Advertisement

On the Multitude of Mathematics Skills: Spatial-Numerical Associations and Geometry Skill?

  • Krzysztof Cipora
  • Philipp A. Schroeder
  • Hans-Christoph Nuerk
Chapter
Part of the Research in Mathematics Education book series (RME)

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.

Keywords

Spatial-Numerical Associations (SNA) Extension Spatial-Numerical Associations Directional Spatial-Numerical Associations SNARC effect Arithmetic skills Cognitive skills SNA Taxonomy Multi-digit number processing Compatibility effect Grounded cognition Embodied cognition Situated cognition Embodied math trainings Number Line Estimation (NLE) Cardinality Ordinality Place identification Place-value activation Place-value computation Place-value integration 

Notes

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.

References

  1. 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.2010.10.009CrossRefGoogle Scholar
  2. 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.pdfGoogle Scholar
  3. 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/10.1037/0096-1523.33.6.1410CrossRefGoogle Scholar
  4. 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/a0028387CrossRefGoogle Scholar
  5. 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/s00426-015-0677-6CrossRefGoogle Scholar
  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/10.1080/17470218.2013.772215CrossRefGoogle Scholar
  7. 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.2014.12.006CrossRefGoogle Scholar
  8. 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.2015.08.013CrossRefGoogle Scholar
  9. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and nummber magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.CrossRefGoogle Scholar
  10. Fischer, M. H., & Rottmann, J. (2005). Do negative numbers have a place on the mental number line? Psychology Science, 47(1), 22–32.Google Scholar
  11. 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/10.1177/0301006616661915CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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.2017.04.011CrossRefGoogle Scholar
  14. 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.2016.05.009CrossRefGoogle Scholar
  15. 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/s10339-015-0715-8CrossRefGoogle Scholar
  16. 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.2008.10.013CrossRefGoogle Scholar
  17. 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.2013.07.013CrossRefGoogle Scholar
  18. 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.0085048CrossRefGoogle Scholar
  19. 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.2013.00740CrossRefGoogle Scholar
  20. 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.1207212109CrossRefGoogle Scholar
  21. 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.2012.06.008CrossRefGoogle Scholar
  22. 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/xge0000182CrossRefGoogle Scholar
  23. 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.12140CrossRefGoogle Scholar
  24. 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.21159CrossRefGoogle Scholar
  25. 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/a0013840CrossRefGoogle Scholar
  26. 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/xlm0000249CrossRefGoogle Scholar
  27. 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.0095756CrossRefGoogle Scholar
  28. Wittgenstein, L. (1953). Philisophical Investigations. New York: Macmillan.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Krzysztof Cipora
    • 1
    • 2
  • Philipp A. Schroeder
    • 1
    • 3
  • Hans-Christoph Nuerk
    • 1
    • 2
    • 4
  1. 1.Department of PsychologyUniversity of TuebingenTuebingenGermany
  2. 2.LEAD Graduate School and Research NetworkUniversity of TuebingenTuebingenGermany
  3. 3.Department of Psychiatry and PsychotherapyUniversity of TuebingenTuebingenGermany
  4. 4.Leibnitz-Institut für WissensmedienTuebingenGermany

Personalised recommendations