Abstract
Battista et al. rightly point out the importance of the relation between spatial and geometric reasoning. They are also working towards more fine-grained analyses considering different aspects of both spatial and mathematical reasoning, and postulate that analyses should examine particular skills, rather than these very general constructs. The authors support their claim with the results of a series of well-designed and carefully conducted studies, using one-on-one interviews, one-on-one teaching experiments, and case studies. They conclude that the ability to visualize objects and build accurate mental models thereof is linked to property-based spatial reasoning.
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Arsalidou, M., & Taylor, M. J. (2011). Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage, 54(3), 2382–2393. https://doi.org/10.1016/j.neuroimage.2010.10.009
Bachot, J., Gevers, W., Fias, W., & Roeyers, H. (2005). Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology, 47(1), 172–183. Retrieved from http://www.pabst-publishers.de/psychology-science/1-2005/ps_1_2005_172-183.pdf
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
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
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
Crollen, V., Vanderclausen, C., Allaire, F., Pollaris, A., & Noël, M.-P. (2015). Spatial and numerical processing in children with non-verbal learning disabilities. Research in Developmental Disabilities, 47, 61–72. https://doi.org/10.1016/J.RIDD.2015.08.013
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and nummber magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.
Fischer, M. H., & Rottmann, J. (2005). Do negative numbers have a place on the mental number line? Psychology Science, 47(1), 22–32.
Fumarola, A., Prpic, V., Fornasier, D., Sartoretto, F., Agostini, T., & Umiltà, C. (2016). The spatial representation of angles. Perception, 45(11), 1320–1330. https://doi.org/10.1177/0301006616661915
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.
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., Maier, C. A., & Shaki, S. (2015). Which numbers do you have in mind? Number generation is influenced by reading direction. Cognitive Processing, 16(S1), 241–244. https://doi.org/10.1007/s10339-015-0715-8
Grabner, R. H., 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(2), 604–608. https://doi.org/10.1016/J.NEUROPSYCHOLOGIA.2008.10.013
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
Huber, S., Fischer, U., Moeller, K., & Nuerk, H.-C. (2013). On the interrelation of multiplication and division in secondary school children. Frontiers in Psychology, 4, 740. https://doi.org/10.3389/fpsyg.2013.00740
Lourenco, S. F., Bonny, J. W., Fernandez, E. P., & Rao, S. (2012). Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic mathematics competence. Proceedings of the National Academy of Sciences of the United States of America, 109(46), 18737–18742. https://doi.org/10.1073/pnas.1207212109
Maloney, E. A., & Beilock, S. L. (2012). Math anxiety: Who has it, why it develops, and how to guard against it. Trends in Cognitive Sciences, 16(8), 404–406. https://doi.org/10.1016/j.tics.2012.06.008
Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C., Hambrick, D. Z., 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
Prado, J., Mutreja, R., & Booth, J. R. (2014). Developmental dissociation in the neural responses to simple multiplication and subtraction problems. Developmental Science, 17(4), 537–552. https://doi.org/10.1111/desc.12140
Prado, J., Mutreja, R., Zhang, H., Mehta, R., Desroches, A. S., Minas, J. E., & Booth, J. R. (2011). Distinct representations of subtraction and multiplication in the neural systems for numerosity and language. Human Brain Mapping, 32(11), 1932–1947. https://doi.org/10.1002/hbm.21159
Schneider, M., Grabner, R. H., & 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
Sella, F., Sader, E., Lolliot, S., & Cohen Kadosh, R. (2016). Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills. Journal of Experimental Psychology: Learning Memory and Cognition, 42(9), 1458–1472. https://doi.org/10.1037/xlm0000249
Viarouge, A., Hubbard, E. M., & McCandliss, B. D. (2014). The cognitive mechanisms of the SNARC effect: An individual differences approach. PLoS One, 9(4), e95756. https://doi.org/10.1371/journal.pone.0095756
Wittgenstein, L. (1953). Philisophical Investigations. New York: Macmillan.
Acknowledgments
KC is supported by a DFG grant [NU 265/3-1] to HCN. KC 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., Nuerk, HC. (2018). On the Multitude of Mathematics Skills: Spatial-Numerical Associations and Geometry Skill?. In: Mix, K., Battista, M. (eds) Visualizing Mathematics. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-98767-5_18
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