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Logo Revista Latinoamericana de Investigación en Matemática Educativa

Special Article

Vol. 17 No. 4(I) (2014): Diciembre

A KINDERGARTNER’S USE OF GESTURES WHEN SOLVING A GEOMETRICAL PROBLEM IN DIFFERENT SPACES OF CONSTRUCTED REPRESENTATION

DOI
https://doi.org/10.12802/relime.13.17410
Submitted
July 6, 2023
Published
2014-12-30

Abstract

This study investigates a kindergartner’s gestures, from a cognitive point of view, in a geometrical activity of communicative character. The activity involves a shape configuration problem in two different types of space of constructed representation (SCR), namely, on the computer and on paper. In this, we follow the cognitive analysis of geometrical thinking by Duval (1998) with a focus on the perceptual and the operative apprehension of geometrical figures. During the activity, the child had to give instructions to an experimenter, so that the latter could compose the given figure on the computer screen using a specific mathematical applet, and on paper, respectively. The child was found to produce iconic and deictic gestures to a different extent in each SCR. Each type of gestures had a different cognitive function in solving the task. These findings provide insight into the personal geometric work space of a young child in carrying out a shape configuration task.

References

  1. Battista, M.T. (1999). The importance of spatial structuring in geometric reasoning. Teaching Children Mathematics, 6 (3), 170–177.
  2. Brousseau, G. (1983): Etude de questions d’enseignement, un exemple: la géométrie. Séminaire de didactique des mathématiques et de l’informatique, (pp. 183–226). Grenoble: IMAG.
  3. Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.
  4. Duval, R. (1995). Geometrical Pictures: Kinds of representation and specific processes. In R. Sutherland and J. Mason (Eds.), Exploiting mental imagery with computers in mathematical education (pp. 142–157). Berlin: Springer.
  5. Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana and V. Villani (eds.), Perspectives on the Teaching of Geometry for the 21st century (pp. 37–51). Dordrecht: Kluwer Academic.
  6. Ericsson, K. A., and Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87 (3), 215–251.
  7. Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory - motor system in reason and language. Cognitive Neuropsychology, 22, 455–479.
  8. Kim, M., Roth, W. M., and Thom, J. (2011). Children’s gestures and the embodied knowledge of geometry. International Journal of Science and Mathematics Education, 9, 207–238.
  9. Kita, S. (2000). How representational gestures help speaking. In D. McNeill (Ed.), Language and gesture (pp. 162–185). Cambridge, UK: Cambridge University Press.
  10. Kuzniak, A. (2009). Un essai sur la nature du travail géométrique en fin de la scolarité obligatoire en France. In A. Gagatsis, A. Kuzniak, E.Deliyianni, and L.Vivier (Eds), Cyprus and France Research in Mathematics Education (pp. 71–90). Lefkosia: University of Cyprus.
  11. Kuzniak, A. (2012). Understanding the Nature of the Geometric Work Through its Development and its Transformations. Proceedings of the 12th International Congress on Mathematical Education. Seoul, Korea. Retrieved on November 4, 2012 from http://www.icme12.org/upload/submission/1922_F.pdf
  12. Kuzniak, A. and Rauscher, J. C. (2011). How do teachers’ approaches to geometric work relate to geometry students’ learning difficulties? Educational Studies in Mathematics, 77 (1), 129–147.
  13. Lavelli, M., Pantoja, A. P. F., Hsu, H., Messinger, D., & Fogel, A. (2005). Using microgenetic designs to study change processes. In D. M. Teti (Ed.), Handbook of research methods in developmental science (pp. 40–65). Malden, MA: Blackwell Publishing.
  14. Levenson, E., Tirosh, D., & Tsamir, P. (2011). Preschool geometry: Theory, research and practical perspectives. Rotterdam: Sense Publishers.
  15. McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: The University of Chicago Press.
  16. Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70, 159–174.
  17. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic - cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5 (1), 37-70.
  18. Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70, 111-126.
  19. Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: a semiotic - cultural perspective on mathematical thinking. In Chick, H. L. & Vincent, J. L. (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 113-120. Melbourne: PME.
  20. Siegler, R. S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 25, 225–73.

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