The difficulties in geometry: A quantitative analysis based on results of mathematics competitions in Italy

Lorenzo Facciaroni 1, Alessandro Gambini 1 * , Lorenzo Mazza 1
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1 Sapienza Università di Roma, Roma, ITALY
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 2, pp. 259-270.
Published Online: 01 November 2022, Published: 01 April 2023
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This paper focuses on the difficulties encountered by Italian students in performing geometry tasks. A quantitative analysis, aimed at understanding the extent of the phenomenon, is carried out using the results of district competitions from the year 2018 to 2020, comparing the scores obtained in geometry questions with those in other areas of Olympic mathematics. In addition, the answers given by the students to a questionnaire administered at the end of the 2020 district competition are analyzed in order to better understand possible motivations behind the phenomenon in question. The results obtained need further confirmation through future research on the topic but represent clear trends worthy of further investigation.


Facciaroni, L., Gambini, A., & Mazza, L. (2023). The difficulties in geometry: A quantitative analysis based on results of mathematics competitions in Italy. European Journal of Science and Mathematics Education, 11(2), 259-270.


  • Anderson, J. R. (1983). Acquisition of proof skills in geometry. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning (pp. 191-219). Springer.
  • Arrigo, G., & Sbaragli, S. (2004). I solidi. Riscopriamo la geometria [The solids. Let’s rediscover geometry]. Carocci Faber.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 420-464). Macmillan Publishing Co, Inc.
  • Cottino L., Sbaragli S. (2004). Le diverse “facce” del cubo [The different “faces” of the cube]. Carocci Faber.
  • Craig, A. J. (2010). Comparing research into mental calculation strategies in mathematics education and psychology. Research in Mathematics Education, 12(1), 73-74.
  • Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. In M. M. Lindquist (Ed.), Learning and teaching geometry, K-12 (pp. 1-16). National Council of Teachers of Mathematics.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
  • Fuys, D. J., Geddes, D., & Tischler, R. W. (1984). English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele. Brooklyn College, C.U.N.Y.
  • Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, 74(2), 163-183.
  • Herbst, P., & Brach, C. (2006). Proving and doing proofs in high school geometry classes: What is it that is going on for students? Cognition and Instruction, 24(1), 73-122.
  • Hill, R. B., & Wicklein, R. C. (1999). A factor analysis of primary mental processes for technological problem solving. Journal of Industrial Teacher Education, 36(2), 83-100.
  • Jordan, N., Hanich, L. B., & Uberti, H. Z. (2013). Mathematical thinking and learning difficulties. In A. J. Baroody, & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructive adaptive expertise (pp. 383-406). Routledge.
  • Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. The University of Chicago Press.
  • Kuzniak, A., & 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.
  • Mainali, B. (2019). Investigating the relationships between preferences, gender, task difficulty, and high school students’ geometry performance. International Journal of Research in Education and Science, 5(1), 224-236.
  • Marushina, A. (2021). Mathematics competitions: What has changed in recent decades. ZDM-Mathematics Education, 53(7), 1591-1603.
  • Mason, M. (2009). The van Hiele levels of geometric understanding. Colección Digital Eudoxus [Eudoxus Digital Collection], 1, 2.
  • Mason, M. M., & Moore, S. D. (1997). Assessing readiness for geometry in mathematically talented middle school students. Journal of Secondary Gifted Education, 8(3), 105-110.
  • Mazza, L., & Gambini, A. (2022). The phenomenon of the gender gap among gifted students: the situation in Italy based on analysis of results in mathematics competitions. Teaching Mathematics and its Applications: An International Journal of the IMA.
  • Mazzocco, M. M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In D. B. Berch, & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29-47). Paul H. Brookes Publishing Co.
  • Mutlu, Y. (2019). Math anxiety in students with and without math learning difficulties. International Electronic Journal of Elementary Education, 11(5), 471-475.
  • Nieto-Said, J. H., & Sánchez-Lamoneda, R. (2022). A curriculum for mathematical competitions. ZDM-Mathematics Education, 54, 1043-1057.
  • Sbaragli, S., & Mammarella, I. C. (2010). L’apprendimento della geometria [The learning of geometry]. In D. Lucangeli, & I. C. Mammarella (Eds.), Psicologia della cognizione numerica. Approcci teorici, valutazione e intervento [Psychology of numerical cognition. Theoretical approaches, evaluation, and intervention]. Franco Angeli.
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36.
  • Soifer, A. (Ed.). (2017). Competitions for young mathematicians: Perspectives from five continents. Springer.
  • Sulistiowati, D. L., Herman, T., & Jupri, A. (2019). Student difficulties in solving geometry problem based on van Hiele thinking level. Journal of Physics: Conference Series, 1157(4), 042118.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. CDASSG project.
  • Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.