Educational Studies in Mathematics

, Volume 94, Issue 1, pp 85–95 | Cite as

A study regarding the spontaneous use of geometric shapes in young children’s drawings

  • José Domingo Villarroel
  • Olga Sanz Ortega


The studies regarding how the comprehension of geometric shapes evolves in childhood are largely based on the assessment of children's responses during the course of tasks linked to the recognition, classification or explanation of prototypes and models. Little attention has been granted to the issue as to what extent the geometric shape turns out to be an expressive tool that young children spontaneously use in their pictorial productions and also, whether or not methodological research approaches aimed at the examination of unprompted usage of geometric shapes in childhood may be useful regarding the study of the development of geometric thinking. This evidence provided by this study is coherent with the assumption that before starting primary education, internal representation of closed curves, quadrilaterals and triangles should have been developed by a significant number of children and, more interestingly, that young children’s graphical expressivity appears liaised to their skill to depict two-dimensional geometric shapes.


Geometric thinking Expressivity Drawings Early education Geometric shape 


  1. Bach, S. (1990). Life paints its own span: On the significance of spontaneous paintings by severely ill children. Zurich: Daimon.Google Scholar
  2. Bonoti, F., Tzouvaleka, E., Bonotis, K., & Vlachos, F. (2015). Do patients with alzheimer's disease draw like young children? An exploratory study. Journal of Alzheimer’s Disease: JAD, 43(4), 1285–1292. doi: 10.3233/JAD-140528 Google Scholar
  3. Chancellor, B., Duncan, A., & Chatterjee, A. (2014). Art therapy for alzheimer’s disease and other dementias. Journal of Alzheimer’s Disease, 39(1), 1–11.Google Scholar
  4. Cherney, I. D., Seiwert, C. S., Dickey, T. M., & Flichtbeil, J. D. (2006). Children’s drawings: A mirror to their minds. Educational Psychology, 26(1), 127–142. doi: 10.1080/01443410500344167 CrossRefGoogle Scholar
  5. Clements, D. H., & Sarama, J. (2009). Shape. In D. H. Clements & J. Sarama (Eds.), Learning and teaching early math: The learning trajectories approach (pp. 123–162). New York: Routledge.Google Scholar
  6. Dillon, M. R., Huang, Y., & Spelke, E. S. (2013). Core foundations of abstract geometry. Proceedings of the National Academy of Sciences of the United States of America, 110(35), 14191–14195. doi: 10.1073/pnas.1312640110 CrossRefGoogle Scholar
  7. Elkoshi, R. (2002). An investigation into children’s responses through drawing, to short musical fragments and complete compositions. Music Education Research, 4(2), 199–211.CrossRefGoogle Scholar
  8. Gallagher, M. (2004). A study of spontaneous drawings of young children; implications for the quality of the learning environment. Questions of Quality CECDE International Conference, Dublin., 9 102–111.Google Scholar
  9. Giofrè, D., Mammarella, I. C., Ronconi, L., & Cornoldi, C. (2013). Visuospatial working memory in intuitive geometry, and in academic achievement in geometry. Learning and Individual Differences, 23, 114–122. doi: 10.1016/j.lindif.2012.09.012.CrossRefGoogle Scholar
  10. Giofrè, D., Mammarella, I. C., & Cornoldi, C. (2014). The relationship among geometry, working memory, and intelligence in children. Journal of Experimental Child Psychology, 123, 112–128.CrossRefGoogle Scholar
  11. Goldner, L., & Levi, M. (2014). Children's family drawings, body perceptions, and eating attitudes: The moderating role of gender. The Arts in Psychotherapy, 41(1), 79–88. doi: 10.1016/j.aip.2013.11.004.CrossRefGoogle Scholar
  12. Hodgson, D. (2006). Understanding the origins of paleoart: The neurovisual resonance theory and brain functioning. Paleoanthropology, 2006, 54–67.Google Scholar
  13. Hodgson, D. (2014). Decoding the blombos engravings, shell beads and diepkloof ostrich eggshell patterns. Cambridge Archaeological Journal, 24(01), 57–69.CrossRefGoogle Scholar
  14. Jolley, R. P., Fenn, K., & Jones, L. (2004). The development of children’s expressive drawing. British Journal of Developmental Psychology, 22(4), 545–567. doi: 10.1348/0261510042378236 CrossRefGoogle Scholar
  15. Kellog, R. (1970). Analyzing children’s art. Mountain View: Mayfield.Google Scholar
  16. Kline, R. B. (2004). Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  17. Levenson, E., Tirosh, D., & Tsamir, P. (2011). Preschool geometry. Theory, research, and practical perspectives. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  18. Lev-Wiesel, R., & Liraz, R. (2007). Drawings vs. narratives: Drawing as a tool to encourage verbalization in children whose fathers are drug abusers. Clinical Child Psychology and Psychiatry, 12(1), 65–75.CrossRefGoogle Scholar
  19. Lorenzi, M. G., & Francaviglia, M. (2011). The role of mathematics in contemporary art at the turn of the millennium. APLIMAT-Journal of Applied Mathematics, 4, 1–4.Google Scholar
  20. Maier, S., & Benz, C. (2013). Selecting shapes–how to children identify familiar shapes in two different educational settings. Paper presented at the Proceedings of the Eighth Congress of European Research in Mathematics Education, 8, Antalya, Turkey. Retrieved from
  21. Malchiodi, C. A. (2012). Understanding children’s drawings Guilford Press.Google Scholar
  22. Morse, D. T. (1999). MINSIZE2: A computer program for determining effect size and minimum sample size for statistical significance for univariate, multivariate, and nonparametric tests. Educational and Psychological Measurement, 59(3), 518–531.CrossRefGoogle Scholar
  23. Pellier, A., Wells, J. A., Abram, N. K., Gaveau, D., & Meijaard, E. (2014). Through the eyes of children: Perceptions of environmental change in tropical forests. Plos One, 8, e103005.CrossRefGoogle Scholar
  24. Piaget, P., & Inhelder, B. (1948). La représentation de l’espace chez l’enfant [The child’s conception of space]. Paris: Presses Universitaires de France.Google Scholar
  25. Prajapati, B., Dunne, M., & Armstrong, R. (2010). Sample size estimation and statistical power analyses. Optometry Today, 16(07).Google Scholar
  26. Rübeling, H., Keller, H., Yovsi, R. D., Lenk, M., Schwarzer, S., & Kühne, N. (2011). Children’s drawings of the self as an expression of cultural conceptions of the self. Journal of Cross-Cultural Psychology, 42(3), 406–424.CrossRefGoogle Scholar
  27. Salmon, A. K., & Lucas, T. (2011). Exploring young children’s conceptions about thinking. Journal of Research in Childhood Education, 25(4), 364–375.CrossRefGoogle Scholar
  28. Siegel, S., & Castellan, N. J. (1988). Non parametric statistics for the behavioral sciences.Google Scholar
  29. Snaddon, J. L., Turner, E. C., & Foster, W. A. (2008). Children’s perceptions of rainforest biodiversity: Which animals have the lion’s share of environmental awareness? Plos One, 7, e2579.CrossRefGoogle Scholar
  30. Spelke, E., Lee, S. A., & Izard, V. (2010). Beyond core knowledge: Natural geometry. Cognitive Science, 34(5), 863–884. doi: 10.1111/j.1551-6709.2010.01110.x CrossRefGoogle Scholar
  31. Treiman, R., & Yin, L. (2011). Early differentiation between drawing and writing in Chinese children. Journal of experimental child psychology, 108(4), 786–801.CrossRefGoogle Scholar
  32. Turgeon, S. M. (2008). Sex differences in children’s free drawings and their relationship to 2D:4D ratio. Personality and Individual Differences, 45(6), 527–532. doi: 10.1016/j.paid.2008.06.006 CrossRefGoogle Scholar
  33. Vallortigara, G. (2012). Core knowledge of object, number, and geometry: A comparative and neural approach. Cognitive Neuropsychology, 29(1–2), 213–236. doi: 10.1080/02643294.2012.654772 CrossRefGoogle Scholar
  34. Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando: Academic Press.Google Scholar
  35. Verpooten, J., & Nelissen, M. (2010). Sensory exploitation and cultural transmission: The late emergence of iconic representations in human evolution. Theory in Biosciences, 129(2–3), 211–221.CrossRefGoogle Scholar
  36. Viera, A. J., & Garrett, J. M. (2005). Understanding interobserver agreement: The kappa statistic. Family Medicine, 37(5), 360–363.Google Scholar
  37. Villarroel, J. D. (2015). Young Children’s drawings of plant life: A study concerning the use of colours and its relationship with age. Journal of Biological Education, (ahead-of-print), 1–13.Google Scholar
  38. Villarroel, J. D., & Infante, G. (2014). Early understanding of the concept of living things: An examination of young children’s drawings of plant life. Journal of Biological Education, 48(3), 119–126.CrossRefGoogle Scholar
  39. Villarroel, J. D., & Ros, I. (2013). Young Children’s conceptions of rainfall: A study of their oral and pictorial explanations. International Education Studies, 6(8), p1.CrossRefGoogle Scholar
  40. Von Petzinger, G. (2009). Making the abstract concrete: The place of geometric signs in french upper palaeolithic parietal art (Unpublished doctoral dissertation). University of Victoria, Victoria BC, Canada. Retrieved from
  41. Wittmann, B. (2015). Jean Piaget and the child's spontaneous geometry. Max Planck institute for the history of science. Retrieved from
  42. Yang, M., Bo, Q. F., & Zhang, X. (2012). The application of geometric elements in modern product design. Applied Mechanics and Materials, 108, 86–90.CrossRefGoogle Scholar
  43. Yang, H., & Noel, A. M. (2006). The developmental characteristics of four-and five-year-old pre-schoolers’ drawing: An analysis of scribbles, placement patterns, emergent writing, and name writing in archived spontaneous drawing samples. Journal of Early Childhood Literacy, 6(2), 145–162.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.University of the Basque Country UPV/EHULeioaSpain

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