Abstract
Tight cognitive links between space and number processing exist. Usually, Spatial-Numerical Associations (SNAs) are interpreted causally: spatial capabilities are a cornerstone of math skill. We question this seemingly ubiquitous assumption. After presenting SNA taxonomy, we show that only some SNAs correlate with math skill. These correlations are not conclusive: (1) Their directions vary (stronger SNA relates sometimes to better, sometimes to poorer skill), (2) the correlations might be explained by mediator variables (e.g., SNA tasks involve cognitive control or reasoning), (3) the hypothetical course of causality is not resolved: For instance, contrary to conventional theories, arithmetic skills can underlie performance in some SNA tasks. However, benefits of SNA trainings on math skills seem to reinforce the claim of primary SNA role. Nevertheless, tasks used in such trainings may tap cognitive operations required in arithmetic, but not SNA representations themselves. Therefore, using space is a powerful tool rather than a cornerstone for math.
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Ashkenazi, S., Mark-Zigdon, N., & Henik, A. (2009). Numerical distance effect in developmental dyscalculia. Cognitive Development, 24(4), 387–400. https://doi.org/10.1016/j.cogdev.2009.09.006
Bachot, J., Gevers, W., Fias, W., & Roeyers, H. (2005). Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology Science, 47(1), 172–183.
Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14(1), 125–135. https://doi.org/10.1111/j.1467-7687.2010.00962.x
Barth, H. C., Starr, A., & Sullivan, J. (2009). Children’s mappings of large number words to numerosities. Cognitive Development, 24(3), 248–264. https://doi.org/10.1016/j.cogdev.2009.04.001
Bloechle, J., Huber, S., & Moeller, K. (2015). In touch with numbers: Embodied and situated effects in number magnitude comparison. Journal of Cognitive Psychology, 27(4), 478–489. https://doi.org/10.1080/20445911.2014.1001760
Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410–1419. https://doi.org/10.1037/0096-1523.33.6.1410
Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189–201. https://doi.org/10.1037/0012-1649.41.6.189
Brysbaert, M. (1995). Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General, 124(4), 434–452. https://doi.org/10.1037/0096-3445.124.4.434
Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 364(1525), 1831–1840. https://doi.org/10.1098/rstb.2009.0028
Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118(1), 32–44. https://doi.org/10.1016/j.cognition.2010.09.005
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. https://doi.org/10.1037/a0028387
Cipora, K., Hohol, M., Nuerk, H.-C., Willmes, K., Brożek, B., Kucharzyk, B., & Nęcka, E. (2016). Professional mathematicians differ from controls in their spatial-numerical associations. Psychological Research, 80(4), 710–726. https://doi.org/10.1007/s00426-015-0677-6
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. https://doi.org/10.1080/17470218.2013.772215
Cipora, K., Patro, K., & Nuerk, H.-C. (2018). Situated influences on spatial-numerical associations. In T. Hubbard (Ed.), Spatial biases in perception and cognition. (pp. 41–59). Cambridge, UK: Cambridge University Press.
Cipora, K., Patro, K., & Nuerk, H.-C. (2015). Are Spatial-Numerical Associations a Cornerstone for Arithmetic Learning? The Lack of Genuine Correlations suggests: No. Mind, Brain, & Education, 9(4), 190–207. https://doi.org/10.1111/mbe.12093
Cohen, D. J., & Blanc-Goldhammer, D. (2011). Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin & Review, 18(2), 331–338. https://doi.org/10.3758/s13423-011-0059-z
Cohen Kadosh, R., & Henik, A. (2007). Can synaesthesia research inform cognitive science? Trends in Cognitive Sciences, 11(4), 177–184. https://doi.org/10.1016/j.tics.2007.01.003
Cohen Kadosh, R., Lammertyn, J., & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84(2), 132–147. https://doi.org/10.1016/j.pneurobio.2007.11.001
Colome, A., Laka, I., & Sebastian-Galles, N. (2010). Language effects in addition: How you say it counts. Quarterly Journal of Experimental Psychology, 63(5), 965–983. https://doi.org/10.1080/17470210903134377
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63–68. https://doi.org/10.1016/j.tine.2013.12.001
Crollen, V., & Noël, M. P. (2015). Spatial and numerical processing in children with high and low visuospatial abilities. Journal of Experimental Child Psychology, 132, 84–98. https://doi.org/10.1016/j.jecp.2014.12.006
Dackermann, T., Fischer, U., Nuerk, H.-C., & Cress, U. (2017). Applying embodied cognition: From useful interventions and their theoretical underpinnings to practical applications. ZDM, 49(4), 545–557. https://doi.org/10.1007/s11858-017-0850-z
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396. https://doi.org/10.1037/0096-3445.122.3.371
de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110(2), 198–207. https://doi.org/10.1016/j.cognition.2008.11.003
de Hevia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21(5), 653–660. https://doi.org/10.1177/0956797610366091
De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103(4), 469–479. https://doi.org/10.1016/j.jecp.2009.01.010
Dietrich, J. F., Huber, S., Dackermann, T., Moeller, K., & Fischer, U. (2016). Place-value understanding in number line estimation predicts future arithmetic performance. British Journal of Developmental Psychology, 34(4), 502–517. https://doi.org/10.1111/bjdp.12146
Dietrich, J. F., Huber, S., & Nuerk, H.-C. (2015). Methodological aspects to be considered when measuring the approximate number system (ANS)—A research review. Frontiers in Psychology, 6, 295. https://doi.org/10.3389/fpsyg.2015.00295
Ebersbach, M., Luwel, K., Frick, A., Onghena, P., & Verschaffel, L. (2008). The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: Evidence for a segmented linear model. Journal of Experimental Child Psychology, 99(1), 1–17. https://doi.org/10.1016/j.jecp.2007.08.006
Eerland, A., Guadalupe, T. M., & Zwaan, R. A. (2011). Leaning to the left makes the Eiffel Tower seem smaller: Posture-modulated estimation. Psychological Science, 22(12), 1511–1514. https://doi.org/10.1177/0956797611420731
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Fias, W., Lauwereyns, J., & Lammertyn, J. (2001). Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. Cognitive Brain Research, 12(3), 415–423. https://doi.org/10.1016/S0926-6410(01)00078-7
Fischer, J. P. (2010). Numerical performance increased by finger training: A fallacy due to regression toward the mean? Cortex, 46(2), 272–273. https://doi.org/10.1016/j.cortex.2008.06.010
Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology, 57(5), 822–826. https://doi.org/10.1212/WNL.57.5.822
Fischer, M. H. (2012). A hierarchical view of grounded, embodied, and situated numerical cognition. Cognitive Processing, 13(Suppl 1), S161–S164. https://doi.org/10.1007/s10339-012-0477-5
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(3), 333–336. https://doi.org/10.1016/j.bandc.2009.10.010
Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition—From single digits to arithmetic. Quarterly Journal of Experimental Psychology, 67(8), 1461–1483. https://doi.org/10.1080/17470218.2014.927515
Fischer, M. H., Shaki, S., & Cruise, A. (2009). It takes just one word to quash a SNARC. Experimental Psychology, 56(5), 361–366. https://doi.org/10.1027/1618-3169.56.5.361
Fischer, U., Moeller, K., Bientzle, M., Cress, U., & Nuerk, H.-C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177–183. https://doi.org/10.3758/s13423-010-0031-3
Fornaciai, M., Cicchini, G. M., & Burr, D. C. (2016). Adaptation to number operates on perceived rather than physical numerosity. Cognition, 151, 63–67. https://doi.org/10.1016/j.cognition.2016.03.006
Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65. https://doi.org/10.1016/S1364-6613(99)01424-2
Galton, F. (1880). Visualised numerals. Nature, 21(533), 252–256. https://doi.org/10.1038/021494e0
Ganor-Stern, D., Tzelgov, J., & Ellenbogen, R. (2007). Automaticity and two-digit numbers. Journal of Experimental Psychology: Human Perception and Performance, 33(2), 483–496. https://doi.org/10.1037/0096-1523.33.2.483
Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. https://doi.org/10.1037/a0026218
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
Georges, C., Hoffmann, D., & Schiltz, C. (2017a). How and why do number-space associations co-vary in implicit and explicit magnitude processing tasks? Journal of Numerical Cognition, 3(2), 182–211. https://doi.org/10.5964/jnc.v3i2.46
Georges, C., Hoffmann, D., & Schiltz, C. (2017b). Mathematical abilities in elementary school: Do they relate to number–space associations? Journal of Experimental Child Psychology, 161, 126–147. https://doi.org/10.1016/j.jecp.2017.04.011
Gibson, L. C., & Maurer, D. (2016). Development of SNARC and distance effects and their relation to mathematical and visuospatial abilities. Journal of Experimental Child Psychology, 150, 301–313. https://doi.org/10.1016/j.jecp.2016.05.009
Göbel, S. M. (2015). Up or down? Reading direction influences vertical counting direction in the horizontal plane—A cross-cultural comparison. Frontiers in Psychology, 6, 228. https://doi.org/10.3389/fpsyg.2015.00228
Göbel, S. M., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2014). Language affects symbolic arithmetic in children: The case of number word inversion. Journal of Experimental Child Psychology, 119(1), 17–25. https://doi.org/10.1016/j.jecp.2013.10.001
Gracia-Bafalluy, M., & Noël, M. P. (2008). Does finger training increase young children’s numerical performance? Cortex, 44(4), 368–375. https://doi.org/10.1016/j.cortex.2007.08.020
Grant, E. (1972). Nicole Oresme and the medieval geometry of qualities and motions. A treatise on the uniformity and difformity of intensities known as “tractatus de configurationibus qualitatum et motuum”: Marshall Clagett (ed. and tr.), edited with an introduction (...). Studies in History and Philosophy of Science Part A, 3(2), 167–182. https://doi.org/10.1016/0039-3681(72)90022-2
Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389–395. https://doi.org/10.3758/BF03202431
Ho, C. S.-H., & Cheng, F. S.-F. (1997). Training in place-value concepts improves children’s addition skills. Contemporary Educational Psychology, 22(4), 495–506. https://doi.org/10.1006/ceps.1997.0947
Hoffmann, D., Hornung, C., Martin, R., & Schiltz, C. (2013). Developing number-space associations: SNARC effects using a color discrimination task in 5-year-olds. Journal of Experimental Child Psychology, 116(4), 775–791. https://doi.org/10.1016/j.jecp.2013.07.013
Hoffmann, D., Mussolin, C., Martin, R., & Schiltz, C. (2014). The impact of mathematical proficiency on the number-space association. PLoS One, 9(1), e85048. https://doi.org/10.1371/journal.pone.0085048
Hoffmann, D., Pigat, D., & Schiltz, C. (2014). The impact of inhibition capacities and age on number-space associations. Cognitive Processing, 15(3), 329–342. https://doi.org/10.1007/s10339-014-0601-9
Hohol, M., Cipora, K., Willmes, K., & Nuerk, H.-C. (2017). Bringing back the balance: Domain-general processes are also important in numerical cognition. Frontiers in Psychology, 8, 499. https://doi.org/10.3389/fpsyg.2017.00499
Huber, S., Klein, E., Moeller, K., & Willmes, K. (2016). Spatial-numerical and ordinal positional associations coexist in parallel. Frontiers in Psychology, 7, 438. https://doi.org/10.3389/fpsyg.2016.00438
Huber, S., Moeller, K., & Nuerk, H.-C. (2014). Dissociating number line estimations from underlying numerical representations. Quarterly Journal of Experimental Psychology, 67(5), 991–1003. https://doi.org/10.1080/17470218.2013.838974
Huber, S., Nuerk, H.-C., Willmes, K., & Moeller, K. (2016). A general model framework for multisymbol number comparison. Psychological Review, 123(6), 667–695. https://doi.org/10.1037/rev0000040
Huber, S., Sury, D., Moeller, K., Rubinsten, O., & Nuerk, H.-C. (2015). A general number-to-space mapping deficit in developmental dyscalculia. Research in Developmental Disabilities, 43–44, 32–42. https://doi.org/10.1016/j.ridd.2015.06.003
Hyde, D. C., Khanum, S., & Spelke, E. S. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92–107. https://doi.org/10.1038/jid.2014.371
Kallai, A. Y., & Tzelgov, J. (2012). The place-value of a digit in multi-digit numbers is processed automatically. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(5), 1221–1233. https://doi.org/10.1037/a0027635
Kim, D., & Opfer, J. E. (2017). A unified framework for bounded and unbounded numerical estimation. Developmental Psychology, 53(6), 1088–1097. https://doi.org/10.1037/dev0000305
Klein, E., Huber, S., Nuerk, H.-C., & Moeller, K. (2014). Operational momentum affects eye fixation behaviour. Quarterly Journal of Experimental Psychology, 67(8), 1614–1625. https://doi.org/10.1080/17470218.2014.902976
Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception & Psychophysics, 71(4), 803–821. https://doi.org/10.3758/APP
Kornblum, S., Hasbroucq, T., & Osman, A. (1990). Dimensional overlap: cognitive basis for stimulus-response compatibility––a model and taxonomy. Psychological Review, 97(2), 253–270. https://doi.org/10.1037//0033295x.97.2.253
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., … von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782–795. https://doi.org/10.1016/j.neuroimage.2011.01.070
Landy, D., Charlesworth, A., & Ottmar, E. (2014). Cutting in line: Discontinuities in the use of large numbers in adults. In Proceedings of the 36th Annual Conference of the Cognitive Science Society (pp. 815–820).
Landy, D., Charlesworth, A., & Ottmar, E. (2017). Categories of large numbers in line estimation. Cognitive Science, 41(2), 326–353. https://doi.org/10.1111/cogs.12342
Landy, D., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. Quarterly Journal of Experimental Psychology, 63(10), 1953–1968. https://doi.org/10.1080/17470211003787619
Landy, D., Silbert, N., & Goldin, A. (2013). Estimating large numbers. Cognitive Science, 37(5), 775–799. https://doi.org/10.1111/cogs.12028
Laski, E. V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50(3), 853–864. https://doi.org/10.1037/a0034321
Laurillard, D. (2016). Learning number sense through digital games with intrinsic feedback. Australasian Journal of Educational Technology, 32(6), 32–44. https://doi.org/10.14742/ajet.3116
LeFevre, J. A., Lira, C. J., Sowinski, C., Cankaya, O., Kamawar, D., & Skwarchuk, S. L. (2013). Charting the role of the number line in mathematical development. Frontiers in Psychology, 4, 641. https://doi.org/10.3389/fpsyg.2013.00641
Leibovich, T., & Henik, A. (2013). Magnitude processing in non-symbolic stimuli. Frontiers in Psychology, 4, 375. https://doi.org/10.3389/fpsyg.2013.00375
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”—The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/s0140525x16000960
Lindemann, O., Alipour, A., & Fischer, M. H. (2011). Finger counting habits in middle eastern and western individuals: An online survey. Journal of Cross-Cultural Psychology, 42(4), 566–578. https://doi.org/10.1177/0022022111406254
Lindskog, M., Winman, A., & Poom, L. (2016). Arithmetic training does not improve approximate number system acuity. Frontiers in Psychology, 7, 1364. https://doi.org/10.3389/fpsyg.2016.01634
Link, T., Huber, S., Nuerk, H.-C., & Moeller, K. (2014). Unbounding the mental number line-new evidence on children’s spatial representation of numbers. Frontiers in Psychology, 4, 1021. https://doi.org/10.3389/fpsyg.2013.01021
Link, T., Moeller, K., Huber, S., Fischer, U., & Nuerk, H.-C. (2013). Walk the number line—An embodied training of numerical concepts. Trends in Neuroscience and Education, 2(2), 74–84. https://doi.org/10.1016/j.tine.2013.06.005
Link, T., Nuerk, H.-C., & Moeller, K. (2014). On the relation between the mental number line and arithmetic competencies. Quarterly Journal of Experimental Psychology, 67(8), 1597–1613. https://doi.org/10.1080/17470218.2014.892517
Loetscher, T., Schwarz, U., Schubiger, M., & Brugger, P. (2008). Head turns bias the brain’s internal random generator. Current Biology, 18(2), R60–R62. https://doi.org/10.1016/j.cub.2007.11.015
Lonnemann, J., Krinzinger, H., Knops, A., & Willmes, K. (2008). Spatial representations of numbers in children and their connection with calculation abilities. Cortex, 44(4), 420–428. https://doi.org/10.1016/j.cortex.2007.08.015
Lyons, I. M., Nuerk, H.-C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144(5), 1021–1035. https://doi.org/10.1037/xge0000094
Maertens, B., De Smedt, B., Sasanguie, D., Elen, J., & Reynvoet, B. (2016). Enhancing arithmetic in pre-schoolers with comparison or number line estimation training: Does it matter? Learning and Instruction, 46, 1–11. https://doi.org/10.1016/j.learninstruc.2016.08.004
Masson, N., & Pesenti, M. (2014). Attentional bias induced by solving simple and complex addition and subtraction problems. Quarterly Journal of Experimental Psychology, 67(8), 1514–1526. https://doi.org/10.1080/17470218.2014.903985
Masson, N., Letesson, C., & Pesenti, M. (2018). Time course of attentional shifts in mental arithmetic: Evidence from gaze metrics. The Quarterly Journal of Experimental Psychology, 71(4), 1009–1019. https://doi.org/10.1080/17470218.2017.1318931
McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69(8), 1324–1333. https://doi.org/10.3758/BF03192949
Miura, I. T., Okamoto, Y., Kim, C. C., Chang, C.-M., Steere, M., & Fayol, M. (1994). Comparisons of children’s cognitive representation of number: China, France, Japan, Korea, Sweden, and the United States. International Journal of Behavioral Development, 17(3), 401–411. https://doi.org/10.1177/016502549401700301
Mix, K., Levine, S., Cheng, Y.-L., Young, C., Hambrick, D., Ping, R., & Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206–1227. https://doi.org/10.1037/xge0000182
Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2009). Children’s early mental number line: Logarithmic or decomposed linear? Journal of Experimental Child Psychology, 103(4), 503–515. https://doi.org/10.1016/j.jecp.2009.02.006
Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H.-C. (2011). Early place-value understanding as a precursor for later arithmetic performance—A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851. https://doi.org/10.1016/j.ridd.2011.03.012
Moeller, K., Shaki, S., Göbel, S. M., & Nuerk, H.-C. (2015). Language influences number processing—A quadrilingual study. Cognition, 136, 150–155. https://doi.org/10.1016/j.cognition.2014.11.003
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520. https://doi.org/10.1038/2151519a0
Nemati, P., Schmid, J., Soltanlou, M., Krimly, J.-T., Nuerk, H.-C., & Gawrilow, C. (2017). Planning and self-control, but not working memory, directly predict multiplication performance in adults. Journal of Numerical Cognition, 3(2), 441–467. https://doi.org/10.5964/jnc.v3i2.61
Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line: A review of multi-digit number processing. Zeitschrift Für Psychologie/Journal of Psychology, 219(1), 3–22. https://doi.org/10.1027/2151-2604/a000041
Nuerk, H.-C., Weger, U., & Willmes, K. (2005). Language effects in magnitude comparison: Small, but not irrelevant. Brain and Language, 92(3), 262–277. https://doi.org/10.1016/j.bandl.2004.06.107
Nuerk, H.-C., Moeller, K., & Willmes, K. (2015). Multi-digit number processing: Overview, conceptual clarifications, and language influences. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford University Press (pp. 106–139). https://doi.org/10.1027/2151-2604/a000040
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–B33. https://doi.org/10.1016/S0010-0277(01)00142-1
Obersteiner, A., Reiss, K., & Ufer, S. (2013). How training on exact or approximate mental representations of number can enhance first-grade students’ basic number processing and arithmetic skills. Learning and Instruction, 23(1), 125–135. https://doi.org/10.1016/j.learninstruc.2012.08.004
Opfer, J. E., & Siegler, R. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55(3), 169–195. https://doi.org/10.1016/j.cogpsych.2006.09.002
Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019. https://doi.org/10.1177/0956797613482944
Patro, K., Fischer, U., Nuerk, H.-C., & Cress, U. (2016). How to rapidly construct a spatial-numerical representation in preliterate children (at least temporarily). Developmental Science, 19(1), 126–144. https://doi.org/10.1111/desc.12296
Patro, K., Nuerk, H.-C., Cress, U., & Haman, M. (2014). How number-space relationships are assessed before formal schooling: A taxonomy proposal. Frontiers in Psychology, 5, 419. https://doi.org/10.3389/fpsyg.2014.00419
Penner-Wilger, M., & Anderson, M. L. (2013). The relation between finger gnosis and mathematical ability: Why redeployment of neural circuits best explains the finding. Frontiers in Psychology, 4, 877. https://doi.org/10.3389/fpsyg.2013.00877
Pesenti, M. (2005). Calculation abilities in expert calculators. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 413–430). New York, NY: Psychology Press.
Petersen, S. E., & Posner, M. I. (2012). The attention system of the human brain: 20 years after. Annual review of neuroscience, 35, 73–89. https://doi.org/10.1146/annurev-neuro-062111-150525
Pfister, R., Schroeder, P. A., & Kunde, W. (2013). SNARC struggles: Instant control over spatial-numerical associations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39(6), 1953–1958. https://doi.org/10.1037/a0032991
Piazza, M., & Izard, V. (2009). How humans count: Numerosity and the parietal cortex. The Neuroscientist, 15(3), 261–273. https://doi.org/10.1177/1073858409333073
Piazza, M., Mechelli, A., Butterworth, B., & Price, C. J. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes? NeuroImage, 15(2), 435–446. https://doi.org/10.1006/nimg.2001.0980
Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109(3), 408–415. https://doi.org/10.1016/j.cognition.2008.09.003
Pinhas, M., Shaki, S., & Fischer, M. H. (2014). Heed the signs: Operation signs have spatial associations. Quarterly Journal of Experimental Psychology, 67(8), 1527–1540. https://doi.org/10.1080/17470218.2014.892516
Pinheiro-Chagas, P., Dotan, D., Piazza, M., & Dehaene, S. (2017). Finger tracking reveals the covert stages of mental arithmetic pedro. Open Mind, 1(1), 30–41. https://doi.org/10.1162/opmi
Pixner, S., Moeller, K., Zuber, J., & Nuerk, H.-C. (2009). Decomposed but parallel processing of two-digit numbers in 1st graders. The Open Psychology Journal, 2, 40–48. https://doi.org/10.2174/1874350100902010040
Ramani, G. B., Siegler, R. S., & Hitti, A. (2012). Taking it to the classroom: Number board games as a small group learning activity. Journal of Educational Psychology, 104(3), 661–672. https://doi.org/10.1037/a0028995
Raz, A., & Buhle, J. (2006). Typologies of attentional networks. Nature Reviews Neuroscience, 7(5), 367–379. https://doi.org/10.1038/nrn1903
Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2, Pt. 1), 274–278. https://doi.org/10.1037/h0028573
Rodic, M., Zhou, X., Tikhomirova, T., Wei, W., Malykh, S., Ismatulina, V., … Kovas, Y. (2015). Cross-cultural investigation into cognitive underpinnings of individual differences in early arithmetic. Developmental Science, 18(1), 165–174. https://doi.org/10.1111/desc.12204
Rubinsten, O., & Sury, D. (2011). Processing ordinality and quantity: The case of developmental dyscalculia. PLoS One, 6(9), e24079. https://doi.org/10.1371/journal.pone.0024079
Sasanguie, D., & Reynvoet, B. (2014). Adults’ arithmetic builds on fast and automatic processing of Arabic digits: Evidence from an audiovisual matching paradigm. PLoS One, 9(2), e87739. https://doi.org/10.1371/journal.pone.0087739
Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(30), e12372. https://doi.org/10.1111/desc.12372
Schneider, M., Grabner, R. H., Zurich, E., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359–372. https://doi.org/10.1037/a0013840
Schroeder, P. A., Nuerk, H.-C., & Plewnia, C. (2017a). Space in numerical and ordinal information: A common construct? Journal of Numerical Cognition, 3(2), 164–181. https://doi.org/10.5964/jnc.v3i2.40
Schroeder, P. A., Nuerk, H.-C., & Plewnia, C. (2017b). Switching between Multiple Codes of SNARC-Like Associations: Two Conceptual Replication Attempts with Anodal tDCS in Sham-Controlled Cross-Over Design. Frontiers in Neuroscience, 11, 654. https://doi.org/10.3389/fnins.2017.00654
Schroeder, P. A., & Pfister, R. (2015). Arbitrary numbers counter fair decisions: Trails of markedness in card distribution. Frontiers in Psychology, 6, 240. https://doi.org/10.3389/fpsyg.2015.00240
Sella, F., Tressoldi, P., Lucangeli, D., & Zorzi, M. (2016). Training numerical skills with the adaptive videogame “The Number Race”: A randomized controlled trial on preschoolers. Trends in Neuroscience and Education, 5(1), 20–29. https://doi.org/10.1016/j.tine.2016.02.002
Shaki, S., & Fischer, M. H. (2014). Random walks on the mental number line. Experimental Brain Research, 232(1), 43–49. https://doi.org/10.1007/s00221-013-3718-7
Shaki, S., Fischer, M. H., & Göbel, S. M. (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. https://doi.org/10.1016/j.jecp.2011.12.005
Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review, 16(2), 328–331. https://doi.org/10.3758/PBR.16.2.328
Shaki, S., & Gevers, W. (2011). Cultural characteristics dissociate magnitude and ordinal information processing. Journal of Cross-Cultural Psychology, 42(4), 639–650. https://doi.org/10.1177/0022022111406100
Siegler, R. S. (2009). Improving the numerical understanding of children from low-income families. Child Development Perspectives, 3(2), 118–124. https://doi.org/10.1111/j.1750-8606.2009.00090.x
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444. https://doi.org/10.1111/j.1467-8624.2004.00684.x
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–243. https://doi.org/10.1111/1467-9280.02438
Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—But not circular ones—Improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545–560. https://doi.org/10.1037/a0014239
Siegler, R. S., Thompson, C. A., & Opfer, J. E. (2009). The logarithmic-to-linear shift: One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3(3), 143–150. https://doi.org/10.1111/j.1751-228X.2009.01064.x
Simner, J., Mayo, N., & Spiller, M. J. (2009). A foundation for savantism? Visuo-spatial synaesthetes present with cognitive benefits. Cortex, 45(10), 1246–1260. https://doi.org/10.1016/j.cortex.2009.07.007
Stavy, R., & Tirosh, D. (2000). How students (mis-) understand science and mathematics: Intuitive rules. New York: Teachers College Press.
Szűcs, D., Nobes, A., Devine, A., Gabriel, F. C., & Gebuis, T. (2013). Visual stimulus parameters seriously compromise the measurement of approximate number system acuity and comparative effects between adults and children. Frontiers in Psychology, 4, 444. https://doi.org/10.3389/fpsyg.2013.00444
Tudusciuc, O., & Nieder, A. (2007). Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. PNAS, 104(36), 14513–14518. https://doi.org/10.1073/pnas.0705495104
van Dijck, J.-P., & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119(1), 114–119. https://doi.org/10.1016/j.cognition.2010.12.013
Verbruggen, F., Liefooghe, B., Notebaert, W., & Vandierendonck, A. (2005). Effects of stimulus-stimulus compatibility and stimulus-response compatibility on response inhibition. Acta Psychologica, 120(3), 307–326. https://doi.org/10.1016/j.actpsy.2005.05.003
Wasner, M., Moeller, K., Fischer, M. H., & Nuerk, H.-C. (2014). Aspects of situated cognition in embodied numerosity: The case of finger counting. Cognitive Processing, 15(3), 317–328. https://doi.org/10.1007/s10339-014-0599-z
Wiemers, M., Bekkering, H., & Lindemann, O. (2014). Spatial interferences in mental arithmetic: Evidence from the motion-arithmetic compatibility effect. Quarterly Journal of Experimental Psychology, 67(8), 1557–1570. https://doi.org/10.1080/17470218.2014.889180
Wiemers, M., Bekkering, H., & Lindemann, O. (2017). Is more always up? Evidence for a preference of hand-based associations over vertical number mappings. Journal of Cognitive Psychology, 29(5), 642–652. https://doi.org/10.1080/20445911.2017.1302451
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 19. https://doi.org/10.1186/1744-9081-2-19
Wood, G., Willmes, K., Nuerk, H.-C., & Fischer, R. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489–525.
Zohar-Shai, B., Tzelgov, J., Karni, A., & Rubinsten, O. (2017). It does exist! A left-to-right spatial–numerical association of response codes (SNARC) effect among native Hebrew speakers. Journal of Experimental Psychology: Human Perception and Performance, 43(4), 719–728. https://doi.org/10.1037/xhp0000336
Zuber, J., Pixner, S., Moeller, K., & Nuerk, H.-C. (2009). On the language specificity of basic number processing: Transcoding in a language with inversion and its relation to working memory capacity. Journal of Experimental Child Psychology, 102(1), 60–77. https://doi.org/10.1016/j.jecp.2008.04.003
Acknowledgments
KC and MS are supported by a DFG grant [NU 265/3-1] to HCN. KC, MS, and HCN are further supported by the LEAD Graduate School & Research Network [GSC1028], which is funded within the framework of the Excellence Initiative of the German federal and state governments. We thank Julianne Skinner for proofreading the manuscript.
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Cipora, K., Schroeder, P.A., Soltanlou, M., Nuerk, HC. (2018). More Space, Better Mathematics: Is Space a Powerful Tool or a Cornerstone for Understanding Arithmetic?. In: Mix, K., Battista, M. (eds) Visualizing Mathematics. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-98767-5_4
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