Knowledge Base

  • Linguistic influences on numerical cognition
    • Conceptual influences
    • Syntactic influences
    • Semantic influences
    • Lexical influences
    • Visuo-spatial-orthographic influences
    • Phonological influences
    • Other language related skills: verbal working memory and other cognitive skills

  • Important papers in the field of numerical cognition
  • Key papers in the field of psycholinguistics

 

Linguistic influences on numerical cognition

 

Ann Dowker and Hans-Christoph Nuerk (2016) suggest that arithmetical and numerical processing are not entirely independent of linguistic influences. They propose a taxonomy of linguistic influences on number processing (see here). They conclude that further research is necessary to examine in more depth the precise influence of individual language characteristics on numerical processing in development.

 

Dowker, A. and Nuerk, H.-C. (2016). Editorial: Linguistic Influences on Mathematics. Frontiers in Psychology 7:1035.

Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2016.01035/full

 

 

Conceptual influences

The linguistic markedness concept suggests that for (almost) every adjective pair, a ground (unmarked) form and a derived (marked) form exist (e.g. efficient and inefficient; marked by “in”). For number parity, the ground form is even, and the derived - odd. This is also the case of German (gerade versus ungerade) and Polish (parzyste versus nieparzyste) languages. Also many would be a ground form, and few – a derived form. Markedness have been repeatedly shown to influence number processing. We consider it as a “conceptual” level of influence because markedness is assumed to be involved in the conceptual preparation of lexical concepts (Levelt et al., 1999).

 

  • Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General, 139, 180-190.

    The authors conducted a series of experiments to examine the role of verbal-spatial coding in explaining the SNARC effect. They concluded that, instead of visuospatial coding (i.e. the “mental number line” hypothesis) verbal-spatial coding is the driving force behind the SNARC effect. It is argued that on a verbal polarity, small numbers are assigned a verbal “small” label on the negative polarity, whereas bigger numbers are assigned a “large” label on the positive polarity. These polarities are also connected to spatial left (-) and right (+) representations, accounting for a facilitations of response when small (left) and large (right) representations are activated. Therefore, it may be claimed that linguistic markedness (which may differ between languages) may at least to some extent cause the SNARC effect.
     

    Can be retrieved from: http://psycnet.apa.org/journals/xge/139/1/180/

 

  • Hines, T. M. (1990). An odd effect: Lengthened reaction times for judgments about odd digits. Memory & Cognition, 18, 40-46.

    The author reports findings from a series of parity judgement experiments, in which response latencies were larger for odd than for even numbers, with the effect being bigger for two and three-digit numbers. The results are explained with regard to linguistic markedness: Drawing comparisons to slower judgements of marked nouns (e.g. “dead” objects vs “alive” objects), the authors hypothesize that odd numbers are linguistically marked, whereas even numbers are processed as a linguistically unmarked concepts. Namely, processing even numbers is much more efficient than odd ones.


    Can be retrieved from: http://link.springer.com/article/10.3758%2FBF03202644

 

  • Huber, S., Klein, E., Graf, M., Nuerk, H.-C., Moeller, K., & Willmes, K. (2014). Embodied markedness of parity? Examining handedness effects on parity judgments. Psychological research, 79, 963-977.

     

    Hubert et al. examined differences in the linguistic markedness of response codes (MARC) effect between right and left handers. The MARC effect describes the results obtained in parity judgment tasks, where right-hand reaction times were smaller for unmarked words (even numbers) and left-hand responses were faster for marked words (odd numbers). In Huber et al.’s study, the results of a parity judgment task indicate that the MARC effect is not modulated by handedness when processing tens digits (only when processing unit digits). However, the direction of the MARC effect depends on the degree of left-handedness.

    Can be retrieved from: http://link.springer.com/article/10.1007%2Fs00426-014-0626-9

 

  • Nuerk, H.-C., Iversen, W., & Willmes, K. (2004). Notational modulation of the SNARC and the MARC (Linguistic Markedness Association of Response Codes) Effect. Quarterly Journal of Experimental Psychology, 57, 835-863.

     

    In this article the SNARC (people respond faster to small numbers with their left hand and to large numbers with their right hand) and MARC (responses are facilitated if stimuli and response codes both have the same linguistic markedness) effect were systematically examined for different number notations (positive Arabic numbers, negative Arabic numbers, number words). In a parity judgement task, the SNARC effect was replicated for all notations except for negative numerals. The MARC effect (i.e. responses to odd numbers were faster on left hand side whereas responses to even numbers were faster on the right hand side) was found for number words in all analyses. A correlational analysis of the reaction time (RT) data produced a clear association of parity and response code for all notations (MARC effect), but little evidence of the SNARC effect.

    Can be retrieved from: http://www.tandfonline.com/doi/abs/10.1080/02724980343000512

 

  • Roettger, T. B., & Domahs, F. (2015). Grammatical number elicits SNARC and MARC effects as a function of task demands. The Quarterly Journal of Experimental Psychology, 68, 1231-1248.

     

    To investigate the extraction of quantity information from German number words and nouns inflected for singular and plural the authors ran two experiments using a two alternative forced choice paradigm. In Experiment 1 they found SNARC effects (a relative left-hand advantage for words denoting small numbers and a right-hand advantage for words denoting large numbers) in semantic tasks (parity decision, quantity comparison), but not in lexical processing tasks (lexical decision, font categorization). In Experiment 2 a SNARC-like effect was observed for grammatical number. The effect interfered with a MARC-like effect based on the markedness asymmetry of singulars and plurals. These two effects appear to be dissociated by response latency rather than task demands.

    Can be retrieved from: http://www.tandfonline.com/doi/abs/10.1080/17470218.2014.979843

 

  • Schroeder, P. A., & Pfister, R. (2015). Arbitrary numbers counter fair decisions: trails of markedness in card distribution. Frontiers in Psychology 6:240.

     

    Number-space and parity-space association effects were tested in a natural setting: Participants dealt playing cards to fictitious players 'seated' to their left or right after reading the card value. SNARC- and MARC-like biases influenced participants into dealing both more cards as well as higher-valued cards to the player to their right. Therefore, there is evidence for linguistically based effects of number (the MARC effect is in response to parity, a linguistic construct) on behaviour.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00240/full

 

Syntactic influences

The grammatical number is an instance of linguistic influence on mathematics on a syntactic level. Languages differ significantly in their use of grammatical number (e.g. in English singular form goes along with number 1 and plural for numbers 2 and greater whereas in some languages like Slovenian there is a separate grammatical number for two). The influence of the grammatical number has been shown in a grammatical SNARC effect (Roettger & Domahs, 2014) and in the development of number concepts in children (Sarnecka, 2016).

 

  • Göbel, S. M., Shaki, S., & Fischer, M. H. (2011). The cultural number line: a review of cultural and linguistic influences on the development of number processing. Journal of Cross-Cultural Psychology, 42, 543-565.
     

    The authors provide a review on the core concepts of numerical cognition, including the “mental number line”. Göbel et al. discuss how culture affects the representation and processing of numbers by arguing that linguistic influences can be observed in exact number processing above 4, while approximate processing is universal and preverbal. Other cultural effects, like reading direction, are also discussed. It is concluded that more studies are needed to examine a cross-cultural perspective and the constraints culture and language, specifically, impose on numerical cognition.

    Can be retrieved from: http://journals.sagepub.com/doi/abs/10.1177/0022022111406251

 

  • Roettger, T. B., & Domahs, F. (2015). Grammatical number elicits SNARC and MARC effects as a function of task demands. The Quarterly Journal of Experimental Psychology, 68, 1231-1248.
     

    To investigate the extraction of quantity information from German number words and nouns inflected for singular and plural the authors ran two experiments using a two alternative forced choice paradigm. In Experiment 1 they found SNARC effects (a relative left-hand advantage for words denoting small numbers and a right-hand advantage for words denoting large numbers) in semantic tasks (parity decision, quantity comparison), but not in lexical processing tasks (lexical decision, font categorization). In Experiment 2 a SNARC-like effect was observed for grammatical number. The effect interfered with a MARC-like effect based on the markedness asymmetry of singulars and plurals. These two effects appear to be dissociated by response latency rather than task demands.

    Can be retrieved from: http://www.tandfonline.com/doi/abs/10.1080/17470218.2014.979843

 

  • Sarnecka, B. W. (2014). On the relation between grammatical number and cardinal numbers in development. Frontiers in Psychology 5 :1132.
     

    The author provides a mini-review on the effects of language specific grammatical number system on how children learn to understand cardinal number words. This means that the understanding of certain important cardinalities, such as 'one' and 'two' are learned quicker or slower depending on the language a child is brought up with, thus contradicting an innate concept of 'oneness' or 'twoness' of objects. The author suggests that these language influences are strong arguments for a constructivist account of number-learning processing rather than a nativist. This means that number learning requires significant conceptual changes and is most likely not something humans are born with.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2014.01132/full
     

 

Semantic influences

Word meanings also influence numerical processing. Daroczy et al. (2015) reviewed text problems and found that numerical properties and semantic properties are often interacting. For instance, addition is more associated with words like “more” and “buy” whereas subtraction is more associated with words like “less” and “sell”.

 

  • Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H.-C. (2015). Word problems: a review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology 6:348.

    The authors provide a review of research on mathematical word problem solving. Despite word problems generally being considered as purely arithmetical problems, there are findings that suggest influences of non-mathematical linguistic components in this kind of problem. The authors claim that a high degree of control in stimuli design is necessary when designing word problems.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00348/full

 

  • Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General, 139, 180-190.
     

    The authors conducted a series of experiments to examine the role of verbal-spatial coding in explaining the SNARC effect. They concluded that, instead of visuospatial coding (i.e. the “mental number line” hypothesis) verbal-spatial coding is the driving force behind the SNARC effect. It is argued that on a verbal polarity, small numbers are assigned a verbal “small” label on the negative polarity, whereas bigger numbers are assigned a “large” label on the positive polarity. These polarities are also connected to spatial left (-) and right (+) representations, accounting for a facilitations of response when small (left) and large (right) representations are activated. Therefore, it may be claimed that linguistic markedness (which may differ between languages) may at least to some extent cause the SNARC effect.

    Can be retrieved from: http://psycnet.apa.org/journals/xge/139/1/180/
     

 

Lexical influences

Two types of lexical properties have been shown to influence numerical cognition: The first involves the inversion property of some languages which means an inversion of units and decades (“one-and-twenty” for 21 e.g. in German). The second one involves power transparency. Some languages are extremely transparent with respect to the power of a given number (e.g. “ten-two” for 12 in Chinese). The power of each two-digit number can be derived directly from the number word. Both these effects have been shown to influence both number acquisition in children (and typical errors children make) as well as number processing in adults.

 

  • Bahnmueller, J., Moeller, K., Mann, A., & Nuerk, H.-C. (2015). On the limits of language influences on numerical cognition–no inversion effects in three-digit number magnitude processing in adults. Frontiers in Psychology 6:1216.

    The authors investigated compatibility effects in a three-digit number comparison task in German and English samples. While there were reliable hundred-decade and hundred-unit compatibility effects, these were not modulated by inversion in the German sample. This suggests that the inversion property may not influence processing of multi-digit numbers comprising more than two digits.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.01216/full

 

  • Domahs, F., Janssen, U., Schlesewsky, M., Ratinckx, E., Verguts, T., Willmes, K., & Nuerk, H.-C. (2007). Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence. Behavioral and Brain Functions, 3, 66.

    Domahs et al provide evidence for neighborhood-consistency effects, challenging a holistic view of decade and unit digit representations. The authors measured behavioral and ERP data during a simple multiplication verification task and found that lure numbers having the same decade digit as the actual result lead to higher reaction times and more errors in judgment than numbers being inconsistent with the result in both digits. The results speak in favor of models like the Interacting Neighbors Model, which assumes a separate representation of digits. Regarding linguistics, the authors draw comparisons between the neighborhood-consistency effect and the neighborhood frequency effect observed in lexical decision tasks, with both effects being associated with similar brain activation patterns.


    Can be retrieved from: http://behavioralandbrainfunctions.biomedcentral.com/articles/10.1186/1744-9081-3-66

 

  • Dowker, A., & Roberts, M. (2015). Does the transparency of the counting system affect children's numerical abilities?. Frontiers in Psychology 6:945. 
     

    School children that were taught to count in either English or Welsh were compared in non-verbal line estimations and transcoding. While there was no difference in global arithmetic abilities, Welsh-taught children tended to perform better in line estimation tasks, especially in numbers over 20. According to the authors, this is due to the transparent nature of the Welsh counting system (11 is counted as one-ten-one) compared to English (11 as an irregular 'eleven').

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00945/full

 

  • Göbel, S. M., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2013). Language affects symbolic arithmetic in children: the case of number word inversion. Journal of Experimental Child Psychology, 119, 17-25.
     

    The authors compared performances of 7-9 year old German and Italian-speaking children in a symbolic addition task. German speaking children showed increased response latencies for more difficult tasks in which a carry operation was needed, which the authors attributed to the effect of number inversion in the German language.

    Can be retrieved from: http://www.academia.edu/14020952/Language_affects_symbolic_arithmetic_in_children_The_case_of_number_word_inversion

 

  • Göbel, S. M. (2015). Up or down? Reading direction influences vertical counting direction in the horizontal plane–a cross-cultural comparison. Frontiers in Psychology 6:228.

    Adults and children from either the UK or Hong Kong counted objects either in vertical arrays or as a square. While English-speaking children tended to count objects from bottom-to-top, all other groups tended to count from top (left)-to-bottom (right). The author concludes that vertical counting is influenced by reading direction.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00228/full

 

  • Helmreich, I., Zuber, J., Pixner, S., Kaufmann, L., Nuerk, H.-C. & Moeller, K. (2011). Language effects on children’s mental number line. Journal of Cross-Cultural Psychology, 42, 598-613.
     

    Number line estimations of Italian- and German-speaking first graders were compared. Italian children’s performance exceeded German children’s estimations, particularly when inversion errors were involved. This indicates that language features affect children’s mental number line.

    Can be retrieved from: http://journals.sagepub.com/doi/abs/10.1177/0022022111406026

 

  • Krinzinger, H., Gregoire, J., Desoete, A., Kaufmann, L., Nuerk, H.-C. & Willmes, K. (2011). Effects of language, curricula on numerical skills in second grade. Journal of Cross-Cultural Psychology, 42, 614-662.
     

    Krinzinger et al conducted a cross-cultural study in which language effects and curricular effects on second graders’ math performance were tested. The results suggest that language indeed affects performance (due to inversion in certain languages); however, it is not the only factor influencing numerical development, since curricular differences also play a role.

    Can be retrieved from: http://journals.sagepub.com/doi/abs/10.1177/0022022111406252

 

  • Mark, W., & Dowker, A. (2015). Linguistic influence on mathematical development is specific rather than pervasive: revisiting the Chinese Number Advantage in Chinese and English children. Frontiers in Psychology 6:203.

    Hong Kong children who were taught in school to count either in English (HK-E) or Chinese (HK-C), as well as a group of UK school children, were compared on counting, numerical abilities and place value representation. Apart from backwards counting, there was no significant difference between groups in any of the given measures. This suggests that different languages had no major effect on mathematical abilities.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00203/full

 

  • Mark, W., & Dowker, A. (2016). Corrigendum: Linguistic influence on mathematical development is specific rather than pervasive: revisiting the Chinese Number Advantage in Chinese and English children. Frontiers in Psychology 7:342.

    A mistake in the abstract of Mark & Dowker (2015, see below) was corrected.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2016.00342/full

 

  • Moeller, K., Zuber, J., Olsen, N., Nuerk, H.-C., & Willmes, K. (2015). Intransparent German number words complicate transcoding – a translingual comparison with Japanese. Frontiers in Psychology 6:740.

    Japanese and German schoolchildren were compared in a transcoding task (i.e. writing numbers by dictation). Japanese children tended to perform better than German children, who struggled with inversion errors (e.g. mistaking 27 with 72). This is likely due to the increased difficulty of the association of symbolic Arabic numbers to their corresponding number words in German.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00740/full

 

  • Nuerk, H.-C., Patro, K., Cress, U., Schild, U., Friedrich, C. K., & Göbel, S. M. (2015). How space-number associations may be created in preliterate children: six distinct mechanisms. Frontiers in Psychology 6:215.

    Spatial-Numerical Associations (SNAs) are considered to be shaped by cultural experiences, such as reading direction. Interestingly, SNAs are often present before reading onset. The authors propose six mechanisms how they can be formed.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00215/full

 

  • Nuerk, H.-C. Weger, U., & Willmes, K. (2005a). Language effects in magnitude comparison: Small, but not irrelevant. Brain and Language, 9, 262-277.

     

    Previous research has observed a unit–decade–compatibility effect in a magnitude comparison task in a German sample (Nuerk, Weger, & Willmes, 2001). Incompatible magnitude comparisons (e.g., 27_91) are slower and less accurately responded to than compatible trials (e.g. 23_98). In this study, Nuerk et al report the same compatibility effect for an English sample indicating that this effect is not language-specific. In cross-linguistic analyses language-specific modulations were observed for number words and Arabic numbers. No indication of a compatibility effect was observed for the non-inverted English number words while in German participants interactions with compatibility for German number words were observed.

    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S0093934X0400210X

 

  • Pixner, S., Zuber, J., Hermanova, V., Kaufmann, L., Nuerk, H.-C. & Moeller, K. (2011a). One language, two number-word systems and many problems: Numerical cognition in the Czech language. Research in Developmental Disabilities, 32, 2683-2689.

     

    In the Czech language exist two different number-word systems within the same language (i.e. “25” can be either coded in non-inverted order “dvadsetpät” [twenty-five] or in inverted order “pätadvadset” [five-and-twenty]). This study investigates the influence of the number-word system on basic numerical processing within Czech culture. 7-year-old Czech-speaking children had to perform a transcoding task in both number-word systems. The results suggest that the development of numerical cognition does not only depend on cultural or educational differences. It is related to the structure and transparency of a given number-word system.


    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S089142221100240

 

  • Pixner, S., Moeller, K., Hermanova, V., Nuerk, H.-C. & Kaufmann, L. (2011b). Whorf reloaded: Language effects on nonverbal number processing in first grade - A trilingual study. Journal of Experimental Child Psychology, 108, 371-382.
     

    The current study aimed at elucidating the influence of language properties on the compatibility effect of Arabic two-digit numbers in Austrian, Italian, and Czech first graders. The number word systems of the three countries differ with respect to their correspondence between name and place value systems (German: inversion, Italian: no inversion, Czech: both forms). The authors interpret the results as evidence for a detrimental influence of an intransparent number word system place value processing. German children showed the most pronounced compatibility effect with respect to both accuracy and speed.

    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S002209651000176

 

  • Pixner, S., Nuerk, H.-C. & Moeller, K. (2015). Einflüsse der Inversion auf die Verarbeitung mehrstelliger Zahlen bei deutschsprachigen Kindern – ein Überblick Lernen und Lernstörungen, 5, 173-188. [in German]
     

    Recent literature on multi-digit number processing and its underlying mechanisms in children is summarized and discussed. The authors pay particular attention to the so-called place-value structure of the Arabic number system and how this structural information influences the development of multi-digit number processing in children.

    Can be retrieved from: http://econtent.hogrefe.com/doi/full/10.1024/2235-0977/a000021

 

  • Prior A., Katz M., Mahajna, I., & Rubinsten, O. (2015). Number word structure in first and second language influences arithmetic skills. Frontiers in Psychology 6:266.

    Arabic-Hebrew bilinguals were compared with Hebrew L1 (first language) speakers who do not speak an inverted language (a language in which tens are spoken after units, i.e. 'seven-and-twenty' instead of 'twenty-seven' for '27'). Participants had to judge the accuracy of addition problems that were presented either aurally in L1 or L2 (second language) or visually. The authors conclude that bilinguals who speak both an inverted (Arabic) and non-inverted (Hebrew) language are more flexible towards numbers presented in an inverted or non-inverted fashion.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00266/full

 

  • Van Rinsveld, A., Brunner, M., Landerl, K., Schiltz, C., & Ugen, S. (2015). The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition. Frontiers in Psychology 6:265.

    A French-German bilingual sample of adolescents and young adults was required to solve simple and complex additions in German and French. It was examined if word structure (i.e. the unit-decade inversion of numbers in German) had an effect, similar to or stronger than bilingual proficiency on addition. While language proficiency was found to be important for complex addition, language-specific word structures had a larger effect on arithmetic performance.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00265/full

 

  • Xenidou-Dervou, I., Gilmore, C., van der Schoot, M., & van Lieshout, E. C. (2015). The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters. Frontiers in Psychology 6:487.

    The authors report two longitudinal studies, of which one was carried out with Dutch children and one with Dutch and English children to compare the differences between a language with and without the inversion of numbers (speaking tens before units, i.e. 'seven-and-twenty' instead of 'twenty-seven'). They demonstrate that development and education affect the symbolic number system more than the non-symbolic number system. The symbolic system is also modulated by language.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00487/full

 

  • Zuber, J., Pixner, S., Moeller, K., & 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. Journal of Experimental Child Psychology, 102, 60-77.
     

    Zuber et al investigate whether the mastery of inversion and of transcoding in general is related to nonnumerical factors such as working memory resources. Therefore, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. Inversion posed a major problem in transcoding. Additionally, different components of working memory skills were differentially correlated with particular transcoding error types. It is discussed how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components.

    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S0022096508000519
     

 

Visuo-spatial-orthographic influences

Visual-spatial-orthographic influences mostly involve the reading/writing direction of a given script. Usually, space-number relations are associated with the dominant reading/writing direction. Visual-spatial-orthographic influences haven been shown for both horizontal and vertical dimensions.

 

  • Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396.
     

    The authors examined differences in accessing parity and number magnitude from Arabic and verbal numerals. Processing these features in Arabic numerals relied on semantic number knowledge, whereas verbal numerals involved an additional transcoding to base 10. In this paper the SNARC effect (Spatial-Numerical Association of Response Codes) was described for the first time. This term refers to a phenomenon that in left-to-right reading cultures small magnitude numbers are responded faster on the left hand side, whereas large magnitude numbers are responded faster on the right hand side. Already in this foundational report of the SNARC effect demonstrated, that SNARC varies depending on reading / writing direction, as well as depends on time spent in given language environment. Namely, the comparison was made between French and Farsi speakers.

    Can be retrieved from: http://psycnet.apa.org/index.cfm?fa=buy.optionToBuy&uid=1993-44067-001

 

  • Fischer, M. H., & Shaki, S. (2015). Two steps to space for numbers. Frontiers in Psychology 6:612.

    In this opinion article, the authors propose that 'spatial mapping is an integral part of semantic number processing'. Namely, they do not solely depend on reading habits or even language / culture in general. The authors encourage further research on origins of spatial-numerical associations (SNAs).

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00612/full

 

  • Göbel, S. M., Shaki, S., & Fischer, M. H. (2011). The cultural number line: a review of cultural and linguistic influences on the development of number processing. Journal of Cross-Cultural Psychology, 42, 543-565.
     

    The authors provide a review on the core concepts of numerical cognition, including the “mental number line”. Göbel et al. discuss how culture affects the representation and processing of numbers by arguing that linguistic influences can be observed in exact number processing above 4, while approximate processing is universal and preverbal. Other cultural effects, like reading direction, are also discussed. It is concluded that more studies are needed to examine a cross-cultural perspective and the constraints culture and language, specifically, impose on numerical cognition.

    Can be retrieved from: http://journals.sagepub.com/doi/abs/10.1177/0022022111406251

 

  • Moeller, K., Shaki, S., Göbel, S. M., & Nuerk, H.-C. (2015). Language influences number processing - a quadrilingual study. Cognition, 136, 150-155.
     

    Moeller et al report, that symbolic number magnitude comparison is influenced by the interaction of reading/writing direction and number word formation. People from cultures where reading direction and the order of tens and units in number words are incongruent tend to exhibit more pronounced unit interference in place-value integration. This effect is not due to differences in education.

    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S0010027714002236

 

  • Rodic M, Tikhomirova T, Kolienko T, Malykh S, Bogdanova O, Zueva DY, Gynku EI, Wan S, Zhou X and Kovas Y (2015) Spatial complexity of character based writing systems and arithmetic in primary school: a longitudinal study. Frontiers in Psychology 6:333.

    Children in the UK and Russia were compared in a longitudinal study on a set of arithmetic and cognitive tasks. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). It was tested if spatial ability predicts mathematical ability and whether the use of a character-based writing system (i.e. Chinese, Japanese) leads to an advantage in the tasks given. The authors conclude that one year of exposure to spatially complex writing systems is not sufficient to provide a clear mathematical advantage over other writing systems.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00333/full
     

 

Phonological influences

Jordan et al. (2015) examined phonological skills in children with difficulties in reading, mathematics or both and found minor influences of phonology on mathematics. Pixner et al. (2016) examined children with cochlear implants, who usually have phonological 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.

 

  • Jordan, J. A., Wylie, J., & Mulhern, G. (2015). Mathematics and reading difficulty subtypes: Minor phonological influences on mathematics for 5–7-years-old. Frontiers in Psychology 6:221.

    In a longitudinal study, young children were screened for mathematics and reading difficulties and categorized into four groups of having either mathematical difficulties (MD), reading difficulties (RD), both (MDRD) or being typical achievers. Over a period of two years, the mathematical developmental pattern of MDRD and MD children was similar. Following these results, the authors conclude that language plays only a minor role in mathematical development.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00221/full

 

  • Pixner, S., Leyrer, M., & Moeller, K. (2014). Number processing and arithmetic skills in children with cochlear implants. Frontiers in Psychology 5:1479.

    Arithmetic skills of children with cochlear implants (CI) were compared to those of a control sample. CI children displayed symptoms of dyscalculia as well as specific difficulties with place-value understanding (i.e. knowing that a digit appearing in a certain position in an arabic numeral corresponds to a certain amount of units, decades, hundreds, etc...) compared to the control sample.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2014.01479/full
     

 

Other language related skills: verbal working memory and other cognitive skills

Several domain-general processes such as for instance verbal working memory play an important role both in number and language processing. Verbal working memory (WM) is associated with complex arithmetic (Ashcraft & Stazyk, 1981). Soltanlou et al. (2016) 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.

 

  • Soltanlou, M., Pixner, S., & Nuerk, H.-C. (2015). Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation. Frontiers in Psychology 6:1062.

    Elementary school children in grade 4 participated in a longitudinal study examining operand-related errors. The contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory was also considered. The authors suggest that mathematical development is characterized by shifts of memory performance. In grade 4 children this may be a shift from verbal to visual and semantic learning due to the introduction of more written tasks.

    Can be retrieved from: http://journal.frontiersin.org/article/10.3389/fpsyg.2015.01062/full

 

  • Zuber, J., Pixner, S., Moeller, K., & 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. Journal of Experimental Child Psychology, 102, 60-77.
     

    Zuber et al investigate whether the mastery of inversion and of transcoding in general is related to nonnumerical factors such as working memory resources. Therefore, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. Inversion posed a major problem in transcoding. Additionally, different components of working memory skills were differentially correlated with particular transcoding error types. It is discussed how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components.

    Can be retrieved from: http://www.sciencedirect.com/science/article/pii/S0022096508000519
     

 

 

Important papers in the field of numerical cognition

 

Key papers in the field of numerical cognition describing phenomena we wish to investigate and tackle linguistic influences on thereof.

 

  • Cipora, K., & Nuerk, H.-C. (2013). Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill. The Quarterly Journal of Experimental Psychology, 66, 1974-1991.

    The authors examined potential differences between mathematically skilled and unskilled participants in SNARC effect. However, even after addressing possible problems that could lead to obtaining non-significant differences in previous studies, the authors present a positive evidence for a null effect (i.e. no difference in the SNARC effect depending on the math skill level).

    Can be retrieved from: www.tandfonline.com/doi/full/10.1080/17470218.2013.772215

 

  • Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive neuropsychology, 20, 487-506.

    Examining fMRI activation and neuropsychological data, the authors suggest three parietal circuits for number processing: the hIPS(horizontal part of the intraparietal sulcus) as a core quantity system for number manipulation; a left angular gyrus area supporting verbal number processing; and a bilateral posterior superior parietal system influencing orientation on spatial dimesions.

    Can be retrieved from: www.tandfonline.com/doi/abs/10.1080/02643290244000239

 

  • Domahs, F., Moeller, K., Huber, S., Willmes, K., & Nuerk, H.-C. (2010). Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures. Cognition, 116, 251-266.

    The authors tested the effect of finger-counting habits on adult mental number representation. In this cross-cultural study, the two groups using an explicit sub-base-five system (hearing and deaf Germans), showed particularly large sub-base-five effects, compared to Chinese participants, supporting the notion that bodily experiences influence abstract cognition.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S0010027710001095

 

  • Grabner, R. H., Ischebeck, A., Reishofer, G., Koschutnig, K., Delazer, M., Ebner, F., & Neuper, C. (2009). Fact learning in complex arithmetic and figural-spatial tasks: The role of the angular gyrus and its relation to mathematical competence. Human Brain Mapping, 30, 2936-2952.

    The authors examined the role of the angular gyrus on arithmetic problem solving in an fMRI study. The results show that angular gyrus activation is not specific for arithmetic problems, but differs between participants with high and low mathematical competence in untrained arithmetic problems.

    Can be retrieved from: onlinelibrary.wiley.com/wol1/doi/10.1002/hbm.20720/full

 

  • Hoeckner., H. S., Moeller, K., Zauner, H., Wood, G., Haider, C., Gaßner, A., & Nuerk, H.-C. (2008). Impairments of the mental number line for two-digit numbers in neglect. Cortex, 44, 429-438.

    The authors examined numerical representations of the full range of two-digit numbers in neglect patients, who made judgements of the arithmetical middle in number triplets. The results indicate that neglect patients show an impaired magnitude representation, i.e. have problem accessing the left side of the mental number line.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S001094520700086X

 

  • Klein, E., Nuerk, H.-C. , Wood, G., Knops, A., & Willmes, K. (2009). The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition. Brain and cognition, 69, 369-381.

    Based on an fMRI study in which the two factors: target identity and distance were manipulated independently, Klein et al contest the notion that two calculation processes (exact vs approximate) are generally distinct. The authors suggest further research to be conducted in order to examine the conditions under which the distinction might be valid.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S027826260800256X

 

  • Klein, E., Moeller, K., Nuerk, H.-C. , & Willmes, K. (2010). On the neuro-cognitive foundations of basic auditory number processing: An fMRI study. Behavioral and Brain Functions, 6, 44.

    Klein et al examined if the automatic activation of magnitude representation observed in visually presented numbers could be found for auditorily presented numbers, as well. The results of the fMRI study the authors conducted indeed indicate that this activation is highly automatic for spoken number words.

    Can be retrieved from: behavioralandbrainfunctions.biomedcentral.com/articles/10.1186/1744-9081-6-42

 

  • Klein, E., Mann, A., Huber, S., Bloechle, J., Willmes, K., Karim, A. A., Nuerk, H.-C. , & Moeller, K.(2013a). Bilateral bi-cephalic tDCS with two active electrodes of the same polarity modulates bilateral cognitive processes differentially. PLoS ONE, 8, e71607.

    Klein et al’s tDCS study supports the notion proposed by the Triple Code Model that magnitude information is represented bilaterally in the intraparietal cortices. Using bilateral bi-cephalic tDCS, the authors showed that stimulation in this area affected numerical tasks and number magnitude processing specifically.

    Can be retrieved from: journals.plos.org/plosone/article

 

  • Klein, E., Moeller, K., Zinsberger, D., Zauner, H., Wood, G., Willmes, K., Haider, C., Gassner, A., & Nuerk, H.-C. (2013b). Object-based neglect in number processing. Behavioral and Brain Functions, 9:5.

    The authors conducted a study with neglect patients to examine how an object-based neglect might influence number processing. The results suggests that neglect patients have trouble integrating multi-digit numbers, since processing of the left part of the numbers is impaired.

    Can be retrieved from: behavioralandbrainfunctions.biomedcentral.com/articles/10.1186/1744-9081-9-5

 

  • Klein, E., Suchan, J., Moeller, K., Karnath, H.-O., Knops, A., Wood, G., Nuerk, H.-C. , & Willmes, K. (2016). Considering structural connectivity in the triple code model of numerical cognition – Differential connectivity for magnitude processing and arithmetic facts. Brain Structure and Functions, 221, 979-955.

    Klein et al evaluated, confirmed and augmented the Triple Code Model by examining the functional involvement of different areas on magnitude processing and arithmetic fact retrieval, as well as the relation between both features.

    Can be retrieved from: link.springer.com/article/10.1007/s00429-014-0951-1%20%20/fulltext.html

 

  • Knops, A., Nuerk, H.-C. , B., F., Vohn, R., & Willmes, K. (2006a). A special role for numbers in working memory? An fMRI study. NeuroImage, 29, 1-14.

    Knops et al challenge the notion of a purely phonological code in verbal Working Memory (vWM). The authors utilized an n-back paradigm with letters and numbers at different levels of vWM, and compared the activation in horizontal parts of the intraparietal sulcus (hIPS).

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S1053811905004908

 

  • Knops, A., Nuerk, H.-C., Sparing, R., Foltys, H., & Willmes, K. (2006b). On the functional role of human parietal cortex in number processing: How gender mediates the impact of a virtual lesion induced by rTMS. Neuropsychologia, 44, 2270-2283.

    Knops et al stimulated participants’ horizontal part of the intraparietal sulcus (hIPS) with TMS while letting them perform a number magnitude comparison task. Male participants displayed a decreased distance effect, while both distance and compatibility effects increased for female participants, indicating that the hIPS is involved in both number magnitude processing, as well as the integration of unit-decade magnitude information.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S0028393206001898

 

 

 

Key papers in the field of psycholinguistics

 

These papers describe important findings in the field of psycholinguistics that may be potentially relevant for considering how language influences number processing.

 

  • Audring, J. (2014). Gender as a complex feature. Language Sciences, 43, 5-17.

    The author discusses how to evaluate the different levels of grammatical gender and the complexity it brings to a certain language. Three domains (complexity of values, assignment and agreement) are examined, as well as the relation between them.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S0388000113001113

 

  • Bierwisch, M. (1967). Syntactic features in morphology: general problems of so-called pronominal inflection in German. To Honour Roman Jakobson, 239-270.

    The author discusses morphological problems by exemplifying German inflection, dealing with the concepts of markedness vs unmarkedness, as well as generalizing his results to other languages.

    Can be retrieved from: www.zas.gwz-berlin.de/708.html

 

  • Caffarra, S., Janssen, N., & Barber, H. A. (2014). Two sides of gender: ERP evidence for the presence of two routes during gender agreement processing. Neuropsychologia, 63, 124-134.

    The authors conducted an ERP study examining the processing of morphosyntactic features. They found evidence supporting two routes used during gender judgement, with both brain hemispheres showing effects at different stages of processing, i.e. differences in processing formal gender cues and gender transparency.

    Can be retrieved from: www.sciencedirect.com/science/article/pii/S0028393214002796

 

 

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