More than simple facts: cross-linguistic differences in place-value processing in arithmetic fact retrieval

Linguistic specificities such as the inversion property of number words (e.g., in German 43 is spoken dreiundvierzig, literally three and  forty) moderate Arabic number processing. So far, cross-linguistic studies have mostly focused on inversion-related effects on simple (e.g., number comparison) and calculation-based (e.g., multi-digit addition) magnitude processing of numerical information. Despite the assumption that multiplication facts are represented in verbal format, not much attention has been paid to inversion-related influences on multiplication fact retrieval. Accordingly, the current study evaluated inversion-related effects on the processing of place-value information in multiplication. In a verification paradigm, the decade consistency effect (i.e., more errors when the decade of a solution probe shares the decade digit with the correct solution) was larger for English- than German-speaking participants for table-related probes. Processing of decade digits might be prioritised in English-speaking participants because the decade digit is named first in English number words, whereas in German number words the unit digit is named first. Our results indicate that (1) the influence of specificities of a verbal number word formation on place-value processing generalise to arithmetic fact retrieval and (2) inversion of number words might even be advantageous in specific cases.

[1]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[2]  J. I. Campbell.  Reading-based interference in cognitive arithmetic. , 1997, Canadian journal of experimental psychology = Revue canadienne de psychologie experimentale.

[3]  Christine Schiltz,et al.  Speaking two languages with different number naming systems: What implications for magnitude judgments in bilinguals at different stages of language acquisition? , 2016, Cognitive Processing.

[4]  Klaus Willmes,et al.  Decade breaks in the mental number line? Putting the tens and units back in different bins , 2001, Cognition.

[5]  S. Dehaene,et al.  Differential Contributions of the Left and Right Inferior Parietal Lobules to Number Processing , 1999, Journal of Cognitive Neuroscience.

[6]  Klaus Willmes,et al.  On The Impact of Different Number Representations in the Number Bisection Task , 2002, Cortex.

[7]  Clarissa A. Thompson,et al.  Modeling individual differences in response time and accuracy in numeracy , 2015, Cognition.

[8]  Yukari Okamoto,et al.  Comparisons of Children's Cognitive Representation of Number: China, France, Japan, Korea, Sweden, and the United States , 1994 .

[9]  Matthias Schlesewsky,et al.  Behavioral and Brain Functions , 2008 .

[10]  Frank Domahs,et al.  What makes multiplication facts difficult. Problem size or neighborhood consistency? , 2006, Experimental psychology.

[11]  M. H. Fischer,et al.  Representation of Multiplication Facts-Evidence for partial verbal coding , 2011, Behavioral and Brain Functions.

[12]  Mark H. Ashcraft,et al.  The production and verification tasks in mental addition: An empirical comparison☆ , 1984 .

[13]  Wim Fias,et al.  The addition of two-digit numbers: exploring carry versus no-carry problems , 2005 .

[14]  Marc Brysbaert,et al.  About the influence of the presentation format on arithmetical-fact retrieval processes , 1997, Cognition.

[15]  B. Boets,et al.  Phonological processing and arithmetic fact retrieval: Evidence from developmental dyslexia , 2010, Neuropsychologia.

[16]  Jeffrey Bisanz,et al.  Multiple routes to solution of single-digit multiplication problems. , 1996 .

[17]  Gordon D. Logan,et al.  On the relation between production and verification tasks in the psychology of simple arithmetic , 1990 .

[18]  Klaus Willmes,et al.  Magnitude representation in sequential comparison of two-digit numbers is not holistic either , 2012, Cognitive Processing.

[19]  M. van der Schoot,et al.  The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters , 2015, Front. Psychol..

[20]  Korbinian Moeller,et al.  On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity. , 2009, Journal of experimental child psychology.

[21]  Yukari Okamoto,et al.  First graders' cognitive representation of number and understanding of place value: Cross-national comparisons: France, Japan, Korea, Sweden, and the United States. , 1993 .

[22]  Jamie I. D. Campbell,et al.  Mental multiplication skill: Structure, process, and acquisition. , 1985 .

[23]  Dana Ganor-Stern,et al.  Automaticity of two-digit numbers. , 2007, Journal of experimental psychology. Human perception and performance.

[24]  Kyoung-Min Lee.  Cortical areas differentially involved in multiplication and subtraction: A functional magnetic resonance imaging study and correlation with a case of selective acalculia , 2000, Annals of neurology.

[25]  Wim Fias,et al.  Sixty-four or four-and-sixty? The influence of language and working memory on children's number transcoding , 2014, Front. Psychol..

[26]  Mark H. Ashcraft,et al.  Children’s Knowledge of Simple Arithmetic: A Developmental Model and Simulation , 1987 .

[27]  K Moeller,et al.  Early place-value understanding as a precursor for later arithmetic performance--a longitudinal study on numerical development. , 2011, Research in developmental disabilities.

[28]  K. Moeller,et al.  (No) Small Adults: Children's Processing of Carry Addition Problems , 2011, Developmental neuropsychology.

[29]  Wim Fias,et al.  Interacting neighbors: A connectionist model of retrieval in single-digit multiplication , 2005, Memory & cognition.

[30]  Pedro Macizo,et al.  The processing of Arabic numbers is under cognitive control , 2012, Psychological Research.

[31]  Jan Lonnemann,et al.  Does number word inversion affect arithmetic processes in adults? , 2015, Trends in Neuroscience and Education.

[32]  Korbinian Moeller,et al.  On the limits of language influences on numerical cognition – no inversion effects in three-digit number magnitude processing in adults , 2015, Front. Psychol..

[33]  Jeffrey Bisanz,et al.  Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts , 1988, Memory & cognition.

[34]  Jamie I. D. Campbell.  Architectures for numerical cognition , 1994, Cognition.

[35]  Silke M. Göbel,et al.  Language influences number processing – A quadrilingual study , 2015, Cognition.

[36]  Korbinian Moeller,et al.  Language affects symbolic arithmetic in children: the case of number word inversion. , 2014, Journal of experimental child psychology.

[37]  Arava Y. Kallai,et al.  The place-value of a digit in multi-digit numbers is processed automatically. , 2012, Journal of experimental psychology. Learning, memory, and cognition.

[38]  Frank Domahs,et al.  To carry or not to carry--is this the question? Disentangling the carry effect in multi-digit addition. , 2010, Acta psychologica.

[39]  Markus F. Damian,et al.  The differential influence of decades and units on multidigit number comparison , 2008, Quarterly journal of experimental psychology.

[40]  Korbinian Moeller,et al.  Language Effects on Children’s Nonverbal Number Line Estimations , 2011 .

[41]  Marc Brysbaert,et al.  The Whorfian hypothesis and numerical cognition: is `twenty-four' processed in the same way as `four-and-twenty'? , 1998, Cognition.

[42]  Klaus Willmes,et al.  Language effects in magnitude comparison: Small, but not irrelevant , 2005, Brain and Language.

[43]  Kyoung-Min Lee,et al.  Arithmetic operation and working memory: differential suppression in dual tasks , 2002, Cognition.