LINGUISTIC INFLUENCES ON MATHEMATICAL COGNITION EDITED BY : Ann Dowker and Hans-Christoph Nuerk PUBLISHED IN : Frontiers in Psychology 1 June 2017 | Linguistic In uences on M athematical Cognition Frontiers in Psychology Frontiers Copyright Statement © Copyright 2007-2017 Frontiers Media SA. All rights reserved. All content included on this site, such as text, graphics, logos, button icons, images, video/audio clips, downloads, data compilations and software, is the property of or is licensed to Frontiers Media SA (“Frontiers”) or its licensees and/or subcontractors. The copyright in the text of individual articles is the property of their respective authors, subject to a license granted to Frontiers. The compilation of articles constituting this e-book, wherever published, as well as the compilation of all other content on this site, is the exclusive property of Frontiers. For the conditions for downloading and copying of e-books from Frontiers’ website, please see the Terms for Website Use. If purchasing Frontiers e-books from other websites or sources, the conditions of the website concerned apply. Images and graphics not forming part of user-contributed materials may not be downloaded or copied without permission. Individual articles may be downloaded and reproduced in accordance with the principles of the CC-BY licence subject to any copyright or other notices. They may not be re-sold as an e-book. As author or other contributor you grant a CC-BY licence to others to reproduce your articles, including any graphics and third-party materials supplied by you, in accordance with the Conditions for Website Use and subject to any copyright notices which you include in connection with your articles and materials. All copyright, and all rights therein, are protected by national and international copyright laws. The above represents a summary only. For the full conditions see the Conditions for Authors and the Conditions for Website Use. ISSN 1664-8714 ISBN 978-2-88945-200-2 DOI 10.3389/978-2-88945-200-2 About Frontiers Frontiers is more than just an open-access publisher of scholarly articles: it is a pioneering approach to the world of academia, radically improving the way scholarly research is managed. The grand vision of Frontiers is a world where all people have an equal opportunity to seek, share and generate knowledge. Frontiers provides immediate and permanent online open access to all its publications, but this alone is not enough to realize our grand goals. Frontiers Journal Series The Frontiers Journal Series is a multi-tier and interdisciplinary set of open-access, online journals, promising a paradigm shift from the current review, selection and dissemination processes in academic publishing. All Frontiers journals are driven by researchers for researchers; therefore, they constitute a service to the scholarly community. At the same time, the Frontiers Journal Series operates on a revolutionary invention, the tiered publishing system, initially addressing specific communities of scholars, and gradually climbing up to broader public understanding, thus serving the interests of the lay society, too. Dedication to Quality Each Frontiers article is a landmark of the highest quality, thanks to genuinely collaborative interactions between authors and review editors, who include some of the world’s best academicians. Research must be certified by peers before entering a stream of knowledge that may eventually reach the public - and shape society; therefore, Frontiers only applies the most rigorous and unbiased reviews. Frontiers revolutionizes research publishing by freely delivering the most outstanding research, evaluated with no bias from both the academic and social point of view. By applying the most advanced information technologies, Frontiers is catapulting scholarly publishing into a new generation. What are Frontiers Research Topics? Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: researchtopics@frontiersin.org 2 June 2017 | Linguistic In uences on M athematical Cognition Frontiers in Psychology LINGUISTIC INFLUENCES ON MATHEMATICAL COGNITION Image by Alexander Artemenko Topic Editors: Ann Dowker, University of Oxford, UK Hans-Christoph Nuerk, University of Tuebingen & LEAD Graduate School and Research Network Tuebingen, Germany For many years, an abstract, amodal semantic magnitude representation, largely independent of verbal linguistic representations, has been viewed as the core numerical or mathematical representation. This assumption has been substantially challenged in recent years. Linguistic properties affect not only verbal representations of numbers,but also numerical magnitude representation, spatial magnitude representations, calculation, parity representation, place-value 3 June 2017 | Linguistic In uences on M athematical Cognition Frontiers in Psychology representation and even early number acquisition. Thus, we postulate that numerical and arith- metic processing are not fully independent of linguistic processing. This is not to say, that in patients, magnitude processing cannot function independently of linguistic processing we just suppose, these functions are connected in the functioning brain. So far, much research about linguistic influences on numerical cognition has simply demonstrated that language influences number without investigating the level at which a particular language influence operates. After an overview, we present new findings on language influences on seven language levels: • Conceptual: Conceptual properties of language • Syntactic: The grammatical structure of languages beyond the word level influences • Semantic: The semantic meaning or existence of words • Lexical: The lexical composition of words, in particular number words • Visuo-spatial-orthographic: Orthographic properties, such as the writing/reading direction of a language. • Phonological: Phonological/phonetic properties of languages • Other language-related skills: Verbal working memory and other cognitive skills related to language representations We hope that this book provides a new and structured overview on the exciting influences of linguistic processing on numerical cognition at almost all levels of language processing. Citation: Dowker, A., Nuerk, H-C., eds. (2017). Linguistic Influences on Mathematical Cognition. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-200-2 4 June 2017 | Linguistic In uences on M athematical Cognition Frontiers in Psychology Table of Contents 1. Introduction, Structure and Overview 06 Editorial: Linguistic Influences on Mathematics Ann Dowker and Hans-Christoph Nuerk 2. Conceptual influences 10 Arbitrary numbers counter fair decisions: trails of markedness in card distribution Philipp A. Schroeder and Roland Pfister 3. Syntactic influences 18 On the relation between grammatical number and cardinal numbers in development Barbara W. Sarnecka 4. Semantic influences 22 Word problems: a review of linguistic and numerical factors contributing to their difficulty Gabriella Daroczy, Magdalena Wolska, Walt Detmar Meurers and Hans-Christoph Nuerk 5. Lexical influences 5.1. Lexical transparency: The case of inversion 35 Intransparent German number words complicate transcoding – a translingual comparison with Japanese Korbinian Moeller, Julia Zuber, Naoko Olsen, Hans-Christoph Nuerk and Klaus Willmes 45 The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters Iro Xenidou-Dervou, Camilla Gilmore, Menno van der Schoot and Ernest C. D. M. van Lieshout 58 On the limits of language influences on numerical cognition – no inversion effects in three-digit number magnitude processing in adults Julia Bahnmueller, Korbinian Moeller, Anne Mann and Hans-Christoph Nuerk 68 The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition Amandine Van Rinsveld, Martin Brunner, Karin Landerl, Christine Schiltz and Sonja Ugen 83 Number word structure in first and second language influences arithmetic skills Anat Prior, Michal Katz, Islam Mahajna and Orly Rubinsten 5.2. Lexical transparency: The case of power transparency 93 Does the transparency of the counting system affect children’s numerical abilities? Ann Dowker and Manon Roberts 5 June 2017 | Linguistic In uences on M athematical Cognition Frontiers in Psychology 100 Linguistic influence on mathematical development is specific rather than pervasive: revisiting the Chinese Number Advantage in Chinese and English children Winifred Mark and Ann Dowker 109 Corrigendum: Linguistic influence on mathematical development is specific rather than pervasive: revisiting the Chinese Number Advantage in Chinese and English children Winifred Mark and Ann Dowker 6. Visuo-spatial-orthographic influences 6.1. Spatial direction of script 110 How space-number associations may be created in preliterate children: six distinct mechanisms Hans-Christoph Nuerk, Katarzyna Patro, Ulrike Cress, Ulrike Schild, Claudia K. Friedrich and Silke M. Göbel 116 Up or down? Reading direction influences vertical counting direction in the horizontal plane – a cross-cultural comparison Silke M. Göbel 128 Two steps to space for numbers Martin H. Fischer and Samuel Shaki 6.2. Spatial complexity of script 131 Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study Maja Rodic, Tatiana Tikhomirova, Tatiana Kolienko, Sergey Malykh, Olga Bogdanova, Dina Y. Zueva, Elena I. Gynku, Sirui Wan, Xinlin Zhou and Yulia Kovas 7. Phonological or auditory influences 142 Mathematics and reading difficulty subtypes: minor phonological influences on mathematics for 5–7-years-old Julie A. Jordan, Judith Wylie and Gerry Mulhern 154 Number processing and arithmetic skills in children with cochlear implants Silvia Pixner, Martin Leyrer and Korbinian Moeller 8. Other language-related influences: Verbal working memory 164 Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation Mojtaba Soltanlou, Silvia Pixner and Hans-Christoph Nuerk EDITORIAL published: 12 July 2016 doi: 10.3389/fpsyg.2016.01035 Frontiers in Psychology | www.frontiersin.org July 2016 | Volume 7 | Article 1035 | Edited and reviewed by: Jessica S. Horst, University of Sussex, UK *Correspondence: Ann Dowker ann.dowker@psy.ox.ac.uk Specialty section: This article was submitted to Developmental Psychology, a section of the journal Frontiers in Psychology Received: 09 May 2016 Accepted: 24 June 2016 Published: 12 July 2016 Citation: Dowker A and Nuerk H-C (2016) Editorial: Linguistic Influences on Mathematics. Front. Psychol. 7:1035. doi: 10.3389/fpsyg.2016.01035 Editorial: Linguistic Influences on Mathematics Ann Dowker 1 * and Hans-Christoph Nuerk 2, 3, 4 1 Experimental Psychology, University of Oxford, Oxford, UK, 2 Department of Psychology, University of Tuebingen, Tuebingen, Germany, 3 Knowledge Media Research Center, University of Tuebingen, Tuebingen, Germany, 4 LEAD Graduate School and Research Network, Tuebingen, Germany Keywords: language, numerical cognition, psychology of arithmetic, verbal counting systems, cross-linguistic research The Editorial on the Research Topic Linguistic Influences on Mathematics For many years, an abstract, amodal semantic magnitude representation, largely independent of verbal linguistic representations, has been viewed as the core numerical or mathematical representation (Dehaene and Cohen, 1995). This assumption has been substantially challenged in recent years (e.g., Miura and Okamoto, 2003; Nuerk et al., 2004, 2005; Dowker et al., 2008; Colomé et al., 2010; Helmreich et al., 2011; Krinzinger et al., 2011; Pixner et al., 2011a,b; Göbel et al., 2014; Imbo et al.; Klein et al.). Linguistic properties affect not only verbal representations of numbers (Seron and Fayol, 1994; Zuber et al., 2009; Pixner et al., 2011a), but also numerical magnitude representation (Nuerk et al., 2005; Pixner et al., 2011b), spatial magnitude representations (Shaki et al., 2009; Helmreich et al., 2011), calculation (Colomé et al., 2010; Krinzinger et al., 2011; Göbel et al., 2014), parity representation (Iversen et al., 2004, 2006; Nuerk et al., 2004), place-value representation (Miura and Okamoto, 2003; for a review, see Nuerk et al.) and even early number acquisition (Sarnecka, this issue). Thus, we postulate that numerical and arithmetic processing are not fully independent of linguistic processing. This is not to say, that in patients, magnitude processing cannot function independently of linguistic processing (e.g., Dehaene and Cohen, 1997), we just suppose, these functions are connected in the functioning brain. So far, much research about linguistic influences on numerical cognition has simply demonstrated that language influences number without investigating the level at which a particular language influence operates. Here we want to distinguish several linguistic levels at which numerical processing may be influenced, according to which we group the articles in our special issue: • Conceptual : Conceptual properties of language • Syntactic: The grammatical structure of languages beyond the word level influences • Semantic: The semantic meaning or existence of words • Lexical: The lexical composition of words, in particular number words • Visuo-spatial-orthographic: Orthographic properties, such as the writing/reading direction of a language. • Phonological: Phonological/phonetic properties of languages • Other language-related skills: Verbal working memory and other cognitive skills related to language representations CONCEPTUAL INFLUENCES Beyond single phonemes, graphemes, words and sentences, linguistic structures are also shaped by linguistic concepts. The linguistic markedness concept suggests that for (almost) each adjective pair, a ground (unmarked) form and a derived (marked) form exist (e.g., efficient and inefficient; marked by “in”). 6 Dowker and Nuerk Editorial: Linguistic Influences on Mathematics We consider the markedness concept “conceptual” (see Nuerk et al., 2004). However, many language models do not consider a conceptual level as such and often the lexical or semantic level is the highest level. Levelt et al. (1999), however, proposed a conceptual level in the language production model. It is the highest level in this model and is assumed to be involved in the conceptual preparation of lexical concepts. In Nuerk et al. (2004, p.859), we suggested that linguistic markedness could operate at just such a conceptual level and that other verbal influences like phonological ones will operate at a different (lower) level, e.g., the phonological encoding in the mental lexicon. Numbers possess several attributes, which can be distinguished into unmarked ground form (large, even, divisible) and marked form (small, odd, indivisible; Hines, 1990). As regards spatial organization “right” is unmarked and “left” is marked (Nuerk et al., 2004). Usually responses are faster, when markedness of stimuli and responses are congruent (e.g., left- odd, right-even). Schroeder and Pfister (this issue) investigated SNARC and MARC effects on card distribution to fellow card players. They observed markedness effects in that magnitude and parity influence card distribution. However, in this natural setting, the markedness effect is inverted to a normal parity judgment task, extending earlier findings in deaf signers (Iversen et al., 2004), and left-handers (Huber et al., 2015). This implies that not only bodily, but also task-specific constraints need to be taken into account, when linguistic effects on mathematical cognition on the construct level are examined. SYNTACTIC INFLUENCES Number processing in real life situations occurs in natural language and is described by grammatical number. (i.e., singular for 1 and plural for numbers 2 and greater in English). Languages differ substantially in their use of grammatical number (see Overmann, 2015) analysis of 905 languages): For instance, 7% of these languages lacked grammatical number altogether despite having lexical numbers. Influences of grammatical numbers on numerical cognition have been shown in two effects. First, Roettger and Domahs (2014) observed a grammatical SNARC effect: singular inflected words elicited faster responses on the left hand side and plural inflected words on the right Second, as beautifully outlined by Sarnecka’s (this issue) review, the sheer existence of certain grammatical number enhances development of number concepts in children. In languages without differentiation between singular and plural, the development of number understanding in children is later. Moreover, grammatical distinction between singular, dual (a grammatical form for “two”) and plural present in several languages further enhances, yet partially hinders number development in children. In some cases, the syntactic structure of a language both influences development of numerical understanding and spatial mappings of numbers. SEMANTIC INFLUENCES Word meanings also influence numerical or arithmetic processing. Daroczy et al. reviewed text problems and found that numerical properties and semantic properties are often interacting. For example, the consistency effect suggests that text problems are easier, when the required operation is consistently associated with the semantics of the words. For instance, addition is more associated with “more,” “buy,” “get,” etc., while subtraction is more associated with “less,” “sell,” “give,” etc. When text problems are presented in a way that makes such associations misleading, children and adults perform less well. This highlights an interrelation between word meaning and preferred arithmetic operations. LEXICAL INFLUENCES Most of the papers in our special issue as well as in the literature are concerned with lexical influences, in particular number words. In general, a transparent number word structure seems to help numerical performance even for problems not involving number words (Nuerk et al., 2015). Two types of lexical influences are discussed in our special issue. The first involves the inversion property. Some languages like Arabic, Dutch and German invert the order of tens and units (“one-and- twenty” for 21), which creates problems in several tasks. Moeller et al. (this issue) compared transcoding (writing numbers to dictation) skills in Japanese and German. The Japanese children did much better. In particular, Japanese children make far fewer inversion errors; but also fewer errors in general. Xenidou-Dervou et al. (this issue) show that the inversion property does not affect all numerical and arithmetic skills. Dutch children (with inversion) lag behind English children in symbolic but not non-symbolic arithmetic. A working memory overload in Dutch was found in non-symbolic, but not symbolic magnitude. However, as Bahnmueller et al. (this issue) show, inversion effects do not even affect all aspects of symbolic number processing. While children’s and adults’ two-digit Arabic number comparison is influenced by inversion properties of a language, adults’ three-digit Arabic number comparison is not. Moreover, van Rinsveld et al. (this issue) found that inversion affected complex but not simple symbolic arithmetic in German-French bilingual secondary pupils. Finally, Prior et al. (this issue) gave Hebrew-Arabic bilinguals oral arithmetic problems, because Arabic but not Hebrew number words possess the inversion property. Participants solved arithmetic problems best when the language structure corresponded to the arithmetic problem. This implies that—contrary to earlier claims—L1 does not completely dominate arithmetic processing, but that both L1 and L2 shape numerical and arithmetic. The second line of research at the lexical level is power transparency. Unlike most European languages, most Asian languages are extremely transparent with respect to the power of a given number (e.g., “ten-two” for 12). From 11 on, children and adults can derive the power of each number directly from the number word. It has been argued that this transparency may be responsible for Asians’ better skills at counting, representing 2-digit numbers, and general arithmetic (Miller et al., 1995; Miura and Okamoto, 2003). However, such results are confounded by the many other educational and Frontiers in Psychology | www.frontiersin.org July 2016 | Volume 7 | Article 1035 | 7 Dowker and Nuerk Editorial: Linguistic Influences on Mathematics cultural differences between countries. One way of obtaining more specific evidence of language effects is to compare children studying in different languages in the same country and educational system. For instance, the Welsh counting system, unlike the English system, is transparent. Dowker et al. (2008) found that children in Welsh-medium primary schools did not do better in arithmetic overall, but showed specific advantages in reading and comparing two-digit numbers. Extending those results Dowker and Roberts observed that Welsh-medium children give more precise and consistent representations of 2- digit numbers on empty number line tasks. Mark and Dowker studied children in Chinese and English medium primary schools in Hong Kong. The Chinese medium children were better at some tasks but not others: e.g., they were better at counting backwards but not forwards; and were not better at number comparison. Thus, we can conclude that lexical influences do affect arithmetic, but not as pervasively as sometimes assumed. VISUO-SPATIAL-ORTHOGRAPHIC INFLUENCES Visual-spatial-orthographic influences mostly involve the reading/writing direction of a given script or its complexity. Usually, space-number relations are associated with the dominant reading/writing direction (for a review see Fischer and Shaki, 2014). However, reading/writing direction already influences spatial-numerical directionality, before children can read or write (Patro and Haman, 2012; Nuerk et al., 2015). Most studies so far have investigated visuo-spatial- orthographic influences on the horizontal left/right dimension. Göbel (this issue) showed that cultural influences on number- space-relations also include the vertical dimension. Fischer and Shaki (this issue) proposed two steps in the shaping of directional space-number representations in adults: “ the spatial dimension selected for mapping of numbers reflects the stimulus and response features of the current task” and “ the orientation of the SNA is influenced by spatial experience.” Relatedly, Rodic et al. examined whether learning spatially complex scripts (e.g., Chinese) is related to mathematical performance. They found no evidence that exposure to a spatially complex script improves mathematics. We conclude that visuo-spatial orthographic skills seem to shape the direction of space-number relations, but not arithmetic skills themselves. PHONOLOGICAL INFLUENCES Jordan et al. examined phonological skills in children with difficulties in reading, mathematics or both and found minor influences on phonology on mathematics. Pixner et al. (this issue) examined children with cochlear implants (CI), who usually have phonological (and also other) language deficits. They found general deficits in such children in multiplication, subtraction and number line estimation, but specific deficits in (verbally mediated) place-value manipulation. We conclude that phonological skills are not related to mathematical functioning per-se , but to verbal representations/manipulations of number. OTHER LANGUAGE-RELATED SKILLS: VERBAL WORKING MEMORY AND OTHER COGNITIVE SKILLS Verbal working memory is associated with complex arithmetic since Ashcraft and Stazyk (1981) seminal paper. Soltanlou et al. (this issue) investigated whether verbal or spatial working memory influences multiplication skill most strongly. They observed an age-related shift from verbal WM to spatial WM influences over time. Thus, working memory data from adults or one children age-group are not representative for its influence in different developmental stages. SUMMARY Linguistic influences on number processing are ubiquitous. They occur at conceptual, semantic, syntactic, lexical, visuo-spatial- orthographic, phonological, and other levels. Research should now address more precisely which language characteristics at which level influence particular numerical tasks at particular ages. AUTHOR CONTRIBUTIONS All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication. ACKNOWLEDGMENTS HN work was supported by funding of the German Research Foundation (DFG NU 265/3-1) on “Linguistic Influences on Numerical Cognition: A cross-cultural investigation using natural specificities of Polish and German languages.” REFERENCES Ashcraft, M. H., and Stazyk, E. H. (1981). Mental addition: a test of three verification models. Mem. Cognit. 9, 185–196. doi: 10.3758/BF03202334 Colomé, À., Laka, I., and Sebastián-Gallés, N. (2010). Language effects in addition: how you say it counts. Q. J. Exp. Psychol. 63, 965–983. doi: 10.1080/17470210903134377 Dehaene, S., and Cohen, L. (1995). Towards an anatomical and functional model of number processing. Math. Cogn. 1, 83–120. Dehaene, S., and Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33, 219–250. doi: 10.1016/S0010-9452(08)70002-9 Dowker, A., Bala, S., and Lloyd, D. (2008). Linguistic influences on mathematical development: how important is the transparency of the counting system? Philos. Psychol. 21, 523–538. doi: 10.1080/09515080802285511 Fischer, M. H., and Shaki, S. (2014). Spatial associations in numerical cognition— From single digits to arithmetic. Q. J. Exp. Psychol. 67, 1461–1483. doi: 10.1080/17470218.2014.927515 Frontiers in Psychology | www.frontiersin.org July 2016 | Volume 7 | Article 1035 | 8 Dowker and Nuerk Editorial: Linguistic Influences on Mathematics Göbel, S. M., Moeller, K., Pixner, S., Kaufmann, L., and Nuerk, H.-C. (2014). Language affects symbolic arithmetic in children: the case of number word inversion. J. Exp. Child Psychol. 119, 17–25. doi: 10.1016/j.jecp.2013.10.001 Helmreich, I., Zuber, J., Pixner, S., Kaufmann, L., Nuerk, H.-C., and Moeller, K. (2011). Language effects on children’s non-verbal number line estimations. J. Cross Cult. Psychol. 42, 598–613. doi: 10.1177/0022022111406026 Hines, T. M. (1990). An odd effect: lengthened reaction times for judgments about odd digits. Mem. Cognit. 18, 40–46. doi: 10.3758/BF03202644 Huber, S., Klein, E., Graf, M., Nuerk, H.-C., Moeller, K., and Willmes, K. (2015). Embodied markedness of parity? Examining handedness effects on parity judgments. Psychol. Res. 79, 963–977. doi: 10.1007/s00426-014-0626-9 Iversen, W., Nuerk, H.-C., Jäger, L., and Willmes, K. (2006). The influence of an external symbol system on number parity representation, or what’s odd about 6? Psychon. Bull. Rev. 13, 730–736. doi: 10.3758/BF03193988 Iversen, W., Nuerk, H.-C., and Willmes, K. (2004). Do signers think differently? The processing of number parity in deaf participants . Cortex 40, 176–178. doi: 10.1016/S0010-9452(08)70940-7 Krinzinger, H., Gregoire, J., Desoete, A., Kaufmann, L., Nuerk, H.-C., and Willmes, K. (2011). Effects of language, curricula on numerical skills in second grade. J. Cross Cult. Psychol. 42, 614–662. doi: 10.1177/0022022111406252 Levelt, W. J. M., Roelofs, A., and Meyer, A. S. (1999). A theory of lexical access in speech production. Behav. Brain Sci. 22, 1–38. doi: 10.1017/s0140525x99001776 Miller, K. F., Smith, C. M., Zhu, J., and Zhang, H. (1995). Preschool origins of cross- national differences in mathematical competence: the role of number-naming systems. Psychol. Sci. 6, 56–60. doi: 10.1111/j.1467-9280.1995.tb00305.x Miura, I. T., and Okamoto, Y. (2003). “Language supports for mathematics understanding and performance.” in The Development of Arithmetic Concepts and Skills, eds A. Baroody and A. Dowker (Mahwah, NJ: Lawrence Erlbaum Associates, Inc.), 229–242. Nuerk, H.-C., Iversen, W., and Willmes, K. (2004). Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect. Q. J. Exp. Psychol. Section A 57, 835–863. doi: 10.1080/02724980343000512 Nuerk, H.-C., Moeller, K., and Willmes, K. (2015). “Multi-digit number processing – overview, conceptual clarifications, and language influences,” in The Oxford Handbook of Numerical Cognition , eds R. Cohen Kadosh and A. Dowker (Oxford: Oxford University Press), 106–139. Nuerk, H.-C., Weger, U., and Willmes, K. (2005). Language effects in magnitude comparison: small, but not irrelevant. Brain Lang. 92, 262–277. doi: 10.1016/j.bandl.2004.06.107 Overmann, K. A. (2015). Numerosity structures the expression of quantity in lexical numbers and grammatical number. Curr. Anthropol. 56, 638–653. doi: 10.1086/683092 Patro, K., and Haman, M. (2012). The spatial–numerical congruity effect in preschoolers. J. Exp. Child Psychol. 111, 534–542. doi: 10.1016/j.jecp.2011.09.006 Pixner, S., Moeller, K., Heˇ rmanová, V., Nuerk, H.-C., and Kaufmann, L. (2011a). Whorf reloaded: language effects on nonverbal number processing in first grade—A trilingual study. J. Exp. Child Psychol. 108, 371–382. doi: 10.1016/j.jecp.2010.09.002 Pixner, S., Zuber, J., Hermanová, V., Kaufmann, L., Nuerk, H.-C., and Moeller, K. (2011b). One language, two number-word systems and many problems: numerical cognition in the Czech language. Res. Dev. Disabil. 32, 2683–2689. doi: 10.1016/j.ridd.2011.06.004 Roettger, T. B., and Domahs, F. (2014). Grammatical number elicits spatial– numerical association of response codes (SNARC) and linguistic markedness of response codes (MARC) effects as a function of task demands. Psychology 57, 835–863. doi: 10.1080/17470218.2014.979843 Seron, X., and Fayol, M. (1994). Number transcoding in children: a functional analysis. Br. J. Dev. Psychol. 12, 281–300. doi: 10.1111/j.2044- 835X.1994.tb00635.x Shaki, S., Fischer, M. H., and Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychon. Bull. Rev. 16, 328–331. doi: 10.3758/PBR.16.2.328 Zuber, J., Pixner, S., Moeller, K., and Nuerk, H.-C. (2009). On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity. J. Exp. Child Psychol. 102, 60–77. doi: 10.1016/j.jecp.2008.04.003 Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Copyright © 2016 Dowker and Nuerk. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Psychology | www.frontiersin.org July 2016 | Volume 7 | Article 1035 | 9 ORIGINAL RESEARCH ARTICLE published: 20 March 2015 doi: 10.3389/fpsyg.2015.00240 Arbitrary numbers counter fair decisions: trails of markedness in card distribution Philipp A. Schroeder 1 * and Roland Pfister 2 1 Department of Psychiatry and Psychotherapy, Neurophysiology and Interventional Neuropsychiatry, University of Tübingen, Tübingen, Germany 2 Department of Psychology III, University of Würzburg, Würzburg, Germany Edited by: Hans-Christoph Nuerk, University of Tübingen, Germany Ann Dowker, University of Oxford, UK Reviewed by: Stefan Huber, Knowledge Media Research Center, Germany Tobias Loetscher, University of South Australia, Australia *Correspondence: Philipp A. Schroeder, Department of Psychiatry and Psychotherapy, Neurophysiology and Interventional Neuropsychiatry, University of Tübingen, Calwerstrasse 14, D-72076 Tübingen, Germany e-mail: philipp.schroeder@ uni-tuebingen.de Converging evidence from controlled experiments suggests that the mere processing of a number and its attributes such as value or parity might affect free choice decisions between different actions. For example the spatial numerical associations of response codes (SNARC) effect indicates the magnitude of a digit to be associated with a spatial representation and might therefore affect spatial response choices (i.e., decisions between a “left” and a “right” option). At the same time, other (linguistic) features of a number such as parity are embedded into space and might likewise prime left or right responses through feature words [odd or even, respectively; markedness association of response codes (MARC) effect]. In this experiment we aimed at documenting such influences in a natural setting. We therefore assessed number-space and parity-space association effects by exposing participants to a fair distribution task in a card playing scenario. Participants drew cards, read out loud their number values, and announced their response choice, i.e., dealing it to a left vs. right player, indicated by Playmobil characters. Not only did participants prefer to deal more cards to the right player, the card’s digits also affected response choices and led to a slightly but systematically unfair distribution, supported by a regular SNARC effect and counteracted by a reversed MARC effect. The experiment demonstrates the impact of SNARC- and MARC-like biases in free choice behavior through verbal and visual numerical information processing even in a setting with high external validity. Keywords: embodied cognition, numerical cognition, SNARC effect, MARC effect, and justice for all, linguistic markedness, free choice INTRODUCTION Like nothing else, numbers are regarded as pure and objective. They are the cornerstone of scientific progress in terms of mea- surements and statistics and they similarly shape global business in various ways—from defining monthly salaries to describing trends at the stock market. But does this objectivity survive when numbers come in contact with human agents? In fact, there seems to be good reason for a positive answer to this question. Numbers obviously allow for rule-based decisions between com- peting options, and a decision that is based on numbers is readily accepted as fair and impersonal (Porter, 1996). At the same time, however, research on human decision making has documented that numbers can systematically bias an agent’s choice behavior via anchoring and adjustment heuristics (Mussweiler and Englich, 2003; Furnham and Boo, 2011). For instance, when asked to estimate the value of a property, laymen and professionals alike rated the price of a real estate higher when they were told a higher listed price before (Northcraft and Neale, 1987). This anchoring bias was found in numerous contexts and research in this domain has shown that heuristic decisions might even integrate nominally irrelevant anchors like telephone and social insurance numbers (Tversky and Kahneman, 1974). Such anchoring effects are of course driven by memory processes rather than by the numbers themselves. Still, recent research on numerical and embodied cognition suggests that the mere presence of a number alone might be sufficient to invoke biases in thoughts and actions (Barsalou, 1999; Fischer, 2006, 2012). These biases built on well-documented associations between numerical magnitude and spatial locations that indicate smaller numbers to be associated with left locations and larger numbers to be associated with right locations [spatial numerical associations of response codes (SNARC) effect; Dehaene et al., 1993; Wood et al., 2008]. Most importantly for the present study, such spatial-numerical associations also affect response choices (Tschentscher et al., 2012; Shaki and Fischer, 2014). That is, when being confronted with smaller numbers, participants showed a preference for choosing a left vs. a right response key (Daar and Pratt, 2008) and, similarly, such small numbers involuntarily prompted left-oriented gaze directions (Ruiz Fernández et al., 2011) and small numbers were produced more likely while turn- ing or gazing to the left (Loetscher et al., 2008, 2010). These automatic biases document that the mere presence of a number is sufficient to bias choices and behavior. Sensory and motor biases induced by the SNARC effect can be considered of high www.frontiersin.org March 2015 | Volume 6 | Article 240 | 10 Schroeder and Pfister Arbitrary numbers counter fair decisions FIGURE 1 | Experimental setup. Participants started each trial by leaving the central home key. They then drew a card, named its value and announced to assign the card to either the left or the right player (represented by two female Playmobil® characters). Card values were predefined according to the rummy game rules and explicitly instructed to the participants. A fair distribution was to be achieved without explicitly counting the values assigned to each player. The experimenter coded each announcement and we analyzed (i) how many cards and points were distributed to each player and (ii) whether digit features (magnitude and parity) affected single response choices. diagnostic merit for the understanding of grounded, embodied, and situated cognition (Fischer, 2012). Findings pertinent to this point range from culture-dependent finger counting habits that influence magnitude representations (Domahs et al., 2010) to bodily postures (Eerland et al., 2011) or even “unusual bodies” (Keehner and Fischer, 2012) that introduce peculiarities in spatial tasks. Together, these studies indicate that numerical associations reliably alter spatial response choices in deliberately employed highly controlled settings where the agent does not pursue any other goals except for deciding spontaneously for a spatially coded response. As a first aim, the present study investigated whether the described bias would also occur in a more externally valid setting such as in situations where the agent aims at fairly and objectively distributing value among other people. We operationalized this situation in terms of a card distribution task in which participants were asked to deal cards of a given value to a player to the left or to the right and additionally announce their value-space choice ( Figure 1 ). If spatial-numerical biases do indeed generalize to this situation, participants should deal more cards with higher values to the right player than to the left player. Of course, these biases do not work in an all or none fashion, but gradually. That is, even though participants prefer choices that are congruent to a number’s spatial association (e.g., a left response to a small number), they also tend to show a fair amount of incongruent choices (e.g., a right response to a small number; Daar and Pratt, 2008). In the natural card playing setting of this study, however, both spatial-numerical associations and marked- ness of parity and space [markedness association of response codes (MARC) effect; Nuerk et al., 2004] might affect choice probabilities for each single card, summing up to an overall biased and th