study. Psychological Research, 83(7), 1444–1464. DOI: 10.1007/s00426-017-0964-5.
While the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to linguistic influences and individual differences influencing symbolic magnitude comparison in a large-scale sample. 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. To the best of our knowledge this is the largest study demonstrating these effects. 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. 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.
Cipora, K., Schroeder, P. A., Soltanlou, M., & Nuerk, H.-C. (2018). More space, better mathematics: Is space a powerful tool or a cornerstone for understanding arithmetic? In K. S. Mix & M. T. Battista (Eds.), Visualizing Mathematics. Research in Mathematics Education (pp. 77-116). Springer, Cham. DOI: 10.1007/978-3-319-98767-5_4.
In this book chapter we aim at providing a comprehensive taxonomy of Spatial-Numerical Associations (SNAs), and their links to mathematic skills. We show that SNAs should not be treated as a unitary phenomenon. Their common denominator is the existence of the link between space and numbers. However, they differ in respect of which aspects of numerical information (cardinality, ordinality, functions; either approximate or exact quantities) are associated with different aspects of space (extensions and directions). They also differ in whether the association is implicit or explicit. We also provide an overview of how different SNAs can be altered by situated influences. Additionally, we identify potential areas of new SNA research.
Preprints
Bahnmueller, J., Cipora, K., Goebel, S. M., Nuerk, H.-C., & Soltanlou, M. (2020). Pick the smaller number: No influence of linguistic markedness on three-digit number processing. https://psyarxiv.com/nwg7p/.
In this study we aim at checking whether the instruction in the magnitude comparison task affects the observed pattern of results. In a typical setup, participants are to select the larger out of two numbers. Here, we asked them to select the smaller, and compared the results to data collected in the typical “pick larger” setup before. We replicated all effects of interest: numerical distance and compatibility effects. Corresponding effect sizes between “pick larger” and the new “pick smaller” were very similar. There were no differences in overall reaction times between setups. Our results show robustness of behavioral signatures of multi-digit number processing, so that they are not dependant on specific task instruction.
Cipora, K.*, Loenneker, H.*, Soltanlou, M., Lipowska, K., Domahs, F., Goebel, S. M., Haman, M., & Nuerk, H.-C. (2019). Syntactic influences on numerical processing in adults: Limited but detectable. https://psyarxiv.com/ewtd4 [*equal contribution].
In this tri-lingual study we were determined to find effects of grammatical number on elementary number processing in educated adults. By designing a dual-task setup in which, depending on the cue, participants were either responding to parity of a number, or to grammatical number (i.e., singular or plural form of a verb “to be”). Even in such a setup, despite increasing saliency of the grammatical number, we did not find straightforward evidence that specificities of Polish grammar directly affect behavioral signatures of elementary number processing. Specifically, the grammatical number has not directly affected the numerical nor grammatical SNARC in Polish speakers. On the other hand, the study shows, that such effects might be way more nuanced, but in general, the effects of grammatical number specificities on elementary number processing in adults are rather limited.
Huber, J. F., Soltanlou, M., Cipora, K., Lipowska, K., Domahs, F., Haman, M., & Nuerk, H.-C. (2020). No Evidence for an Influence of Grammatical Number in Two-Digit Magnitude and Place-Value Processing in Adults. https://psyarxiv.com/9e7jk.
In this paper we looked at effects of grammatical number in adult Polish speakers in the task, in which the numerical magnitude is task-relevant. Specifically, we looked at two-digit number comparison presented as both Arabic notation and number words. Using carefully matched materials we could disentangle grammatical number compatibility (plural follows either the numerically smaller or larger number) as well as unit-decade compatibility and the decade distance. Grammatical number did not contribute to the explanation of the data beyond unit-decade compatibility, distance effect and SNARC effect and, thus, seems to be negligible in two-digit number comparison.
Haman, M., Lipowska, K., Soltanlou, M., Cipora, K., Domahs, F., & Nuerk, H.-C. (2020). The plural still counts: Cross-linguistic study of the symbolic numerical magnitude comparison task in Polish and German-speaking preschoolers. https://psyarxiv.com/ge8zq.
A total of 152 Polish and 124 German children aged 3;0-6;11 participated in the study. We expected that the inconsistent grammatical number for numbers above 4 would make it difficult for Polish children to exceed the limit of four (which is developmentally followed by the induction of counting principles), and generally would make more difficult to operate with numbers above 4. Indeed, Polish children, later than German, reached the so-called "CP-knowers" stage and, even after reaching it, they still performed worse when comparing symbolic numerical quantities, despite the equal level of control variables (age, level of familiarity with numerical symbols, or working memory capacity). It suggests that grammatical number irregularities affect number concept acquisition in preschoolers.
Conference contributions
Smaczny, S., Soltanlou, M., Goebel, S.M., Nuerk, H.-C., Cipora, K. (2017). The parity congruency effect depends on the target: Evidence for automatic place-value processing. Workshop: Linguistic and Cognitive influences on numerical cognition. Tuebingen: Germany. Poster.
In this study, in which we tested groups of English- and German-speaking adults, we show that not only magnitude but also parity is automatically processed in multi-digit numbers. Despite predictions on language modulation of this effect related to unit-decade inversion in German (e.g., 21 in German is named one-and-twenty) and lack of such inversion in English, in this study we did not find any language effects.
Schlenker, M.-L., Heubner, L., Soltanlou, M., Cipora, K., Goebel, S.M., Domahs, F., Lipowska, K., Haman, M., Nuerk, H.-C. (2017). Which factors affect response speed in a two-digit number parity judgment task: a cross-lingual study. Part I: Arabic notation. Workshop: Linguistic and Cognitive influences on numerical cognition. Tuebingen: Germany. Poster.
Schlenker, M.-L., Heubner, L., Soltanlou, M., Cipora, K., Goebel, S.M., Domahs, F., Lipowska, K., Haman, M., Nuerk, H.-C. (2017). Which factors affect response speed in a two-digit number parity judgment task: a cross-lingual study. Part II: Number words. Workshop: Linguistic and Cognitive influences on numerical cognition. Tuebingen: Germany. Poster.
Heubner, L., Schlenker, M.-L., Soltanlou, M., Cipora, K., Goebel, S.M., Domahs, F., Lipowska, K., Haman, M., Nuerk, H.-C. (2017). Which factors affect response speed in a two-digit number parity judgment task: a cross-lingual study. Part III: Auditory presentation. Workshop: Linguistic and Cognitive influences on numerical cognition. Tuebingen: Germany. Poster.
In this collection of three posters, we present which numerical and non-numerical factors influence times needed for parity judgments of two-digit numbers. We used different notations (Arabic numbers, number words, and auditory numbers), and tested English-, German-, and Polish-speaking healthy adults. Interestingly, strongest language effects were observed in case of numbers presented auditorily. Several numerical properties such as divisibility by 4 were influencing the reaction times. Interestingly, the least pronounced influences were observed in case of Arabic notation. Parity congruency was also a rubust factor influencing parity decisions.
Cipora, K., Soltanlou, M., Lipowska, K., Loenneker, H.D., Domahs, F., Göbel, S.M., Haman, M., & Nuerk, H.-C. (2018). Influences of grammatical number on numerical processing in educated adults. Third Jean Piaget Conference: The origin of numbers. Geneva: Switzerland. Poster.
In this study we investigated whether inconsistencies in grammatical number influence numerical processing in adults. We tested 98 Polish, German, and English native speakers. Participants were presented with short sentences, e.g., “There is/are 23/36” [number corresponding either with singular or plural in Polish]. They were cued whether they are to classify the grammatical number of the verb or number parity.
No language differences were observed in the grammatical judgement. For parity judgment, Polish, but not English or German speakers, responded faster when the verb form corresponded to the grammatical number of the presented number. This result suggests that when grammatical number is made salient, it influences numerical processing in adults providing another instance of linguistic influence on numerical cognition.
Haman, M., Cipora, K., Domahs, F., Lipowska, K., Nuerk, H.-C., & Soltanlou, M. (2019). The impact of grammar on acquisition of the exact number system revealed by magnitude comparison task in Polish and German preschoolers. XXXVIIth European Workshop on Cognitive Neuropsychology, Bressanone, Italy.
In the light of the previous research, according to which grammar may both support or hinder the process of acquisition of the exact meanings of number-words, we have formulated two hypotheses: (1) coincidence of smaller numerical magnitudes with plural verb, and larger magnitudes with singular verbs may delay acquisition of exact meanings of numbers above 4 in Polish children, if compared to languages using regular mapping of grammatical number to numerical magnitude (e.g. German). (2) Polish syntax stresses contrast between small (2-4) vs large (5-9) number ranges, so it may facilitate cross-range numerical magnitude comparison. To test these hypotheses Polish and German preschoolers were administered computerized symbolic magnitude task. We have found three-way interaction between language, numerical range, and the phase of mastering meanings of number-words (indicated by Give-a-number task), which show both expected effects. Polish children generally performed below the level of German children, except for cross-range comparison in the group at the earlier stage of acquisition of the exact number system.
Neumann. J., Soltanlou, M., Cipora, K., Lipowska, K., Domahs, F., Haman, M., & Nuerk, H.-C. (2018). Linguistic influences on symbolic magnitude comparison in preschoolers. Workshop: Integrating Educational and Cognitive Perspectives on Mathematics, Tuebingen, Germany.
In this poster we present preliminary results of the preschoolers study, which is now available as preprint by Haman et al. (2020). We conclude that due to grammatical complexity, the preschoolers have a harder time with larger numbers, and mastering symbolic numbers takes longer as compared to other languages such as German. In Polish, small and large numbers belong to different categories, which may have helped in the cross-range comparison to differentiate between the numbers and to make up for the complexity to offset the difference between the languages. Further factors such as cultural effects and cognitive skills are also discussed.
Lipowska, K., Soltanlou, M., Cipora, K., Domahs, F., Nuerk, H.-C., & Haman, M. (2018). Spatial-numerical associations in non-symbolic and symbolic magnitude comparison in preschoolers. Workshop: Integrating Educational and Cognitive Perspectives on Mathematics, Tuebingen, Germany.
In this poster we are also presenting some preliminary data from the preschoolers study. Researching SNA in preschool children may help better understand these phenomena, as at this age children are not yet formally taught mathematics. Up till now, the evidence for the existence of SNA in such children is sparse and not straightforward. In the present study, we aimed to investigate the presence of SNA in German and Polish children, whether their spatial organisation of number representations changes with age, and if it may depend on linguistic factors. We tested preschoolers (3-7 year-olds) with non-symbolic and symbolic magnitude comparison tasks in a within-subject design. Children also performed several control tasks and handedness was recorded. Analyses of non-symbolic magnitude comparison task suggested an interaction of SNA with language. German children responded quicker to fewer dots when both sets were in small number range and to more dots when both sets were in large number range. No SNARC was observed in the accuracy in German children. Interestingly, Polish children revealed a reversed SNARC effect in the response time, however, a usual SNARC effect was observed in the accuracy. No SNARC effects were found in Symbolic magnitude comparison task. Overall, despite some similarities in results between groups, opposite SNAs was observed in the response times. The results imply that SNA may be influenced not only by cultural, but also linguistic factors.
Public activity
Bahnmueller, J., Nuerk, H.-C., & Cipora, K. (2020). Forty-Two or Two-and-Forty: Learning Maths in Different Languages. Frontiers for Young Minds 8, 84. doi: 10.3389/frym.2020.00084.
How does language affect learning mathematics? Does the language one speaks affect the way one counts? Does the language affect only children, or everyone, who needs to use numbers in another language, for instance after moving to another country? In the paper Forty-Two or Two-and-Forty: Learning Maths in Different Languages, we try to explain links between mathematics and language to 8-11-year-olds. As a part of collection of articles Everything you and your teachers need to know about the learning brain published in Frontiers for Young Minds, this freely available paper will be soon translated to German, French, Spanish, Portuguese, and Dutch.
Soltanlou M. & Artemenko C. (2020) Using Light to Understand How the Brain Works in the Classroom. Frontiers for Young Minds. 8,88. doi: 10.3389/frym.2020.00088.
How can we use the light to understand the learning brain? In the paper Using Light to Understand How the Brain Works in the Classroom, we try to explain the functional Near-Infrared Spectroscopy and potential of using this method to understand how brain learns in a classromm to 8-11-year-olds. As a part of collection of articles Everything you and your teachers need to know about the learning brain published in Frontiers for Young Minds, this freely available paper will be soon translated to German, French, Spanish, Portuguese, and Dutch.