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Embodied numerical representations and their association with multi-digit arithmetic performance

  • Roberta BarrocasEmail author
  • Stephanie Roesch
  • Verena Dresen
  • Korbinian Moeller
  • Silvia Pixner
Research Article
  • 34 Downloads

Abstract

There is a well-documented association between fingers and numbers, which was claimed to stem from the use of finger-based strategies for counting and calculating during childhood. Recently, it has been argued that this may lead to a concomitant activation of finger-based alongside other numerical representations when encountering single-digit numbers. Indeed, the occurrence of such a co-activation is supported by observed influences of finger counting habits on different numerical tasks, including single-digit arithmetic problem solving. In this study, we pursued the question whether the influence of finger-based representations on arithmetic generalizes to multi-digit arithmetic by investigating the association between the recognition of canonical and non-canonical finger patterns and multi-digit arithmetic in adults. Results indicated that canonical finger-based numerical representations were significantly associated with addition performance only, whereas non-canonical finger-based representations were associated significantly with all four arithmetic operations. We argue that, because non-canonical patterns do not benefit from the iconicity of canonical patterns, their magnitude may need to be constructed through magnitude manipulation which may in turn increase associations with mental arithmetic. In sum, our findings provide converging evidence for a functional association between finger-based representations and arithmetic performance.

Keywords

Finger counting Arithmetic Embodied cognition Embodied numerosity 

Notes

Funding

This study was partially funded by the Leibniz-WissenschaftsCampus Cognitive Interfaces (IWM-WCT TP11 “Digits grasp digits”) supporting the first author.

Compliance with ethical standards

Conflict of interest

No conflict of interest was reported by any authors.

References

  1. Andres M, Davare M, Pesenti M, Olivier E, Seron X (2004) Number magnitude and grip aperture interaction. NeuroReport 15(18):2773–2777PubMedGoogle Scholar
  2. Andres M, Seron X, Olivier E (2007) Contribution of hand motor circuits to counting. J Cogn Neurosci 19(4):563–576CrossRefGoogle Scholar
  3. Badets A, Pesenti M, Olivier E (2010) Response-effect compatibility of finger-numeral configurations in arithmetical context. Q J Exp Psychol 63(1):16–22.  https://doi.org/10.1080/17470210903134385 CrossRefGoogle Scholar
  4. Bender A, Beller S (2012) Nature and culture of finger counting: diversity and representational effects of an embodied cognitive tool. Cognition 124(2):156–182.  https://doi.org/10.1016/j.cognition.2012.05.005 CrossRefPubMedGoogle Scholar
  5. Berteletti I, Booth JR (2015) Perceiving fingers in single-digit arithmetic problems. Front Psychol 6:226.  https://doi.org/10.3389/fpsyg.2015.00226 CrossRefPubMedPubMedCentralGoogle Scholar
  6. Butterworth B (1999) The mathematical brain. Macmillan, LondonGoogle Scholar
  7. Campbell JI (1999) Division by multiplication. Mem Cogn 27(5):791–802CrossRefGoogle Scholar
  8. Campbell JID, Xue Q (2001) Cognitive arithmetic across cultures. J Exp Psychol Gen 130:299–315CrossRefGoogle Scholar
  9. Cragg L, Richardson S, Hubber PJ, Keeble S, Gilmore C (2017) When is working memory important for arithmetic? The impact of strategy and age. PLoS ONE 12(12):e0188693.  https://doi.org/10.1371/journal.pone.0188693 CrossRefPubMedPubMedCentralGoogle Scholar
  10. Di Luca S, Pesenti M (2008) Masked priming effect with canonical finger numeral configurations. Exp Brain Res 185(1):27–39.  https://doi.org/10.1007/s00221-007-1132-8 CrossRefPubMedGoogle Scholar
  11. Di Luca S, Pesenti M (2010) Absence of low-level visual difference between canonical and noncanonical finger-numeral configurations. Exp Psychol 57(3):202–207.  https://doi.org/10.1027/1618-3169/a000025 CrossRefPubMedGoogle Scholar
  12. Di Luca S, Pesenti M (2011) Finger numeral representations: more than just another symbolic code. Front Psychol.  https://doi.org/10.3389/fpsyg.2011.00272 CrossRefPubMedPubMedCentralGoogle Scholar
  13. Di Luca S, Granà A, Semenza C, Seron X, Pesenti M (2006) Finger–digit compatibility in Arabic numeral processing. Q J Exp Psychol 59(9):1648–1663.  https://doi.org/10.1080/17470210500256839 CrossRefGoogle Scholar
  14. Di Luca S, Lefèvre N, Pesenti M (2010) Place and summation coding for canonical and non-canonical finger numeral representations. Cognition 117(1):95–100.  https://doi.org/10.1016/j.cognition.2010.06.008 CrossRefPubMedGoogle Scholar
  15. Domahs F, Krinzinger H, Willmes K (2008) Mind the gap between both hands: evidence for internal finger-based number representations in children’s mental calculation. Cortex 44(4):359–367.  https://doi.org/10.1016/j.cortex.2007.08.001 CrossRefPubMedGoogle Scholar
  16. Domahs F, Moeller K, Huber S, Willmes K, Nuerk HC (2010) Embodied numerosity: implicit hand-based representations influence symbolic number processing across cultures. Cognition 116(2):251–266.  https://doi.org/10.1016/j.cognition.2010.05.007 CrossRefPubMedGoogle Scholar
  17. Fischer M (2012) Space and embodied cognition of number and quantity. Cogn Process 13:13–14CrossRefGoogle Scholar
  18. Fischer MH, Brugger P (2011) When digits help digits: spatial-numerical associations point to finger counting as prime example of embodied cognition. Front Psychol 2:260.  https://doi.org/10.3389/fpsyg.2011.00260 CrossRefPubMedPubMedCentralGoogle Scholar
  19. Fuson KC (1988) Springer series in cognitive development. Children’s counting and concepts of number. Springer, New YorkCrossRefGoogle Scholar
  20. Fuson KC, Hall JW (1983) The acquisition of early number word meanings: a conceptual analysis and review. In: Ginsburg HP (ed) The development of mathematical thinking. Academic Press, New YorkGoogle Scholar
  21. Haffner J, Baro K, Parzer P, Wu H, Resch F (2005) Diagnostik mathematischer Basiskompetenzen im Grundschulalter: Der Heidelberger Rechentest HRT. In: Hasselhorn M, Marx H, Schneider W (eds) Diagnostik von Mathematikleistungen. Hogrefe, Göttingen, pp 125–152Google Scholar
  22. Holm S (1979) A simple sequential rejective method procedure. Scand J Stat 6:65–70Google Scholar
  23. Ifrah G (2000) The universal history of numbers: from prehistory to the invention of the computer. Wiley, New York, NYGoogle Scholar
  24. Imbo I, Vandierendonck A, Fias W (2011) Passive hand movements disrupt adults’ counting strategies. Front Psychol 2(SEP):1–5.  https://doi.org/10.3389/fpsyg.2011.00201 CrossRefGoogle Scholar
  25. Kaufmann L, Vogel SE, Wood G, Kremser C, Schocke M, Zimmerhackl LB, Koten JW (2008) A developmental fMRI study of nonsymbolic numerical and spatial processing. Cortex 44(4):376–385.  https://doi.org/10.1016/j.cortex.2007.08.003 CrossRefPubMedGoogle Scholar
  26. Klein E, Moeller K, Willmes K, Nuerk HC, Domahs F (2011) The influence of implicit hand-based representations on mental arithmetic. Front Psychol 2(SEP):1–7.  https://doi.org/10.3389/fpsyg.2011.00197 CrossRefGoogle Scholar
  27. Krinzinger H, Koten JW, Horoufchin H, Kohn N, Arndt D, Sahr K, Konrad K, Willmes K (2011) The role of finger representations and saccades for number processing: an fMRI study in children. Front Psychol 2(DEC):1–12.  https://doi.org/10.3389/fpsyg.2011.00373 CrossRefGoogle Scholar
  28. Lakoff G, Núñez RE (2000) Where mathematics comes from: how the embodied mind brings mathematics into being. Basic Books, New YorkGoogle Scholar
  29. Lee IA, Preacher KJ (2013) Calculation for the test of the difference between two dependent correlations with one variable in common [computer software]. http://quantpsy.org. Accessed 16 Aug 2019
  30. LeFevre JA, Morris J (1999) More on the relation between division and multiplication in simple arithmetic: evidence for mediation of division solutions via multiplication. Mem Cogn 27(5):803–812CrossRefGoogle Scholar
  31. LeFevre J-A, Sadesky GS, Bisanz J (1996) Selection of procedures in mental addition: reassessing the problem size effect in adults. J Exp Psychol Learn Mem Cogn 22(1):216–230CrossRefGoogle Scholar
  32. LeFevre J-A, DeStefano D, Penner-Wilger M, Daley KE (2006) Selection of procedures in mental subtraction. Can J Exp Psychol 60(3):209–220CrossRefGoogle Scholar
  33. Marghetis T, Núñez R, Bergen BK (2014) Doing arithmetic by hand: hand movements during exact arithmetic reveal systematic, dynamic spatial processing. Q J Exp Psychol 67(8):1579–1596.  https://doi.org/10.1080/17470218.2014.897359 CrossRefGoogle Scholar
  34. McCloskey M (1992) Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia. Cognition 44:107–157.  https://doi.org/10.1016/0010-0277(92)90052-J CrossRefPubMedGoogle Scholar
  35. Michaux N, Masson N, Pesenti M, Andres M (2013) Selective interference of finger movements on basic addition and subtraction problem solving. Exp Psychol 60(3):197–205.  https://doi.org/10.1027/1618-3169/a000188 CrossRefPubMedGoogle Scholar
  36. Moeller K, Nuerk H-C (2012) Fingerbasierte Repräsentationen als verkörperlichte Vorläuferfähigkeit mathematischer Kompetenzen: ein Plädoyer für mehr Dialog zwischen Fachdidaktik und Neuropsychologie. Lernen und Lernstörungen 1:63–71CrossRefGoogle Scholar
  37. Moeller K, Martignon L, Wessolowski S, Engel J, Nuerk HC (2011) Effects of finger counting on numerical development the opposing views of neurocognition and mathematics education. Front Psychol 2(NOV):1–5.  https://doi.org/10.3389/fpsyg.2011.00328 CrossRefGoogle Scholar
  38. Moeller K, Fischer U, Link T, Wasner M, Huber S, Cress U, Nuerk HC (2012) Learning and development of embodied numerosity. Cogn Process 13(1 SUPPL):271–274.  https://doi.org/10.1007/s10339-012-0457-9 CrossRefGoogle Scholar
  39. Nuerk H-C, Weger U, Willmes K (2001) Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition 82(1):B25–B33CrossRefGoogle Scholar
  40. Pika S, Nicoladis E, Marentette P (2009) How to order a beer: cultural differences in the use of conventional gestures for numbers. J Cross Cult Psychol 40(1):70–80CrossRefGoogle Scholar
  41. Rusconi E, Walsh V, Butterworth B (2005) Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia.  https://doi.org/10.1016/j.neuropsychologia.2005.01.009 CrossRefPubMedGoogle Scholar
  42. Simon O, Mangin JF, Cohen L, Le Bihan D, Dehaene S (2002) Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron 33(3):475–487CrossRefGoogle Scholar
  43. Simon O, Kherif F, Flandin G, Poline J, Riviere D, Mangin J, Le Bihan D, Dehaene S (2004) Automatized clustering and functional geometry of human parietofrontal networks for language, space, and number. NeuroImage 23(3):1192–1202CrossRefGoogle Scholar
  44. Sixtus E, Fischer MH, Lindemann O (2017) Finger posing primes number comprehension. Cogn Process 18:237–248.  https://doi.org/10.1007/s10339-017-0804-y CrossRefPubMedGoogle Scholar
  45. Soylu F, Newman SD (2016) Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study. Cogn Process 17:67–77.  https://doi.org/10.1007/s10339-015-0737-2 CrossRefPubMedGoogle Scholar
  46. Soylu F, Raymond D, Gutierrez A, Newman SD (2017) The differential relationship between finger gnosis, and addition and subtraction: an fMRI study. J Numer Cogn 3(3):694–715.  https://doi.org/10.5964/jnc.v3i3.102 CrossRefGoogle Scholar
  47. Steiger JH (1980) Tests for comparing elements of a correlation matrix. Psychol Bull 87:245–251CrossRefGoogle Scholar
  48. Tschentscher N, Hauk O, Fischer MH, Pulvermüller F (2012) You can count on the motor cortex: finger counting habits modulate motor cortex activation evoked by numbers. NeuroImage 59(4):3139–3148.  https://doi.org/10.1016/j.neuroimage.2011.11.037 CrossRefPubMedGoogle Scholar
  49. Verguts T, De Moor W (2005) Two-digit comparison: decomposed, holistic, or hybrid? Exp Psychol 52(3):195–200CrossRefGoogle Scholar
  50. Verguts T, Fias W (2004) Representation of number in animals and humans: a neural model. J Cogn Neurosci 16:1493–1504CrossRefGoogle Scholar
  51. Wasner M, Moeller K, Fischer M, Nuerk H-C (2014) Related but not the same: ordinality, cardinality and 1-to-1 correspondence in finger-based numerical representations. J Cogn Psychol.  https://doi.org/10.1080/20445911.2014.964719 CrossRefGoogle Scholar

Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Leibniz-Institut fuer WissensmedienTübingenGermany
  2. 2.Institute of PsychologyUMIT – Private University for Health Sciences, Medical Informatics and TechnologyHall in TirolAustria
  3. 3.LEAD Graduate School and Research Network, Department of PsychologyUniversity of TübingenTübingenGermany

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