Five Years of Comparison Between Euclidian Plane Geometry and Spherical Geometry in Primary Schools: An Experimental Study

Alessandro Gambini 1 *
More Detail
1 Sapienza Università di Roma, ITALY
* Corresponding Author
EUR J SCI MATH ED, Volume 9, Issue 4, pp. 230-243. https://doi.org/10.30935/scimath/11250
OPEN ACCESS   1307 Views   1026 Downloads
Download Full Text (PDF)

ABSTRACT

We present the result of an eight-year didactic experiment in two primary school classes involving comparative geometry activities: a comparison between Euclidean plane geometry and spherical geometry that took place over five years. Following the didactic experiment, three years on from the end of the experiment, final questionnaires were administered and codified in order to evaluate the project’s effect on the pupils’ school performance and attitude, especially with regard to mathematics.
Keywords: comparative geometry, Lénárt spheres

CITATION

Gambini, A. (2021). Five Years of Comparison Between Euclidian Plane Geometry and Spherical Geometry in Primary Schools: An Experimental Study. European Journal of Science and Mathematics Education, 9(4), 230-243. https://doi.org/10.30935/scimath/11250

REFERENCES

  • Antonini, S., & Maracci, M. (2013). Straight on the sphere: meanings and artefacts. In A.M. Lindmeier & A. Heinze, Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 33-40). PME.
  • Baldazzi, L., Gambini, A., & Tusa, R. (2013). Un percorso di geometria comparativa tra sfera e piano con bambini di Scuola Primaria: una didattica efficace con la Sfera di Lénárt [A path of comparative geometry between sphere and plane with Primary School children: effective teaching with Lénárt’s Sphere]. In B. D’Amore & Sbaragli (Eds.), Atti del convegno nazionale: Incontri con la matematica n.33. Castel San Pietro Terme (Bo). Pitagora.
  • Baldazzi, L., Gambini, A., & Tusa, R. (2013). Un percorso di geometria comparativa tra sfera e piano con bambini di prima e seconda primaria: da Parmenide alle esplorazioni nel mondo della geometria sferica [A path of comparative geometry between sphere and plane with first and second grade children: from Parmenides to explorations in the world of spherical geometry]. In B. D’Amore & Sbaragli (Eds) (2013). La didattica della matematica come chiave di lettura delle situazioni d’aula. Atti del convegno nazionale: Incontri con la matematica n.27. Castel San Pietro Terme (Bo). Pitagora.
  • Bolondi, G., Ferretti, F., & Gambini, A. (2014). The relation between mathematical object/mathematical name: conceptual changes among designation, description, denotation, denomination and definition. EMU University Press. https://doi.org/10.30935/scimath/9640
  • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. and Trans.).
  • D’Amore, B. (1999). Elementi di didattica della matematica [Elements of mathematics teaching]. Pitagora Editrice Bologna.
  • Di Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13(1), 27-48. https://doi.org/10.1007/s10857-009-9134-z
  • diSessa, A. A. (2006). A history of conceptual change research: Threads and fault lines. In K. Sawye (Ed.), Cambridge handbook of the learning sciences (pp. 265-281). Cambridge University Press. https://doi.org/10.1017/CBO9780511816833.017
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processes. In R. Sutherland, & J. Mason (Eds.), Exploiting mental imagery with computers in mathematical education (pp. 142-157). Springer. https://doi.org/10.1007/978-3-642-57771-0_10
  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning, Retrieved from ERIC ED 466 379.
  • Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3-4), 455-479. https://doi.org/10.1080/02643290442000310
  • Gambini, A., & Lénárt, I. (2021). Basic geometric concepts in the thinking of in-service and pre-service mathematics teachers. Education Sciences, 11(7), 350. https://doi.org/10.3390/educsci11070350
  • Jones, K. (2011). The value of learning geometry with ICT: Lessons from innovative educational research. In A. Oldknow, & C. Knights (Eds.), Mathematics education with digital technology (pp. 39-45). Continuum.
  • Kotarinou, P., & Stathopoulou, C. (2017). ICT and liminal performative space for hyperbolic geometry’s teaching. In Mathematics and technology (pp. 75-98). Springer, Cham. https://doi.org/10.1007/978-3-319-51380-5_5
  • Laborde, C., Kynigos, C., Hollebrands, K., & Strässer, R. (2006). Teaching and learning geometry with technology. In A. Guitiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275-304). Sense. https://doi.org/10.1163/9789087901127_011
  • Lénárt, I. (1993). Alternative models on the drawing ball. Educational Studies in Mathematics, 24(3), 277-312. https://doi.org/10.1007/BF01275428
  • Lénárt, I. (1996). From geometry to geometries: an aspect of changing the geometry curriculum. ICME.
  • Lénárt, I. (2007). Comparative geometry in general education. In J. Szendrei (Ed.), Proceedings of CIEAEM 59 (pp. 250-256), Dobogokö, Hungary.
  • Ministero dell’Università e della Ricerca - MIUR (2012). Indicazioni nazionali per il curricolo della scuola dell’infanzia e del primo ciclo d’istruzione [National guidelines for the nursery school curriculum and the first cycle of education].
  • Oldknow, A. (2008). ICT bringing mathematics to life and life to mathematics. In W.-C. Yang, M. Majewski, T. de Alwis, & K. Khairiree (Eds.), Electronic proceedings of the 13th Asian Technology Conference in Mathematics (n.p.). Suan Sunandha Rajabhat University.
  • Sbaragli, S. (2005). Misconcezioni inevitabili e misconcezioni evitabili [Unavoidable misconceptions and avoidable misconceptions]. La matematica e la sua didattica, 1, 57-71.
  • Speranza, F. (1988). Salviamo la geometria! [Let’s save the geometry!]. La matematica e la sua didattica, 3, pp.6-14.
  • Stipek, D., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (1998). Can a teacher intervention improve classroom practices and student motivation in mathematics? The Journal of Experimental Education, 66(4), 319-337. https://doi.org/10.1080/00220979809601404
  • Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. Harvard University Press.
  • Yıldırım, A., & Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (5th Ed.). Seçkin Publishing. Social Sciences Series.