Оливера Ђокић, Маријана Зељић

DOI Number
First page
Last page


This research is a pedagogical study of theoretical frameworks of development of students’ geometrical thinking in various forms, particularly students’ geometric reasoning in teaching geometry: 1) model of van Hieles’ levels of understanding of geometry, 2) theory of figural concepts of Fischbein and 3) paradigms of Houdement-Kuzniak development of geometrical thinking. The aim of our research was to analyze the three theoretical framework and explain the reasons for their choice and expose them in terms of finding opportunities to permeate and connect them into one complete theory. The study used a descriptive-analytical and analytical-critical method of theoretical analysis. The results show that from each of the three theoretical frameworks we can clearly notice and distinguish geometric objects, as the students do not see them. They see them blended and structured in a series of procedures, and for that very reason we can say that they are poorly linked. We also opened questions for further research of geometric object as an important element for content domain geometry within mathematics curriculum.


geometry, model of van Hiele, theory of Fischbein, paradigms of Houdement˗Kuzniak, geometric object.


Антонијевић, Р. (2014). Развој математичког мишљења код ученика као аспект процеса интелектуалног васпитања [The development of mathematical thinking of students as an aspect of the process of intellectual education]. Настава и васпитање, 63(2), 215–227.

Braconne-Michoux, A. (2013). Which Geometrical Working Spaces for the Primary School Preservice Teachers? In: Ubuz, B., Haser, Ç. & Mariotti, M. A. (еds.): Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (605–614). Ankara: Middle East Technical University.

BSRLM (Ed.) (1998). Geometry Working Group: Theoretical Frameworks for the Learning of Geometrical Reasoning. In: From Informal Proceedings (18-1&2, p. 29–34). King's College London and University of Birmingham.

Clements, D.H. & Battista, M.T. (1992). Geometry and Spatial Reasoning. In D. A. Grouws (Eds.), Handbook of Research on Mathematics Teaching and Learning (p. 420–464). New York: Macmillan Publishing Copmany.

Dreyfus, T. (1990). Advanced Mathematical Thinking. In P. Nesher and J. Kilpatrick (Eds.), Mathematics and Cognition. A Research Synthesis by the International Group for the Psychology of Mathematics Education (ICMI Studies, p. 113–134). Cambridge University Press. DOI: 10.1017/CBO9781139013499.008

Ђокић, О. (2014). Ван Хилов модел [The model of Van Hiele]. У Лексикон образовних термина [Lexicon of educational terms] (стр. 76). Београд: Учитељски факултет.

Ђокић, О. (2013). Реално окружење у почетној настави геометрије [Realistic Mathematics in Teaching and Learning Elementary Geometry] (Doctoral dissertation). Retrieved from


Fischbein, E. (1993). The Theory of Figural Concepts. Educational Studies in Mathematics, 24(2), 139-162. DOI: 10.1007/BF01273689

Gutiérrez, A. (2014). Geometry. In P. Andrews and T. Rowland (Eds.), MasterClass in Mathematics Education ̶ International Perspectives on Teaching and Learning (p. 151–164). London: Bloomsbury.

Gutiérrez, A., Kuzniak, A. & Straesser, R. (2006). Research on geometrical thinking. In: Bosch, M. (Ed.), Proceedings of the 4th Congress of the European Society for Research in Mathematics Education (725–726). FUNDEMI IQS: Universitat Ramon Llull.

Hershkowitz, R. (1998). About reasoning in geometry. In C. Mammana and V. Villani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century (p. 29–37). Springer Netherlands, Kluwer Academic Publishers. DOI: 10.1007/978-94-011-5226-6

Hershkowitz, R. (1990). Psychological Aspects of Learning Geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education (ICMI Studies, p. 70–95). Cambridge: Cambridge University Press. DOI: 10.1017/CBO9781139013499.006

Houdement, C. and Kuzniak, A. (2003). Elementary geometry split into different geometrical paradigms. In: Mariotti, M. A. (Ed.): Proceedings of CERME 3 (1–9). Department of Mathematics of the University of Pisa.

Јелић, М. и Ђокић, О. (2017). Ка кохерентној структури уџбеника математике ̶ анализа уџбеника према структурним блоковима ТИМСС истраживања [Towards a coherent structure of mathematics textbook ̶ textbook analysis through structural blocks of TIMSS methodology]. Иновације у настави, 30(1), 67–81. DOI: 10.5937/inovacije1701067J

Kadijevich, Dj. M., Žakelj, A. & Gutvajn, N. (2015). Explaining Differences for Serbia and Slovenia in Mathematics Achivement in Fourth Grade. Настава и васпитање, 64(1), 21–37. DOI: 10.5937/nasvas1501021K

Kuzniak A. (2014). Understanding Geometric Work through Its Development and Its Transformations. In S. Rezat et al. (eds.), Transformation ̶ A Fundamental Idea of Mathematics Education (p. 311–325). Springer Science+Business Media. DOI: 10.1007/978-1-4614-3489-4_15

Марјановић, М. М. и Зељић, М. (2006). Кроз геометрију до реалних бројева [Through geometry to real numbers]. Настава математике, 51(1-2), 2–11.

Panaoura, G. & Gagatsis, A. (2010). The Geometrical Reasoning of Primary and Secondary School Students. In: Durand-Guerrier, V., Soury-Lavergne, S. & Arzarello, F. (еds.): Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (746–755). Institut National De Recherche Pédagogique.

Романо, Д. А. (2009). О геометријском мишљењу [About geometry thinking]. Настава математике, 54(2-3), 1–11.

Van Hiele, P. (1986). Structure and Insight: A Theory of Mathematics Education. London: Academic Press.



  • There are currently no refbacks.

Print ISSN: 0353-7919
Online ISSN: 1820-7804