Zusammenfassung
Zahlen werden nicht als eine einzige Entität verarbeitet. Eine häufige Beobachtung im klinischen Alltag ist, dass Patienten bestimmte Aufgaben mit Zahlen problemlos ausführen können, während ihnen andere einfache Aufgaben große Schwierigkeiten bereiten. So können beispielsweise Patienten mit Läsionen im Versorgungsgebiet der linken Arteria cerebri media im Allgemeinen Größenvergleiche zwischen arabischen Zahlen noch ohne Fehler ausführen, während sie gleichzeitig unfähig sind, selbst einfachste Zahlen sicher zu benennen. Zahlreiche fMRT-Studien haben sich in den letzten Jahren mit der funktional-anatomischen Basis solcher neuropsychologischer Phänomene beschäftigt und zu einer Verfeinerung und Erweiterung unserer Vorstellungen darüber, wie das Gehirn Zahlen verarbeitet, geführt.
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Literatur
Andres M, Seron X, Olivier E (2007) Contribution of hand motor circuits to counting. J Cogn Neurosci 19: 563–576
Arsalidou M, Taylor MJ (2010) Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage 54: 2382–2393
Ashcraft MH, Kirk EP (2001) The relationships among working memory, math anxiety, and performance. J Exp Psychol Gen 130: 224–237
Barsalou LW (1999) Perceptual symbol systems. Behav Brain Sci 22: 577–660
Büchel C, Coull JT, Friston KJ (1999) The predictive value of changes in effective connectivity for human learning. Science 283: 1538–1541
Butterworth B (1999) The mathematical brain. Macmillan, London
Cohen L, Dehaene S, Chochon F, Lehéricy S, Naccache L (2000) Language and calculation within the parietal lobe: A combined cognitive, anatomical and fMRI study. Neuropsychologia 38: 1426–1440
Cohen Kadosh R, Walsh V (2009) Numerical representation in the parietal lobes: Abstract or not abstract? Behav Brain Sciences 32: 313–373
Cohen Kadosh R, Cohen Kadosh K, Kaas A, Henik A, Goebel R (2007) Notation-dependent and -independent representations of numbers in the parietal lobes. Neuron 53: 307–314
Dehaene S (1992) Varieties of numerical abilities. Cognition 44: 1–42
Dehaene S (2007) Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. In: Haggard P, Rossetti Y (eds) Attention & Performance XXII. Sensori-Motor Foundations of Higher Cognition. Harvard University Press, Cambridge, MA, pp 527–574
Dehaene S (2009) Origins of mathematical intuitions. Ann NY Acd Sci 1156: 232–259
Dehaene S, Cohen L (1995) Towards an anatomical and functional model of number processing. Math Cogn 1: 83–120
Dehaene S, Cohen L (1997) Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33: 219–250
Dehaene S, Bossini S, Giraux P (1993) The mental representation of parity and number magnitude. J Exp Psychol Gen 122: 371–396
Dehaene S, Piazza M, Pinel P, Cohen L (2003) Three parietal circuits for number processing. Cogn Neuropsychol 20: 487–506
Delazer M, Domahs F, Bartha L, Brenneis C, Lochy A, Trieb T, Benke T (2003) Learning complex arithmetic – a fMRI study. Cogn Brain Res 18: 76–88
Delazer M, Domahs F, Lochy A, Bartha L, Brenneis C, Trieb T (2004) The acquisition of arithmetic knowledge – an FMRI study. Cortex 40: 166–167
Delazer M, Ischebeck A, Domahs F, Zamarian L, Koppelstaetter F, Siedentopf CM, Kaufmann L, Benke T, Felber S (2005) Learning by strategies and learning by drill: Evidence from an fMRI study. Neuroimage 25: 838–849
Di Luca S, Pesenti M (2011) Finger numeral representations: more than just another symbolic code. Front Psychol 2: 272. DOI:10.3389/ fpsyg.2011.00272
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
Eger E, Sterzer P, Russ MO, Giraud AL, Kleinschmidt A (2003) A number representation in human intraparietal cortex. Neuron 37: 719–725
Fehr T, Weber J, Willmes K, Herrmann M (2010) Neural correlates in exceptional mental arithmetic – About the neural architecture of prodigious skills. Neuropsychologia 48: 1407–1416
Fias W, Brysbaert M, Geypens F, d‘Ydevalle G (1996) The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Math Cogn 2: 95–110
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. J Exp Psychol Gen 139: 180–190
Göbel SM, Johansen-Berg H, Behrens T, Rushworth MFS (2004) Response- selection related parietal activation during number comparison. J Cogn Neurosci 16: 1536–1551
Grabner RH, Ansari D, Reishofer G, Stern E, Ebner F, Neuper C (2007) Individual differences in mathematical competence predict parietal brain activation during mental calculation. Neuroimage 38: 346–356
Grabner RH, Ansari D, Koschutnig K, Reishofer G, Ebner F, Neuper C (2009) To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia 47: 604–608
Grill-Spector K (2006) Selectivity of adaptation in single units: Implications for fMRI experiments. Neuron 49: 170–171
Grill-Spector K, Malach R (2001) FMR-adaptation: A tool for studying the functional properties of human cortical neurons. Acta Psychol (Amst) 107: 293–321
Grill-Spector K, Henson R, Martin A (2006) Repetition and the brain: Neural models of stimulus-specific effects. Trends Cogn Sci 10: 14–23
Hoeckner SH, Zauner H, Moeller K, 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
Hubbard EM, Piazza M, Pinel P, Dehaene S (2005) Interactions between number and space in parietal cortex. Nat Rev Neurosci 6: 435–448
Imbo I, Vandierendonck A, De Rammelaere S 2007a) The role of working memory in the carry operation of mental arithmetic: Number and value of the carry. Q J Exp Psychol 60: 708–731
Imbo I, Vandierendonck A, Vergauwe E (2007b) The role of working memory in carrying and borrowing. Psychol Res 71: 467–483
Ischebeck A, Zamarian L, Siedentopf C, Koppelstatter F, Benke T, Felber S, Delazer M (2006) How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage 30: 1365–1375
Ischebeck A, Zamarian L, Egger K, Schocke M, Delazer M (2007) Imaging early practice effects in arithmetic. Neuroimage 36: 993–1003
Jacob SN, Nieder A (2009) Notation-independent representation of fractions in the human parietal cortex. J Neurosci 29: 4652–4657
Kaufmann L, Nuerk H-C (2005) Numerical development: Current issues and future perspectives. Psychology Science 47: 142–170
Kaufmann L, Koppelstaetter F, Delazer M, Siedentopf C, Rhomberg P, Golaszewski S, Felber S, Ischebeck A (2005) Neural correlates of distance and congruity effects in a numerical Stroop task: an event-related fMRI study. NeuroImage 25: 888–898
Kaufmann L, Koppelstaetter F, Siedentopf C, Haala I, Haberlandt E, Zimmerhackl LB, Felber S, Ischebeck A (2006) Neural correlates of a number-size interference task in children. NeuroReport 17: 587–591
Kaufmann L, Vogel S, Wood G, Kremser C, Schocke M, Zimmerhackl LB, Koten JW (2008) A developmental fMRI study of nonsymbolic numerical and spatial processing. Cortex 44: 376–385
Kaufmann L, Wood G, Rubinsten O, Avishai H (2011) Metaanalyses of Developmental fMRI Studies Investigating Typical and Atypical Trajectories of Number Processing and Calculation. Dev Neuropsychol 36: 763–787
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 Cogn 69: 369–381
Klein E, Moeller K, Nuerk H-C, Willmes K (2010a) On the neuro-cognitive foundations of basic auditory number processing: An fMRI study. Behav Brain Funct 6: 44
Klein E, Willmes K, Dressel K, Domahs F, Wood G, Nuerk H-C, Moeller K (2010b) Categorical and continuous – Disentangling the neural correlates of the carry effect in multi-digit addition. Behav Brain Funct 6: 70
Knops A, Nuerk H-C, Fimm B, Vohn R, Willmes K (2006) A special role for numbers in working memory? An fMRI study. NeuroImage 29: 1–14
Knops A, Thirion B, Hubbard EM, Michel V, Dehaene S (2009) Recruitment of an area involved in eye movements during mental arithmetic. Science 324: 1583–1585
Kong J, Wang C, Kwong K, Vangel M, Chuac E, Gollub R (2005) The neural substrate of arithmetic operations and procedure complexity. Cogn Brain Res 22: 397–405
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: 373
Liu X, Banich MT, Jacobson BL, Tanabe JL (2004) Common and distinct neural substrates of attentional control in an integrated Simon and spatial Stroop task as assessed by event-related fMRI. Neuro- Image 22: 1097–1106
McCloskey M (1992) Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition 44: 107–157
Menon V, Rivera SM, White CD, Eliez S, Glover GH, Reiss AL (2000) Functional optimisation of arithmetic processing in perfect performers. Cogn Brain Res 9: 343–345
Miller EK (2000) The prefrontal cortex and cognitive control. Nat Rev Neurosci 1: 58–65
Moeller K, Nuerk H-C (2012) Zählen und Rechnen mit den Fingern: Hilfe, Sackgasse oder bloßer Übergang auf dem Weg zu komplexen arithmetischen Kompetenzen? Lernen und Lernstörungen 1: 49–69
Moeller K, Fischer MH, Nuerk H-C, Willmes K (2009) Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking. Q J Exp Psychol 62: 324–335
Nieder A, Dehaene S (2009) Representation of Number in the Brain. Ann Rev Neurosci 32: 185–208
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: B25–33
Nuerk H-C, Iversen W, Willmes K (2004) Notational modulation of the SNARC and the MARC (Linguistic Markedness Association of Response Codes) Effect. Q J Exp Psychol A 57: 835–863
Nuerk H-C, Graf M, Willmes K (2006) Grundlagen der Zahlenverarbeitung und des Rechnens [Foundations of number processing and calculation]. In Sprache, Stimme, Gehör: Zeitschrift für Kommunikationsstörungen 30: 147–153
Nuerk, H-C, Moeller K, Klein E, Willmes K, Fischer MH (2011) Extending the Mental Number Line – A Review of Multi-Digit Number Processing. J Psychol 219: 3–22
Nuerk H-C, Willmes K (2005) On the magnitude representations of two-digit numbers. Psychol Sci 47: 52–72
Pesenti M, Thioux M, Seron X, De Volder A (2000) Neuroanatomical substrates of Arabic number processing, numerical comparison and simple addition: a PET study. J Cogn Neurosci 12: 461–479
Piazza M, Pinel P, Le Bihan D, Dehaene S (2007) A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53: 293–305
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: 680–688
Rickard TC, Romero SG, Basso G, Wharton C, Flitman S, Grafman J (2000) The calculating brain: An fMRI study. Neuropsychologia 38: 325–335
Rivera SM, Reiss AL, Eckert, MA, Menon V (2005) Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cereb Cortex 15: 1779–1790
Sato M, Cattaneo L, Rizzolatti G, Gallese V (2007) Numbers within our hands: modulation of corticospinal excitability of hand muscles during numerical judgment. J Cogn Neurosci 19: 684–693
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: 475–487
Snyder A (2001) Paradox of the Savant mind – The provocative exceptions to our understanding of intellectual ability. Nature 413: 251–252
Snyder A (2009) Explaining and inducing savant skills: Privileged access to lower level, less-processed information. Philosl Trans R Soc Lond B Biol Sci 364: 1399–1405
Thompson JC, Abbott DF, Wheaton KJ, Syngeniotis A, Puce A (2004) Digit representation is more than just hand waving. Cogn Brain Res 21: 412–417
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: 3139–3148
Umiltà C, Priftis K, Zorzi M (2009) The spatial representation of numbers: evidence from neglect and pseudoneglect. Exp Brain Res 192: 561–569
Walsh V (2003) A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn Sci 7: 483–488
Willmes K (2008) Acalculia. In: Goldenberg G, Miller BL (eds) Handbook of Clinical Neurology, Vol 88 (3rd series). Neuropsychology and behavioral neurology. Elsevier, Lisse, pp 339–358
Wood G, Nuerk H-C, Willmes K (2006) Neural representations of twodigit numbers: A parametric fMRI study. NeuroImage 46: 358–367
Wood G, Nuerk HC, Moeller K, Geppert B, Schnitker R, Weber J, Willmes K (2008a) All for one but not one for all: How multiple number representations are recruited in one numerical task. Brain Res 1187: 154–166
Wood G, Willmes K, Nuerk H-C, Fischer M (2008b) On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychol Sci Q 59: 489–525
Zamarian L, Ischebeck A, Delazer M (2009) Neuroscience of learning arithmetic – Evidence from brain imaging studies. Neurosci Biobehav Rev 33: 909–925
Zorzi M, Priftis K, Umiltà C (2002) Neglect disrupts the mental number line. Nature 417: 138–139
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Nuerk, HC., Klein, E., Willmes, K. (2013). Zahlenverarbeitung und Rechnen. In: Schneider, F., Fink, G.R. (eds) Funktionelle MRT in Psychiatrie und Neurologie. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29800-4_27
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