Theory and Practice in the Curriculum

Theory and Practice in the Curriculum

The Trend of Content Presentation and Levels of van Hiele Related to Quadrilaterals in Elementary Mathematics Textbooks

Document Type : Original Article

Authors
Ebrahim Reyhani 1
Narges Yaftian 2
Amir Esmaeili 1
Abdellah Hesam 1
1 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
2 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
10.22034/cstp.2026.578671.1142
Abstract
Understanding quadrilaterals, as one of the more challenging topics in geometry, is influenced substantially by the content of mathematics textbooks, particularly at the elementary level. The purpose of the present study was to examine the progression of content related to quadrilaterals and the corresponding Van Hiele levels of geometric thinking in elementary mathematics textbooks, in order to explore the extent to which these materials reflect the levels of thinking expected from students. The study employed a descriptive–analytical design with a qualitative approach. Relevant sections concerning quadrilaterals were purposefully selected from the textbooks. Data were collected using content-analysis forms based on Van Hiele levels, whose face and content validity were confirmed by experts in mathematics education. Inter-rater reliability for the coding process was ensured using Cohen’s kappa coefficient. The findings indicated that the presented content includes the introduction of names and visual representations, prototypical examples, drawing methods, hands-on activities and construction tasks, properties related to sides, angles, diagonals, and symmetry, hierarchical or partition-based relationships, and the sum of interior angles. This content corresponds to Van Hiele levels 1 through 3, with level 2 being the predominant level. In terms of content progression, squares and rectangles are introduced for the first time in grade one, while trapezoids, parallelograms, and rhombi are introduced in grade four. Moreover, none of the quadrilaterals are formally defined using the term “definition,” although the presentations in the grade four textbook are more closely aligned with formal definitions.
Keywords
content analysis
elementary mathematics textbooks
quadrilaterals
van Hiele theory
Subjects
Refrences
Abdullah, A. H., & Shin, B. (2019). A comparative study of quadrilaterals topic content in mathematics textbooks between Malaysia and South Korea. Journal on Mathematics Education, 10(3), 315-340.
Akar, N., & Işıksal-Bostan, M. (2022). The didactic transposition of quadrilaterals: the case of 5th grade in Turkey. International Journal of Mathematical Education in Science and Technology, 55(3), 628-649.
Alamian, V. , Seyyedi, M. and Habibi, M. (2018). Identifying the misconceptions of eighth grade students on geometry skills and the use of van Hiele theory to improve their geometry skills. Journal of Educational Innovations, 17(3), 123-147. [in Persian]
Altiparmak, K., & Gürcan, G. (2021). Examination of 4th grade students' definitions for square, rectangle and triangle geometric shapes. Education Quarterly Reviews, 4(3), 304-321.
Avcu, R. (2019). A comparison of mathematical features of Turkish and American textbook definitions regarding special quadrilaterals. International Journal of Mathematical Education in Science and Technology, 50(4), 577-602.
Bakhshalizadeh, S. and broojerdian, N. (2017). Identifying the primary school fourth grade students’ common misconceptions in content area of geometry and measurement: A comparison of their performance with the mean performance at international level. Journal of Educational Innovations, 16(4), 101-126. [in Persian]
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.
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48.
Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151–178). Reston, VA: National Council of Teachers of Mathematics.
Crowley, M. (1987). The van Hiele Model of Development of Geometric Thought. In Learning and Teaching Geometry K-12. In Mary M. Lindquist & Albert P. Shulte (Eds.), 1987 Yearbook of the National Council of Teacher of Mathematics, 1-16. Reston, Va. NCTM.
Cybulski, F. C., Oliveira, H., & Cyrino, M. C. D. C. T. (2024). Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 20(8), em2490.
De Villiers, M., Govender, R., & Patterson, N. (2009). Defining in geometry. In T. V. Craine, & R. Rubenstein (Eds.), Understanding geometry for a changing world (pp. 189-203.( Reston, VA: National Council of Teachers of Mathematics.
Elbehary, S. G. A., Fahem, S. M., & Peni, N. R. N. (2023). Track prospective mathematics teachers' understanding of special quadrilaterals: An exploration of level 3 of geometric thinking. Futurity Education, 3(3), 20-45.
Ersando, M. JR.P. (2026). Integrating education for sustainable development into elementary mathematics: an action research on curriculum mapping, teacher experiences, and instructional guide validation. International Journal of Innovative Research in Multidisciplinary Education, 5(2), 146-153.
Sprenger, M. (2026). Pre-service teachers’ and children’s conceptual understanding of quadrilaterals. In T. Meaney et al. (Eds.), Engaging with Mathematics in the Early Years (pp. 321-334). Springer.
Fan, L., Qi, C., Seah, W. T., & Liu, Q. (2025). Research on mathematics textbooks in relation to curriculum development and instructional reform: recent advances and future directions. ZDM–Mathematics Education, 57(5), 845-857.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: development status and directions. ZDM, 45, 633-646.
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), 3-20.
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.
Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph Series, 3, 1-196.
Gholamazad, S. (2023). Implementation of the mathematics curriculum of the first cycle of elementary education: challenges and solutions. Journal of Theory & Practice in Curriculum, 20(10), 395-426. [in Persian]
Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55, 153-166.
Halat, E. (2008). In-service middle and high school mathematics teachers: Geometric reasoning stages and gender. The Mathematics Educator, 18(1), 8-14.
Hershkowitz, R. (1990). Psychological aspects of learning geometry. In Mathematics and cognition (pp. 70-95). Cambridge University Press.
Janah, M., Rahardi, R., & Rahardjo, S. (2024). Analysis of geometry concept sequence in student textbooks based on van Hiele's theory. PRISMA, 13(2), 295-302.
Kalyankar, V. K. (2019). The van Hiele Analysis of Curricular Materials: A Comparative Study. Doctoral dissertation in mathematics, University of Arkansas.
Macit, B., & Tabak, S. (2026). Identifying misconceptions of 5th grade students regarding triangles and quadrilaterals. Education Mind, 5(1), 1-16.
Mason, M. (2009). The van Hiele levels of geometric understanding. Colección Digital Eudoxus, 1(2), 4-8.
Miller, S. M. (2018). An analysis of the form and content of quadrilateral definitions composed by novice pre-service teachers. The Journal of Mathematical Behavior, 50, 142-154.
Morgan, C. (2006) What is a definition for in school mathematics? In M, Bosch, (Ed.), European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 861-871.
Musser, G. L., Peterson, B. E., & Burger, W. F. (2013). Mathematics for Elementary Teachers: A Contemporary Approach. John Wiley & Sons.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. . Reston: VA: The National Council of Teachers of Mathematics, Inc.
Nggaba, M. E., & Ndakularak, I. L. (2025). Level of student’s geometry thinking on quadrilateral topic. EDUMATSAINS (Journal Pendidikan Matematika Dan Sains), 9(2), 77–89.
Pagiling, S. L., & Nur'aini, K. D. (2022). Specialized content knowledge lower secondary school teachers on quadrilaterals. PYTHAGORAS: Journal Matematika dan Pendidikan Matematika, 17(1), 333-345.
Pusey, E. L. (2003). The van Hiele model of reasoning in geometry: A literature review. Unpublished master’s thesis, North Carolina State University, Raleigh, NC, United States.
Reyhani, E. (2005). Introduction to Piaget’s theory and van Hiele theory. Journal of Roshd Mathematics Education, 22(2), 12-22. [in Persian]
Rezat, S., Fan, L., & Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. ZDM, 53(6), 1189-1206.
Siew, N. M., Chong, C. L., & Abdullah, M. R. (2013). Facilitating students' geometric thinking through van Hieles phase-based learning using tangram. Journal of Social Sciences, 9(3), 101-111.
Usiskin, Z., Griffin, J., Witonsky, D., & Willmore, E. (2008). The classification of quadrilaterals: A study of definition. Charlotte, NC: Information Age Publishing.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and Middle School Mathematics: Teaching Developmentally (10th Edition), Pearson Education Limited.
Yaftian, N. and Safabakhsh, A. (2019). Content analysis of grade 8 geometry, using van Hiele levels of geometric thinking. Journal of Roshd Mathematics Education, 36(3), 4-11. [in Persian]
Zeybek, Z. (2017). Learning to understand inclusion relations of quadrilaterals. The Eurasia Proceedings of Educational and Social Sciences, 6, 9-13.
Žilková, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences,3(1), 30-37.
Theory and Practice in the Curriculum
Volume 14, Issue 27
March 2026
Pages 111-140