Pre-service Middle School Mathematics Teachers’ (Mis)conceptions of Definitions, Classifications, and Inclusion Relations of Quadrilaterals

Gamze Baktemur 1, Rukiye Ayan Civak 2 * , Mine Isiksal Bostan 3
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1 Ministry of National Education, TURKEY
2 Izmir Democracy University, TURKEY
3 Middle East Technical University, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 9, Issue 4, pp. 183-198.
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The purpose of this study is to examine pre-service middle school mathematics teachers’ (mis)conceptions related to definitions, classifications, and inclusion relations of convex quadrilaterals through a case study research design. The participants of the study were 20 pre-service middle school mathematics teachers who attended a must course, “The Methods of Teaching Mathematics” in a public university in Ankara, Turkey. Purposive sampling strategy was used to select the participants. The data were collected through an achievement test before and after taking the methods of teaching mathematics course. The findings of the study revealed that pre-service teachers had misconceptions in hierarchical classification of quadrilaterals, dual inclusion relations (e.g., rhombus-trapezoid), and difficulty in formulating minimal definitions of quadrilaterals before taking the course. However, the findings also indicated that the course had a positive impact for eliminating those misconceptions and supporting their conceptions. Several suggestions were made based on these findings.


Baktemur, G., Ayan Civak, R., & Isiksal Bostan, M. (2021). Pre-service Middle School Mathematics Teachers’ (Mis)conceptions of Definitions, Classifications, and Inclusion Relations of Quadrilaterals. European Journal of Science and Mathematics Education, 9(4), 183-198.


  • Akkaş, E. N., & Türnüklü, E. (2015). Middle school mathematics teachers’ pedagogical content knowledge regarding student knowledge about quadrilaterals. Elementary Education Online, 14(2), 744-756.
  • Aktaş, D. Y., & Cansız-Aktaş, M. (2012). Eighth grade students’ understanding and hierarchical classification of quadrilaterals. Elementary Education Online, 11(3), 714-728.
  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797-810.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59, 389-407.
  • Brunheira, L., & da Ponte, J. P. (2019). From the classification of quadrilaterals to the classification of prisms: An experiment with prospective teachers. The Journal of Mathematical Behavior, 53, 65-80.
  • Burton, M., Daane, C. J., & Giesen, J. (2008). Infusing Mathematics content into a methods course: impacting content knowledge for teaching.
  • Chapman, O. (2011). Elementary school teachers’ growth in inquiry-based teaching of mathematics. ZDM, 43, 951-963.
  • Clements, D. H. & Battista, M. T. (1992). Geometry and spatial reasoning. In D. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 420- 464). MacMillan.
  • De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11-18.
  • Erdoğan, E. O. & Dur, Z. (2014). Preservice mathematics teachers’ personal figural concepts and classifications of quadrilaterals. Australian Journal of Teacher Education, 39(6), 107-133.
  • Fraenkel, J. R., Wallen, N. E. & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). McGraw-Hill.
  • Fujita, T. & Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (PME 30), 3, 129-136.
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60-72.
  • Fujita, T., & Jones, K. (2007), Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing. Research in Mathematics Education, 9(1&2), 3-20.
  • Jarrett, D. (1997). Inquiry strategies for science and mathematics learning.
  • Jaworski, B. (2004). Grappling with complexity: Co-learning in inquiry communities in mathematics teaching development. Proceedings of the 28th conference of the international group for the psychology of mathematics education, Bergen University College, 17–36.
  • Jones, K., & Tzekaki, M. (2016). Research on the teaching and learning of geometry. In A. Gutiérrez, G. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 109-149). Sense Publishers.
  • Karakuş, F., & Erşen, Z. B. (2016). Examining pre-service primary school teachers’ definitions and classifications toward quadrilaterals. Karaelmas Journal of Educational Sciences, 4, 38-49.
  • Loc, N. P., Tong, D. H., & Hai, N. T. B. (2017). The investigation of primary school students’ ability to identify quadrilaterals: a case of rectangle and square. The International Journal of Engineering and Science (IJES), 6(3), 93-99.
  • Matthews, M. E., & Seaman, W. I. (2007). The effects of different undergraduate mathematics courses on the content knowledge and attitude towards mathematics of preservice elementary teachers.
  • Matthews, M., Rech, J., & Grandgenett, N. (2010). The impact of content courses on pre-service elementary teachers’ mathematical content knowledge. Teacher Education Faculty Publications.
  • Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1,2,3,4,5, 6, 7 ve 8. sınıflar) [Mathematics curriculum (for grades 1,2,3,4,5, 6, 7, and 8)]. MEB.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics.
  • Özkan, M., & Bal, A. P. (2017). Analysis of the misconceptions of 7th grade students on polygons and specific quadrilaterals. Eurasian Journal of Educational Research, 6, 161-182.
  • Öztoprakçı, S. (2014). Pre-service middle school mathematics teachers’ understanding of quadrilaterals through the definitions and their relationships (Unpublished Doctoral Dissertation). Middle East Technical University, Ankara, Turkey.
  • Park, S., & Oliver, J. S. (2008). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38, 261-284.
  • Quinn, R. J. (1997). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. The Journal of Educational Research, 91(2), 108-114.
  • Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 5(1), 1-22.
  • Smith, M. E., Swars, S. L., Smith, S. Z., Hart, L. C. & Haardörfer, R. (2012) Effects of an additional mathematics content course on elementary teachers’ mathematical beliefs and knowledge for teaching. Action in Teacher Education, 34(4), 336-348.
  • Türnüklü, E. (2014). Construction of inclusion relations of quadrilaterals: analysis of pre-service elementary mathematics teachers’ lesson plans. Education and Science, 39(173), 198-208.
  • Ulusoy, F. (2016). Developing prospective mathematics teachers’ knowledge for teaching quadrilaterals through a video case-based learning environment (Unpublished Doctoral Dissertation). Middle East Technical University, Ankara, Turkey.
  • van de Walle, J. A., Karp, K. S., & Bay-Williams J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th Ed.). Pearson Education, Inc.
  • Yin, R. K. (2003). Case study research design and methods. Sage‌.
  • Youngs, P., & Qian, H. (2013). The influence of university courses and field experiences on Chinese elementary candidates’ mathematical knowledge for teaching. Journal of Teacher Education, 64(3), 244-261.
  • Zeybek, Z. (2017). Learning to understand inclusion relations of quadrilaterals. The Eurasia Proceedings of Educational & Social Sciences (EPESS), 6, 9-13.
  • Zilkova, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 1339-1488.