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Number line estimation and complex mental calculation: Is there a shared cognitive process driving the two tasks?

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Abstract

It is widely accepted that different number-related tasks, including solving simple addition and subtraction, may induce attentional shifts on the so-called mental number line, which represents larger numbers on the right and smaller numbers on the left. Recently, it has been shown that different number-related tasks also employ spatial attention shifts along with general cognitive processes. Here we investigated for the first time whether number line estimation and complex mental arithmetic recruit a common mechanism in healthy adults. Participants’ performance in two-digit mental additions and subtractions using visual stimuli was compared with their performance in a mental bisection task using auditory numerical intervals. Results showed significant correlations between participants’ performance in number line bisection and that in two-digit mental arithmetic operations, especially in additions, providing a first proof of a shared cognitive mechanism (or multiple shared cognitive mechanisms) between auditory number bisection and complex mental calculation.

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References

  • Ambrosini E, Vallesi A (2016) Asymmetry in prefrontal resting-state EEG spectral power underlies individual differences in phasic and sustained cognitive control. NeuroImage 124:843–857

    Article  PubMed  Google Scholar 

  • Anelli F, Lugli L, Baroni G, Borghi AM, Nicoletti R (2014) Walking boosts your performance in making additions and subtractions. Front Psychol 5:1459

    Article  PubMed  PubMed Central  Google Scholar 

  • Ashcraft MH, Battaglia J (1978) Cognitive arithmetic: evidence for retrieval and decision processes in mental addition. J Exp Psychol Hum Learn Mem 4(5):527

    Article  Google Scholar 

  • Association WM (2013) World Medical Association Declaration of Helsinki: ethical principles for medical research involving human subjects. JAMA 310(20):2191

    Article  CAS  Google Scholar 

  • Avancini C, Galfano G, Szűcs D (2014) Dissociation between arithmetic relatedness and distance effects is modulated by task properties: an ERP study comparing explicit vs. implicit arithmetic processing. Biol Psychol 103:305–316

    Article  PubMed  PubMed Central  Google Scholar 

  • Barrouillet P, Mignon M, Thevenot C (2008) Strategies in subtraction problem solving in children. J Exp Child Psychol 99(4):233–251

    Article  PubMed  Google Scholar 

  • Binder J, Marshall R, Lazar R, Benjamin J, Mohr J (1992) Distinct syndromes of hemineglect. Arch Neurol 49(11):1187

    Article  CAS  PubMed  Google Scholar 

  • Campbell JI, Gunter R (2002) Calculation, culture, and the repeated operand effect. Cognition 86(1):71–96

    Article  PubMed  Google Scholar 

  • Cattaneo Z, Fantino M, Silvanto J, Vallar G, Vecchi T (2011) Tapping effects on numerical bisection. Exp Brain Res 208(1):21–28

    Article  PubMed  Google Scholar 

  • Corbetta M, Shulman GL (2011) Spatial neglect and attention networks. Annu Rev Neurosci 34:569

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dehaene S, Cohen L (2007) Cultural recycling of cortical maps. Neuron 56(2):384–398

    Article  CAS  PubMed  Google Scholar 

  • Dehaene S, Mehler J (1992) Cross-linguistic regularities in the frequency of number words. Cognition 43(1):1–29

    Article  CAS  PubMed  Google Scholar 

  • Dehaene S, Bossini S, Giraux P (1993) The mental representation of parity and number magnitude. J Exp Psychol Gen 122(3):371

    Article  Google Scholar 

  • Diedenhofen B, Musch J (2015) cocor: a comprehensive solution for the statistical comparison of correlations. PLoS ONE 10(4):e0121945

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Faul F, Erdfelder E, Buchner A, Lang A-G (2009) Statistical power analyses using G* Power 3.1: tests for correlation and regression analyses. Behav Res Methods 41(4):1149–1160

    Article  PubMed  Google Scholar 

  • Fierro B, Brighina F, Oliveri M, Piazza A, La Bua V, Buffa D, Bisiach E (2000) Contralateral neglect induced by right posterior parietal rTMS in healthy subjects. NeuroReport 11(7):1519–1521

    Article  CAS  PubMed  Google Scholar 

  • Fischer MH, Warlop N, Hill RL, Fias W (2004) Oculomotor bias induced by number perception. Exp Psychol 51(2):91–97

    Article  PubMed  Google Scholar 

  • Göbel SM, Calabria M, Farnè A, Rossetti Y (2006) Parietal rTMS distorts the mental number line: simulating ‘spatial’ neglect in healthy subjects. Neuropsychologia 44(6):860–868

    Article  PubMed  Google Scholar 

  • Goldin-Meadow S, Cook SW, Mitchell ZA (2009) Gesturing gives children new ideas about math. Psychol Sci 20(3):267–272

    Article  PubMed  PubMed Central  Google Scholar 

  • Halberda J, Ly R, Wilmer JB, Naiman DQ, Germine L (2012) Number sense across the lifespan as revealed by a massive Internet-based sample. Proc Natl Acad Sci 109(28):11116–11120

    Article  CAS  PubMed  Google Scholar 

  • Izard V, Dehaene S (2008) Calibrating the mental number line. Cognition 106(3):1221–1247

    Article  PubMed  Google Scholar 

  • Jewell G, McCourt ME (2000) Pseudoneglect: a review and meta-analysis of performance factors in line bisection tasks. Neuropsychologia 38(1):93–110

    Article  CAS  PubMed  Google Scholar 

  • Jost K, Beinhoff U, Hennighausen E, Rösler F (2004) Facts, rules, and strategies in single-digit multiplication: evidence from event-related brain potentials. Cogn Brain Res 20(2):183–193

    Article  Google Scholar 

  • Knops A, Viarouge A, Dehaene S (2009) Dynamic representations underlying symbolic and nonsymbolic calculation: evidence from the operational momentum effect. Atten Percept Psychophys 71(4):803–821

    Article  PubMed  Google Scholar 

  • Kong J, Wang C, Kwong K, Vangel M, Chua E, Gollub R (2005) The neural substrate of arithmetic operations and procedure complexity. Cogn Brain Res 22(3):397–405

    Article  Google Scholar 

  • Lefevre J-A, Bisanz J, Mrkonjic L (1988) Cognitive arithmetic: evidence for obligatory activation of arithmetic facts. Mem Cognit 16(1):45–53

    Article  CAS  PubMed  Google Scholar 

  • Lindemann O, Tira MD (2015) Operational momentum in numerosity production judgments of multi-digit number problems. Zeitschrift für Psychologie 219:50–57

    Article  Google Scholar 

  • Loetscher T, Brugger P (2007) Exploring number space by random digit generation. Exp Brain Res 180(4):655–665

    Article  PubMed  Google Scholar 

  • Loetscher T, Schwarz U, Schubiger M, Brugger P (2008) Head turns bias the brain’s internal random generator. Curr Biol 18(2):R60–R62

    Article  CAS  PubMed  Google Scholar 

  • Longo MR, Lourenco SF (2007) Spatial attention and the mental number line: evidence for characteristic biases and compression. Neuropsychologia 45(7):1400–1407

    Article  PubMed  Google Scholar 

  • Longo MR, Lourenco SF (2010) Bisecting the mental number line in near and far space. Brain Cognit 72(3):362–367

    Article  Google Scholar 

  • Lorch RF, Myers JL (1990) Regression analyses of repeated measures data in cognitive research. J Exp Psychol Learn Mem Cognit 16(1):149

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Masson N, Pesenti M (2014) Attentional bias induced by solving simple and complex addition and subtraction problems. Q J Exp Psychol 67(8):1514–1526

    Article  Google Scholar 

  • Masson N, Pesenti M (2016) Interference of lateralized distractors on arithmetic problem solving: a functional role for attention shifts in mental calculation. Psychol Res 80(4):640–651

    Article  PubMed  Google Scholar 

  • McCloskey M, Aliminosa D, Sokol SM (1991) Facts, rules and procedures in normal calculation: evidence from multiple single-patient studies of impaired arithmetic fact retrieval. Brain Cognit 17(2):154–203

    Article  CAS  Google Scholar 

  • McCrink K, Dehaene S, Dehaene-Lambertz G (2007) Moving along the number line: operational momentum in nonsymbolic arithmetic. Percept Psychophys 69(8):1324–1333

    Article  PubMed  Google Scholar 

  • Moeller K, Fischer M, Nuerk H-C, Willmes K (2009) Eye fixation behaviour in the number bisection task: evidence for temporal specificity. Acta Physiol 131(3):209–220

    CAS  Google Scholar 

  • Montefinese M, Sulpizio V, Galati G, Committeri G (2015a) Age-related effects on spatial memory across viewpoint changes relative to different reference frames. Psychol Res 79(4):687–697

    Article  PubMed  Google Scholar 

  • Montefinese M, Zannino GD, Ambrosini E (2015b) Semantic similarity between old and new items produces false alarms in recognition memory. Psychol Res 79(5):785–794

    Article  PubMed  Google Scholar 

  • Montefinese M, Turco C, Piccione F, Semenza C (2017) Causal role of the posterior parietal cortex for two-digit mental subtraction and addition: a repetitive TMS study. NeuroImage 155:72–81

    Article  PubMed  Google Scholar 

  • Morey RD (2008) Confidence intervals from normalized data: a correction to Cousineau (2005). Tutor Quant Methods for Psychol 4:61–64

    Article  Google Scholar 

  • Muluh E, Vaughan C, John L (2011) High resolution event-related potentials analysis of the arithmetic-operation effect in mental arithmetic. Clin Neurophysiol 122(3):518–529

    Article  CAS  PubMed  Google Scholar 

  • Myachykov A, Cangelosi A, Ellis R, Fischer MH (2015) The oculomotor resonance effect in spatial–numerical mapping. Acta Physiol 161:162–169

    Google Scholar 

  • Myachykov A, Ellis R, Cangelosi A, Fischer MH (2016) Ocular drift along the mental number line. Psychol Res 80:379–388

    Article  PubMed  PubMed Central  Google Scholar 

  • Nieder A, Miller EK (2003) Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37(1):149–157

    Article  CAS  PubMed  Google Scholar 

  • Pearson K, Filon LNG (1898) Mathematical contributions to the theory of evolution. IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation. Philos Trans R Soc Lond Ser A Contain Pap Math Phys Character 191:229–311

    Article  Google Scholar 

  • Piazza M, Izard V, Pinel P, Le Bihan D, Dehaene S (2004) Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44(3):547–555

    Article  CAS  PubMed  Google Scholar 

  • Pinhas M, Fischer MH (2008) Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition 109(3):408–415

    Article  PubMed  Google Scholar 

  • Pinhas M, Shaki S, Fischer MH (2014) Heed the signs: operation signs have spatial associations. Q J Exp Psychol 67(8):1527–1540

    Article  Google Scholar 

  • Pizzamiglio L, Committeri G, Galati G, Patria F (2000) Psychophysical properties of line bisection and body midline perception in unilateral neglect. Cortex 36(4):469–484

    Article  CAS  PubMed  Google Scholar 

  • Priftis K, Zorzi M, Meneghello F, Marenzi R, Umiltà C (2006) Explicit versus implicit processing of representational space in neglect: dissociations in accessing the mental number line. J Cogn Neurosci 18(4):680–688

    Article  PubMed  Google Scholar 

  • Priftis K, Pitteri M, Meneghello F, Umiltà C, Zorzi M (2012) Optokinetic stimulation modulates neglect for the number space: evidence from mental number interval bisection. Front Hum Neurosci 6(23.10):3389

    Google Scholar 

  • Protopapas A (2007) Check vocal: a program to facilitate checking the accuracy and response time of vocal responses from DMDX. Behav Res Methods 39(4):859–862

    Article  PubMed  Google Scholar 

  • Ranzini M, Carbè K, Gevers W (2017) Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection. Neuropsychologia 99:225–235

    Article  PubMed  Google Scholar 

  • Rotondaro F, Merola S, Aiello M, Pinto M, Doricchi F (2015) Dissociation between line bisection and mental-number-line bisection in healthy adults. Neuropsychologia 75:565–576

    Article  PubMed  Google Scholar 

  • Rousseeuw PJ, Verboven S (2002) Robust estimation in very small samples. Comput Stat Data Anal 40(4):741–758

    Article  Google Scholar 

  • Schneider W, Eschman A, Zuccolotto A (2002) E-Prime: user’s guide. Psychology Software Incorporated, Pittsburgh

    Google Scholar 

  • Schwarz W, Keus IM (2004) Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses. Percept Psychophys 66(4):651–664

    Article  PubMed  Google Scholar 

  • Storer L, Demeyere N (2014) Disruptions to number bisection after brain injury: neglecting parts of the mental number line or short-term memory impairments? Brain Cognit 86:116–123

    Article  Google Scholar 

  • van Dijck JP, Gevers W, Lafosse C, Fias W (2011) The heterogeneous nature of number–space interactions. Front Hum Neurosci 5:182

    PubMed  Google Scholar 

  • Verboven S, Hubert M (2005) LIBRA: a MATLAB library for robust analysis. Chemometr Intell Lab Syst 75(2):127–136

    Article  CAS  Google Scholar 

  • Verboven S, Hubert M (2010) Matlab library LIBRA. Wiley Interdiscip Rev Comput Stat 2(4):509–515

    Article  Google Scholar 

  • Wiemers M, Bekkering H, Lindemann O (2014) Spatial interferences in mental arithmetic: evidence from the motion–arithmetic compatibility effect. Q J Exp Psychol 67(8):1557–1570

    Article  Google Scholar 

  • Winter B, Matlock T, Shaki S, Fischer MH (2015) Mental number space in three dimensions. Neurosci Biobehav Rev 57:209–219

    Article  PubMed  Google Scholar 

  • Zhou X, Chen C, Dong Q, Zhang H, Zhou R, Zhao H et al (2006) Event-related potentials of single-digit addition, subtraction, and multiplication. Neuropsychologia 44(12):2500–2507

    Article  PubMed  Google Scholar 

  • Zorzi M, Priftis K, Umiltà C (2002) Brain damage: neglect disrupts the mental number line. Nature 417(6885):138–139

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

This work was supported by the University of Padua (CPDA131328 and NEURAT STPD11B8HM_004).

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Correspondence to Maria Montefinese.

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Handling editor: Luigia Carlucci Aiello (Sapienza University of Rome);

Reviewers: Pom Charras (University Paul Valery Montpellier) and an anonymous reviewer.

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Montefinese, M., Semenza, C. Number line estimation and complex mental calculation: Is there a shared cognitive process driving the two tasks?. Cogn Process 19, 495–504 (2018). https://doi.org/10.1007/s10339-018-0867-4

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