Spatial associations in numerical cognition—From single digits to arithmetic

REFERENCES

• Aiello, M., Merola, S., & Doricchi, F. (2013). Small numbers in the right brain: Evidence from patients without and with spatial neglect. Cortex, 49, 348–351. doi: 10.1016/j.cortex.2012.06.002
   PubMed Web of Science ®Google Scholar
• Andres, M., Michaux, N., & Pesenti, M. (2012). Common substrate for mental arithmetic and finger representation in the parietal cortex. NeuroImage, 62, 1520–1528. doi: 10.1016/j.neuroimage.2012.05.047
   PubMed Web of Science ®Google Scholar
• Ashcraft, M., & Battaglia, J. (1978). Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology: Human Learning and Memory, 4(5), 527–538.
   Google Scholar
• Ashkenazi, S., & Henik, A. (2010). A disassociation between physical and mental number bisection in developmental dyscalculia. Neuropsychologia, 48, 2861–2868. doi: 10.1016/j.neuropsychologia.2010.05.028
   PubMed Web of Science ®Google Scholar
• Bachot, J., Gevers, W., Fias, W., & Roeyers, H. (2005). Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology Science Quarterly, 47, 172–183.
   Google Scholar
• Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. doi: 10.1146/annurev.psych.59.103006.093639
   PubMed Web of Science ®Google Scholar
• Ben Nathan, M., Shaki, S., Salti, M., & Algom, D. (2009). Numbers and space: Associations and dissociations. Psychonomic Bulletin and Review, 16(3), 578–582. doi: 10.3758/PBR.16.3.578
   PubMed Web of Science ®Google Scholar
• Berch, D. B., Foley, E. J., Hill, R. J., & Ryan, P. M. (1999). Extracting parity and magnitude from Arabic numerals: Developmental changes in number processing and mental representation. Journal of Experimental Child Psychology, 74, 286–308. doi: 10.1006/jecp.1999.2518
   PubMed Web of Science ®Google Scholar
• Bonato, M., Priftis, K., Marenzi, R., & Zorzi, M. (2009). Normal and impaired reflexive orienting of attention after central nonpredictive cues. Journal of Cognitive Neuroscience, 21(4), 745–759. doi: 10.1162/jocn.2009.21054
   PubMed Web of Science ®Google Scholar
• Brooks, J. L., Della Sala, S., & Darling, S. (2014). Representational pseudoneglect: A review. Neuropsychology Review, 24, 148–165. doi: 10.1007/s11065-013-9245-2
   PubMed Web of Science ®Google Scholar
• Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society London, B (Biological Sciences), 364(1525), 1831–1840. doi: 10.1098/rstb.2009.0028
   PubMed Web of Science ®Google Scholar
• Bull, R., Cleland, A. A., & Mitchell, T. (2013). Sex differences in the spatial representation of number. Journal of Experimental Psychology: General, 142(1), 181–192. doi: 10.1037/a0028387
   PubMed Web of Science ®Google Scholar
• Calabria, M., & Rossetti, Y. (2005). Interference between number processing and line bisection: A methodology. Neuropsychologia, 43, 779–783. doi: 10.1016/j.neuropsychologia.2004.06.027
   PubMed Web of Science ®Google Scholar
• Carlson, R. A., Avraamides, M. N., Cary, M., & Strasberg, S. (2007). What do the hands externalize in simple arithmetic? Journal of Experimental Psychology: Learning, Memory, and Cognition, 33, 747–756.
   PubMed Web of Science ®Google Scholar
• Casarotti, M., Michielin, M., Zorzi, M., & Umiltà, C. (2007). Temporal order judgment reveals how number magnitude affects visuospatial attention. Cognition, 102, 101–117. doi: 10.1016/j.cognition.2006.09.001
   PubMed Web of Science ®Google Scholar
• Casasanto, D. (2009). Embodiment of abstract concepts: Good and bad in right- and left-handers. Journal of Experimental Psychology: General, 138, 351–367. doi: 10.1037/a0015854
   PubMed Web of Science ®Google Scholar
• Cattaneo, Z., Fantino, M., Tinti, C., Silvanto, J., & Vecchi, T. (2010). Crossmodal interaction between the mental number line and peripersonal haptic space representation in sighted and blind individuals. Attention, Perception & Psychophysics, 72(4), 885–890. doi: 10.3758/APP.72.4.885
   PubMed Web of Science ®Google Scholar
• Chen, Q., & Verguts, T. (2012). Spatial intuition in elementary arithmetic: A neurocomputational account. PLoS ONE, 7(2), e31180. doi:10.1371/journal.pone.0031180 doi: 10.1371/journal.pone.0031180
   PubMed Web of Science ®Google Scholar
• 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. Quarterly Journal of Experimental Psychology, 66(10), 1974–1991. doi: 10.1080/17470218.2013.772215
   PubMed Web of Science ®Google Scholar
• Crollen, V., Dormal, G., Seron, X., Lepore, F., & Collignon, O. (2011). Embodied numbers: The role of vision in the development of number–space interactions. Cortex, 49, 276–283. doi: 10.1016/j.cortex.2011.11.006
   PubMed Web of Science ®Google Scholar
• Cutini, S., Scarpa, F., Scatturin, P., Dell Aqua, R., & Zorzi, M. (2012). Number–space interactions in the human parietal cortex: Enlightening the SNARC effect with functional near-infrared spectroscopy. Cerebral Cortex, 24(2), 444–451. doi: 10.1093/cercor/bhs321
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (2012). The number sense: How the mind creates mathematics (2nd ed.). Oxford: University Press.
   Google Scholar
• Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371–396. doi: 10.1037/0096-3445.122.3.371
   Web of Science ®Google Scholar
• Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56(2), 384–398. doi: 10.1016/j.neuron.2007.10.004
   PubMed Web of Science ®Google Scholar
• De Hevia, M. D., Girelli, L., & Vallar, G. (2006). Numbers and space: A cognitive illusion? Experimental Brain Research, 168, 254–264. doi: 10.1007/s00221-005-0084-0
   PubMed Web of Science ®Google Scholar
• De Hevia, M.-D., Izard, V., Coubart, A., Spelke, E. S., & Streri, A. (2014). Representations of space, time, and number in neonates. Proceedings of the National Academy of Sciences, in press.
   Google Scholar
• DeStefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353–386. doi: 10.1080/09541440244000328
   Web of Science ®Google Scholar
• van Dijck, J.-P., Abrahamse, E. L., Acar, F., Ketels, B., & Fias, W. (2014). A working memory account of the interaction between numbers and spatial attention. The Quarterly Journal of Experimental Psychology, 67, 1500–1513.
   Web of Science ®Google Scholar
• van Dijck, J.-P., Abrahamse, E. L., Majerus, S., & Fias, W. (2013).Spatial attention interacts with serial-order retrieval from verbal working memory. Psychological Science, 24(9), 1854–1859. doi: 10.1177/0956797613479610
   PubMed Web of Science ®Google Scholar
• van Dijck, J.-P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113, 248–253. doi: 10.1016/j.cognition.2009.08.005
   PubMed Web of Science ®Google Scholar
• Dodd, M. D., & van der Stigchl, S., Leghari, M. A., Fung, G., & Kingstone, A. (2008). Attentional SNARC: There's something special about numbers (let us count the ways). Cognition, 108, 810–818. doi: 10.1016/j.cognition.2008.04.006
   PubMed Web of Science ®Google Scholar
• Domahs, F., Kaufmann, L., & Fischer, M. H. (2012). Handy numbers: Finger counting and numerical cognition. Special Research Topic in Frontiers Media SA. ISBN: 978-2-88919-059-1.
   Google Scholar
• Dotan, D., & Dehaene, S. (2013). How do we convert a number into a finger trajectory? Cognition, 129, 512–529. doi: 10.1016/j.cognition.2013.07.007
   PubMed Web of Science ®Google Scholar
• Fias, W., & Fischer, M. H. (2005). Spatial representation of numbers. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 43–54). New York: Psychology Press.
   Google Scholar
• Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology, 57(5), 822–826. doi: 10.1212/WNL.57.5.822
   PubMed Web of Science ®Google Scholar
• Fischer, M. H. (2003). Spatial representations in number processing—Evidence from a pointing task. Visual Cognition, 10(4), 493–508. doi: 10.1080/13506280244000186
   Web of Science ®Google Scholar
• Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44, 386–392. doi: 10.1016/j.cortex.2007.08.004
   PubMed Web of Science ®Google Scholar
• Fischer, M. H. (2012a). The spatial mapping of numbers—Its origin and flexibility. In Y. Coello & A. Bartolo (Eds.), Language and action in cognitive neurosciences (pp. 225–242). London: Psychology Press.
   Google Scholar
• Fischer, M. H. (2012b). A hierarchical view of grounded, embodied and situated numerical cognition. Cognitive Processing, 13, S161–S164. doi:10.1007/s10339-012-0477-5 doi: 10.1007/s10339-012-0477-5
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., & Brugger, P. (2011). When digits help digits: Spatial-numerical associations point to finger counting as prime example of embodied cognition. Frontiers in Psychology, 2, 260. doi: 10.3389/fpsyg.2011.00260
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., & Campens, H. (2009). Pointing to numbers and grasping magnitudes. Experimental Brain Research, 192(1), 149–153. doi: 10.1007/s00221-008-1622-3
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6(6), 555–556. doi: 10.1038/nn1066
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., & Mills, R. A., & Shaki, S. (2010). How to cook a SNARC: Number placement in text rapidly changes spatial-numerical associations. Brain and Cognition, 72, 333–336. doi: 10.1016/j.bandc.2009.10.010
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Shaki, S., & Cruise, A. (2009). It takes only one word to quash the SNARC. Experimental Psychology, 56(5), 361–366. doi: 10.1027/1618-3169.56.5.361
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51(2), 91–97. doi: 10.1027/1618-3169.51.2.91
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., & Zwaan, R. A. (2008). Embodied language—A review of the role of the motor system in language comprehension. Quarterly Journal of Experimental Psychology, 61(6), 825–850. doi: 10.1080/17470210701623605
   PubMed Web of Science ®Google Scholar
• Fuson, K. C. (1988). Children's counting and concepts of number. New York: Springer.
   Google Scholar
• van Galen, M., & Reitsma, P. (2008). Developing access to number magnitude: A study of the SNARC effect in 7- to 9-year-olds. Journal of Experimental Child Psychology, 101, 99–113. doi: 10.1016/j.jecp.2008.05.001
   PubMed Web of Science ®Google Scholar
• Galfano, G., Rusconi, E., & Umilta, C. (2006). Number magnitude orients attention, but not against one's will. Psychonomic Bulletin and Review, 13, 869–874. doi: 10.3758/BF03194011
   PubMed Web of Science ®Google Scholar
• Gevers, W., Reynvoet, B., & Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition, 87, B87–B95. doi: 10.1016/S0010-0277(02)00234-2
   PubMed Web of Science ®Google Scholar
• Gevers, W., Reynvoet, B., & Fias, W. (2004). The mental representation of ordinal sequences is spatially organised: Evidence from days of the week. Cortex, 40, 171–172. doi: 10.1016/S0010-9452(08)70938-9
   PubMedGoogle Scholar
• 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. doi: 10.1037/a0017688
   PubMed Web of Science ®Google Scholar
• Gevers, W., Verguts, T., Reynvoet, B., Caessens, B., & Fias, W. (2006). Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance, 32(1), 32–44.
   PubMed Web of Science ®Google Scholar
• Glenberg, A. M., Witt, J. K., & Metcalfe, J. (2013). From the Revolution to Embodiment: 25 Years of Cognitive Psychology. Perspectives on Psychological Science, 8(5), 573–585. doi: 10.1177/1745691613498098
   Web of Science ®Google Scholar
• Göbel, S. M., Fischer, M. H., & Shaki, S. (2014). Experience counts: Transmitting culture through space. Poster at the European workshop on Cognitive Neuropsychology. Bressanone, Italy.
   Google Scholar
• Goldin-Meadow, S., & Alibali, M. W. (2013). Gesture's role in speaking, learning and creating language. Annual Review of Psychology, 64, 257–283. doi: 10.1146/annurev-psych-113011-143802
   PubMed Web of Science ®Google Scholar
• Goldstone, R. L., Landy, D. H., & Son, Y. L. (2013). The education of perception. Topics in Cognitive Sciences, 2, 265–284. doi: 10.1111/j.1756-8765.2009.01055.x
   Web of Science ®Google Scholar
• Hartmann, M., Gashaj, V., Stahnke, A., & Mast, F. W. (2014). There is more than “more is up”: Hand and foot responses reverse the vertical association of number magnitudes. Journal of Experimental Psychology: Human Perception and Performance. doi: 10.1037/a0036686
   PubMed Web of Science ®Google Scholar
• Hartmann, M., Grabherr, L., & Mast, F. W. (2012). Moving along the mental number line: Interactions between whole-body motion and numerical cognition. Journal of Experimental Psychology: Human Perception and Performance, 38, 1416–1427. doi:10.1037/a0026706
   PubMed Web of Science ®Google Scholar
• Hauk, O., Johnsrude, I., & Pulvermüller, F. (2004). Somatotopic representation of action words in human motor and premotor cortex. Neuron, 41, 301–307. doi: 10.1016/S0896-6273(03)00838-9
   PubMed Web of Science ®Google Scholar
• Herrera, A., Macizo, P., & Semenza, C. (2008). The role of working memory in the association between number magnitude and space. Acta Psychologica, 128, 225–237. doi: 10.1016/j.actpsy.2008.01.002
   PubMed Web of Science ®Google Scholar
• Hoffmann, D., Hornung, C., Martin, R., & Schiltz, C. (2013). Developing number-space associations: SNARC effects using a colour-discrimination task in 5 year olds. Journal of Experimental Child Psychology, 116, 775–791. doi: 10.1016/j.jecp.2013.07.013
   PubMed Web of Science ®Google Scholar
• Holmes, K. J., & Lourenco, S. F. (2012). Orienting numbers in mental space: Horizontal organization trumps vertical. Quarterly Journal of Experimental Psychology, 65, 1044–1051. doi: 10.1080/17470218.2012.685079
   PubMed Web of Science ®Google Scholar
• Hubbard, T. (2005). Representational momentum and related displacements in spatial memory: A review of the findings. Psychonomic Bulletin & Review, 12(5), 822–851. doi: 10.3758/BF03196775
   PubMed Web of Science ®Google Scholar
• Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448. doi: 10.1038/nrn1684
   PubMed Web of Science ®Google Scholar
• Hung, Y. H., Hung, D. L., Tzeng, O. J. L., & Wu, D. H. (2008). Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition, 106(3), 1441–1450. doi: 10.1016/j.cognition.2007.04.017
   PubMed Web of Science ®Google Scholar
• Hutchinson, S., & Louwerse, M. (2014). Language statistics explain the spatial–numerical association of response codes. Psychonomic Bulletin & Review, 21, 470–478. doi: 10.3758/s13423-013-0492-2
   PubMed Web of Science ®Google Scholar
• Ito, Y., & Hatta, T. (2004). Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect. Memory & Cognition, 32, 662–673. doi: 10.3758/BF03195857
   PubMed Web of Science ®Google Scholar
• Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221–1247.
   Google Scholar
• Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceeding of the National Academy of Sciences, 106(25), 10382–10385. doi: 10.1073/pnas.0812142106
   PubMed Web of Science ®Google Scholar
• Jeannerod, M. (2006). Motor cognition. Oxford: University Press.
   Google Scholar
• Jiang, M., Cooper, J., & Alibali, M. (2014). Spatial factors influence arithmetic performance: The case of the minus sign. The Quarterly Journal of Experimental Psychology, 67, 1626–1642.
   Web of Science ®Google Scholar
• Klein, E., Huber, S., Nuerk, H.-C., & Moeller, K. (2014). Operational momentum affects eye fixation behaviour. The Quarterly Journal of Experimental Psychology, 67, 1614–1625.
   Web of Science ®Google Scholar
• Knops, A., Dehaene, S., Berteletti, I., & Zorzi, M. (2014). Can Approximate Mental Calculation Account for Operational Momentum in Addition and Subtraction? The Quarterly Journal of Experimental Psychology, 67, 1541–1556.
   Web of Science ®Google Scholar
• Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009b). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585. doi: 10.1126/science.1171599
   PubMed Web of Science ®Google Scholar
• Knops, A., Viarouge, A., & Dehaene, S. (2009a). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception & Psychophysics, 71, 803–821. doi: 10.3758/APP.71.4.803
   PubMed Web of Science ®Google Scholar
• Knops, A., Zitzmann, S., & McCrink, C. (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4, 325. doi: 10.3389/fpsyg.2013.00325
   PubMed Web of Science ®Google Scholar
• Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
   Google Scholar
• Landy, D., & Goldstone, R. L. (2007). How abstract is symbolic thought? Journal of Experimental Psychology: Learning, Memory, & Cognition, 33(4), 720–733.
   PubMed Web of Science ®Google Scholar
• Landy, D., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. The Quarterly Journal of Experimental Psychology, 63(10), 1953–1968. doi: 10.1080/17470211003787619
   Web of Science ®Google Scholar
• Landy, D. H., Jones, M. N., & Goldstone, R. L. (2008). How the appearance of an operator affects its formal precedence. In Proceedings of the Thirtieth Annual Conference of the Cognitive Science Society (pp. 2109–2114). Washington, DC: Cognitive Science Society.
   Google Scholar
• Lefevre, J., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory & Cognition, 16, 45–53. doi: 10.3758/BF03197744
   PubMed Web of Science ®Google Scholar
• Lindemann, O., Abolafia, J. M., Pratt, J., & Bekkering, H. (2007). Coding strategies in number space: Memory requirements influence spatial-numerical associations. The Quarterly Journal of Experimental Psychology, 61(4), 515–524. doi: 10.1080/17470210701728677
   Web of Science ®Google Scholar
• Lindemann, O., & Tira, M. D. (2011). Operational Momentum in Numerosity Production Judgments of Multi-Digit Number Problems. Zeitschrift für Psychologie/Journal of Psychology, 219(1), 50–57. doi: 10.1027/2151-2604/a000046
   Web of Science ®Google Scholar
• Link, T., Nuerk, H. C., & Moeller, K. (2014). On the relation between the mental number line and arithmetic competencies. The Quarterly Journal of Experimental Psychology, 67, 1597–1613.
   Web of Science ®Google Scholar
• Loetscher, T., Bockisch, C., Nicholls, M., & Brugger, P. (2010). Eye position predicts what number you have in mind. Current Biology, 20(6), 264–265. doi: 10.1016/j.cub.2010.01.015
   PubMed Web of Science ®Google Scholar
• Loetscher, T., Schwarz, U., Schubiger, M., & Brugger, P. (2008). Head turns bias the brain's internal random generator. Current Biology, 18(2), 60–62. doi: 10.1016/j.cub.2007.11.015
   Web of Science ®Google Scholar
• Luchins, A. (1942). Mechanization in problem solving. Psychological Monographs, 54, 1–22. doi: 10.1037/h0093502
   Google Scholar
• Lugli, L., Baroni, G., Anelli, F., Borghi, A. M., & Nicoletti, R. (2013). Counting is easier while experiencing a congruent motion. PLoS One, 8, e64500. doi: 10.1371/journal.pone.0064500
   PubMed Web of Science ®Google Scholar
• Marghetis, T., Núñez, R., & Bergen, B. (2014). Doing arithmetic by hand: Hand movements during exact arithmetic reveal systematic, dynamic spatial processing. The Quarterly Journal of Experimental Psychology, 67, 1579–1596.
   Web of Science ®Google Scholar
• Masson, N., & Pesenti, M. (2014). Attentional bias induced by solving simple and complex addition and subtraction problems. The Quarterly Journal of Experimental Psychology, 67, 1514–1526.
   Web of Science ®Google Scholar
• McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69(8), 1324–1333. doi: 10.3758/BF03192949
   PubMed Web of Science ®Google Scholar
• McCrink, K., & Opfer, J. (in press). Development of Spatial-Numerical Associations. Current Directions in Psychological Science.
   Web of Science ®Google Scholar
• McCrink, K., & Wynn, K. (2009). Operational momentum in large-number addition and subtraction by 9-month-olds. Journal of Experimental Child Psychology, 103, 400–408. doi: 10.1016/j.jecp.2009.01.013
   PubMed Web of Science ®Google Scholar
• Meier, B. P., & Robinson, M. D. (2004). Why the sunny side is up: Associations between affect and vertical position. Psychological Science, 15, 243–247.
   Google Scholar
• Moeller, K., & Nuerk, H. C. (2011). Psychophysics of number representation. Zeitschrift für Psychologie/Journal of Psychology, 219(1), 64–70. doi: 10.1027/2151-2604/a000048
   Web of Science ®Google Scholar
• Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520. doi: 10.1038/2151519a0
   PubMed Web of Science ®Google Scholar
• Nicholls, M. E. R., Loftus, A. M., & Gevers, W. (2008). Look, no hands: A perceptual task shows that number magnitude induces shifts of attention. Psychonomic Bulletin & Review, 15(4), 413–418. doi: 10.3758/PBR.15.2.413
   PubMed Web of Science ®Google Scholar
• Nuerk, H. C., Iversen, W., & Willmes, K. (2004). Notational modulation of the SNARC effect and the MARC (linguistic markedness of response codes) effect. Quarterly Journal of Experimental Psychology, 57A, 835–863. doi: 10.1080/02724980343000512
   Web of Science ®Google Scholar
• Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line. Zeitschrift für Psychologie/Journal of Psychology, 219(1), 3–22. doi: 10.1027/2151-2604/a000041
   Web of Science ®Google Scholar
• 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. doi: 10.1016/S0010-0277(01)00142-1
   PubMed Web of Science ®Google Scholar
• Nuerk, H. C., Wood, G., & Willmes, K. (2005). The universal SNARC effect. Experimental Psychology, 52, 187–194. doi: 10.1027/1618-3169.52.3.187
   PubMed Web of Science ®Google Scholar
• Nunez, R. (2011). No Innate Number Line in the Human Brain. Journal of Cross-Cultural Psychology, 42(4), 651–668. doi: 10.1177/0022022111406097
   Web of Science ®Google Scholar
• Nunez, R., Douan, D., & Nikoulina, A. (2011). Squeezing, striking, and vocalizing: Is number representation fundamentally spatial? Cognition, 120, 220–235. doi: 10.1016/j.cognition.2011.05.001
   Web of Science ®Google Scholar
• Opfer, J. E., Thompson, C. A., & Furlong, E. E. (2010). Early development of spatial numeric associations: Evidence from spatial and quantitative performance of preschoolers. Developmental Science, 13(5), 761–771. doi: 10.1111/j.1467-7687.2009.00934.x
   PubMed Web of Science ®Google Scholar
• Pasqualotto, A., Taya, S., & Proulx, M. J. (2014). Sensory deprivation: Visual experience alters the mental number line. Behavioral Brain Research, 261, 110–113. doi: 10.1016/j.bbr.2013.12.017
   PubMed Web of Science ®Google Scholar
• Patro, K., & Haman, M. (2012). The spatial-numerical congruity effect in preschoolers. Journal of Experimental Child Psychology, 111, 534–542. doi: 10.1016/j.jecp.2011.09.006
   PubMed Web of Science ®Google Scholar
• Pinhas, M. & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408–415. doi: 10.1016/j.cognition.2008.09.003
   PubMed Web of Science ®Google Scholar
• Pinhas, M., & Fischer, M. H. (2009, January). Addition is where the big numbers are: Evidence for an inverse operational momentum effect. Poster presented at the 27th European Workshop on Cognitive Neuropsychology, Bressanone, Italy.
   Google Scholar
• Pinhas, M., Shaki, S., & Fischer, M. H. (2014). Heed the signs: Operation signs have spatial associations. The Quarterly Journal of Experimental Psychology, this issue.
   Web of Science ®Google Scholar
• Pinhas, M., Tzelgov, J. & Ganor-Stern, D. (2012). Estimating linear effects in ANOVA designs: The easy way. Behavior Research Methods, 44(3), 788–794. doi: 10.3758/s13428-011-0172-y
   PubMed Web of Science ®Google Scholar
• Posner, M. I. (1980). Orienting of attention. The Quarterly Journal of Experimental Psychology, 32(1), 3–25. doi: 10.1080/00335558008248231
   PubMed Web of Science ®Google Scholar
• Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132, 416–442. doi: 10.1037/0033-2909.132.3.416
   PubMed Web of Science ®Google Scholar
• Pulvermüller, F. (2005). Brain mechanisms linking language and action. Nature Reviews Neuroscience, 6, 576–582. doi: 10.1038/nrn1706
   PubMed Web of Science ®Google Scholar
• Pulvermüller, F. (2013). How neurons make meaning: Brain mechanisms for embodied and abstract-symbolic semantics. Trends on Cognitive Sciences, 17(9), 458–470. doi: 10.1016/j.tics.2013.06.004
   PubMed Web of Science ®Google Scholar
• Rashidi-Ranjbar, N., Goudarzvand, M., Jahangiri, S., Brugger, P., & Loetscher, T. (2014). No horizontal numerical mapping in a culture with mixed reading habits. Frontiers in Human Neuroscience, 8, 72. doi: 10.3389/fnhum.2014.00072
   PubMed Web of Science ®Google Scholar
• Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2), 274–278. doi: 10.1037/h0028573
   Google Scholar
• Riello, M., & Rusconi, E. (2011). Unimanual SNARC effect: Hand matters. Frontiers in Psychology, 2, 372. doi:10.3389/fpsyg.2011.00372 doi: 10.3389/fpsyg.2011.00372
   PubMed Web of Science ®Google Scholar
• Ristic, J., Wright, A., & Kingstone, A. (2006). The number line effect reflects top-down control. Psychonomic Bulletin and Review, 13, 862–868. doi: 10.3758/BF03194010
   PubMed Web of Science ®Google Scholar
• Rugani, R., Salva, O. R., & Regolin, L. (2014). Lateralized mechanisms for encoding of object. Behavioral evidence from an animal model: The domestic chick (Gallus gallus). Frontiers in Psychology, 5, 150. doi:10.3389/fpsyg.2014.00150 doi: 10.3389/fpsyg.2014.00150
   PubMed Web of Science ®Google Scholar
• Rusconi, E., Dervinis, M., Verbruggen, F., & Chambers, C. D. (2013). Critical time course of right fronto-parietal involvement in mental number space. Journal of Cognitive Neuroscience, 25, 465–483. doi: 10.1162/jocn_a_00330
   PubMed Web of Science ®Google Scholar
• Rusconi, E., Galfano, G., Speriani, V., & Umilta, C. (2004). Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval. Quarterly Journal of Experimental Psychology, 57A(8), 1485–1511. doi: 10.1080/02724980343000873
   Web of Science ®Google Scholar
• Rusconi, E., Kwan, B., Giordano, B., Umiltà, C., & Butterworth, B. (2005). Spatial representation of pitch height: The SMARC effect. Cognition, 99, 113–129. doi: 10.1016/j.cognition.2005.01.004
   PubMed Web of Science ®Google Scholar
• Scheepers, C., & Sturt, P. (2014). Bi-directional syntactic priming across cognitive domains: From arithmetic to language and back. The Quarterly Journal of Experimental Psychology, 67, 1643–1654.
   Web of Science ®Google Scholar
• Schneider, E., Maruyama, M., Dehaene, S., & Sigman, M. (2012). Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas. Cognition, 125(3), 475–490. doi: 10.1016/j.cognition.2012.06.015
   PubMed Web of Science ®Google Scholar
• Schwarz, W., & Keus, I. (2004). Moving the eyes along the mental number line: Comparing SNARC effects with manual and saccadic responses. Perception and Psychophysics, 66, 651–664. doi: 10.3758/BF03194909
   PubMed Web of Science ®Google Scholar
• Schwarz, W., & Müller, D. (2006). Spatial associations in number-related tasks. Experimental Psychology, 53, 4–15. doi: 10.1027/1618-3169.53.1.4
   PubMed Web of Science ®Google Scholar
• Shaki, S., & Fischer, M. H. (2008). Reading space into numbers—A cross-linguistic comparison of the SNARC effect. Cognition, 108, 590–599. doi: 10.1016/j.cognition.2008.04.001
   PubMed Web of Science ®Google Scholar
• Shaki, S., & Fischer, M. H. (2012). Multiple spatial mappings in numerical cognition. Journal of Experimental Psychology: Human Perception and Performance, 38(3), 804–809.
   PubMed Web of Science ®Google Scholar
• Shaki, S., & Fischer, M. H. (2014). Random Walks on the Mental Number Line. Experimental Brain Research, 232, 43–49. doi: 10.1007/s00221-013-3718-7
   PubMed Web of Science ®Google Scholar
• Shaki, S., Fischer, M., & Göbel, S. (2012). Direction counts: A comparative study of spatially directional counting biases in cultures with different reading directions. Journal of Experimental Child Psychology, 112(2), 275–281. doi: 10.1016/j.jecp.2011.12.005
   PubMed Web of Science ®Google Scholar
• Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin and Review, 16(2), 328–331. doi: 10.3758/PBR.16.2.328
   PubMed Web of Science ®Google Scholar
• Shaki, S., Sery, N., & Fischer, M. H. (2014). 1+2 is more than 2+1: Violation of commutativity and unit invariance in mental arithmetic. Journal of Cognitive Psychology (in revision).
   Google Scholar
• Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Develoopment, 75(2), 428–444. doi: 10.1111/j.1467-8624.2004.00684.x
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Opfer, J. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243. doi: 10.1111/1467-9280.02438
   PubMed Web of Science ®Google Scholar
• Song, J.-H., & Nakayama, K. (2008). Numerical comparison in a visually guided manual reaching task. Cognition, 106, 994–1003. doi: 10.1016/j.cognition.2007.03.014
   PubMed Web of Science ®Google Scholar
• Stoianov, I., Kramer, P., Umilta, C., & Zorzi, M. (2008). Visuospatial priming of the mental number line. Cognition, 106, 770–779. doi: 10.1016/j.cognition.2007.04.013
   PubMed Web of Science ®Google Scholar
• Towse, J. N., & Cheshire, A. (2007). Random number generation and working memory. European Journal of Cognitive Psychology, 19(3), 374–394. doi: 10.1080/09541440600764570
   Web of Science ®Google Scholar
• Tschentscher, N., Hauk, O., Fischer, M. H., & Pulvermüller, F. (2012). You can count on the motor cortex: Finger counting habits modulate motor cortex activation evoked by numbers. NeuroImage, 59, 3139–3148. doi: 10.1016/j.neuroimage.2011.11.037
   PubMed Web of Science ®Google Scholar
• Tzelgov, J., Zohar-Shai, B., & Nuerk, H. C. (2013). On defining quantifying and measuring the SNARC effect. Frontiers in Psychology, 4, 302. doi:10.3389/fpsyg.2013.00302 doi: 10.3389/fpsyg.2013.00302
   PubMed Web of Science ®Google Scholar
• Ulrich, R., & Maienborn, C. (2010). Left-right coding of past and future in language: The mental timeline during sentence processing. Cognition, 117(2), 126–138. doi: 10.1016/j.cognition.2010.08.001
   PubMed Web of Science ®Google Scholar
• Van Gompel, R. P. G., Fischer, M. H., Murray, W., & Hill, R. L. (2007). Eye movements: A window on mind and brain. Oxford: Elsevier.
   Google Scholar
• Viarouge, A., Hubbard, E., & Dehaene, S. (2014). The organization of spatial reference frames involved in the SNARC effect. The Quarterly Journal of Experimental Psychology, 67, 1484–1499.
   Web of Science ®Google Scholar
• Wasner, M., Moeller, K., Fischer, M. H., & Nuerk, H. C. (in press). How situated cognition influences memory retrieval: The case of finger counting habits. Cognitive Processing.
   Google Scholar
• Werner, K., & Raab, M. (2013). Moving to solution. Experimental Psychology, 60, 403–409. doi: 10.1027/1618-3169/a000213
   PubMed Web of Science ®Google Scholar
• Werner, K., & Raab, M. (2014). Moving your eyes to solution: Effects of movement on the perception of a problem-solving task. The Quarterly Journal of Experimental Psychology, 67, 1571–1578.
   Web of Science ®Google Scholar
• White, S. L. J., Szucs, D., & Soltész, F. (2011). Symbolic number: The integration of magnitude and spatial representations in children aged 6 to 8 years. Frontiers in Psychology, 2, 392. doi:10.3389/fpsyg.2011.00392 doi: 10.3389/fpsyg.2011.00392
   PubMed Web of Science ®Google Scholar
• Wiemers, M., Bekkering, H., & Lindemann, O. (2014). Spatial Interferences in Mental Arithmetic: Evidence from the Motion-Arithmetic Compatibility Effect. The Quarterly Journal of Experimental Psychology, 67, 1557–1570.
   Web of Science ®Google Scholar
• Winter, B., & Matlock, T. (2013). More is up … and right: Random number generation along two axes. In M. Knauff, M. Pauen, N. Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp. 3789–3974). Austin, TX: Cognitive Science Society.
   Google Scholar
• Wood, G., Nuerk, H.-C., Willmes, K., & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489–525.
   Google Scholar
• Zhou, F., Zhao, Q., Chen, C., & Zhou, X. (2012). Mental representations of arithmetic facts: Evidence from eye movement recordings supports the preferred operand-order specific representation hypothesis. Quarterly Journal of Experimental Psychology, 65(4), 661–674. doi: 10.1080/17470218.2011.616213
   PubMed Web of Science ®Google Scholar
• Zorzi, M., Bonato, M., Treccani, B., Scalambrin, G., Marenzi, R., & Priftis, K. (2012). Neglect impairs explicit processing of the mental number line. Frontiers in Human Neuroscience, 6, 125. doi: 10.3389/fnhum.2012.00125
   PubMed Web of Science ®Google Scholar
• Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417, 138–139. doi: 10.1038/417138a
   PubMed Web of Science ®Google Scholar