AN INVESTIGATION ON PRIMARY SCHOOL STUDENTS’ 3D GEOMETRIC THINKING
This study aims to investigate how primary school students’ three-dimensional geometric thinking changes across grades. The survey model was used, and the study group was comprising of 520 primary school students in a large city of Turkey. In the study, the Three-Dimensional Geometric Thinking Test, which is a paper and pencil test, was used to collect data. The scores taken from the test were compared across the grades and the relationships between the components of three-dimensional geometric thinking were examined. The findings showed that as the grades increased, students’ scores taken from the Three-Dimensional Thinking Test also increased significantly. Moreover, a medium and positive correlation was found between the components of three-dimensional geometric thinking. The results of the study revealed that grade level is a significant variable on three-dimensional geometric thinking, yet some important three-dimensional geometric thinking skills can be developed independent from the grade level. The current study intends to shed light on the development of three-dimensional geometric thinking starting from early grades, and to provide important information for organizing the three-dimensional geometric content in the curriculum and its implementation.
Keywords: Geometric thinking, three-dimensional geometric thinking (3DGT), geometry teaching, primary school students.
Altun, T. (2011). İlköğretim öğrencilerinin bilgisayara yönelik tutumlarının incelenmesi: Trabzon ili örneği [Examining upper primary level students’ attitudes towards computers on the basis of different variables: Sample of Trabzon]. Turkish Journal of Computer and Mathematics Education, 2(1), 69-86.
Akkurt-Denizli, Z. (2016). 1-4. sınıf düzeylerine yönelik üç boyutta geometrik düşünme testinin geliştirilmesi, uygulanması ve sonuçlarının değerlendirilmesi [The development, application and evaluatıon of a three dimensional reasoning test for grades 1 to 4] (Unpublished Doctorate Thesis). Anadolu University, Eskişehir.
Akkurt-Denizli, Z., & Erdoğan, A. (2018). Development of a three dimensional geometric thinking test for early graders. Journal on Mathematics Education, 9(2), 213-226.
Ambrose, R., & Kenehan, G. (2009). Children’s evolving understanding of polyhedra in the classroom. Mathematical Thinking and Learning, 11(3), 158-176.
Battista, M. T., & Clements, D. H. (1996). Students' understanding of 3D rectangular arrays of cubes source. Journal for Research in Mathematics Education, 27(3), 258-292.
Battista, M. T., & Clements, D. H. (1998). Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4, 258-264.
Battista, M. (2004). Applying cognition-based assessment to elementary school students’ development of understanding of area and volume measurement. Mathematıcal Thınkıng And Learnıng, 6(2), 185-204.
Ben–Chaim, D., Lappan, G., & Houang, R. T. (1985). Visualizing rectangular solids made of small cubes: Analyzing and affecting students’ performance. Educational Studies in Mathematics, 16(4), 389-409.
Büyüköztürk, Ş. (2007). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences]. Ankara: Pegem Publishing.
Büyüköztük, Ş., Çakmak Kılıç, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2010). Bilimsel araştırma yöntemleri [Scientific research methods]. Ankara: Pegem Publishing.
Clements, D. H. (2004). Major the]mes and recommendations geometric and spatial thinking in young children. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 7-77). Mahwah: Lawrence Erlbaum Associates Publishers.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.
Cohen, N. (2003). Curved solids nets. In The 27th International Group for the Psychology of Mathematics Education Conference, 13-18 July 2003 (p. 2, 229-236), Honolulu, HI: CRDG, College of Education, University of Hawai’i.
Conceicao, J., & Rodrigues, M. (2020). First-grade students' strategies for 2D/3D transformations. Psicologia em Pesquisa, 14(2), 112-129. ISSN 1982-1247. http://dx.doi.org/10.34019/1982-1247.2020.v14.27595.
Creswell, J. W. (2002). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Upper Saddle River, NJ: Pearson Education.
Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2010). Sosyal bilimler için çok değişkenli istatistik [Multivariate Statistics for Social Sciences]. Ankara: Pegem Publishing.
Deregowski, J. B., & Bentley, A. M. (1987). Seeing the impossible and building the likely. The British Psychological Society, 78, 91-97.
Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactiques des Sciences Cognitives, 5, 37-65.
Erbaş, A. K., Kertil, M., Çetinkaya, B, Çakıroğlu, E., Alacalı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: temel kavramlar ve farklı yaklaşımlar [Mathematical modeling in mathematics education: basic concepts and different approaches]. Educational Sciences: Theory & Practice, 14(4), 1-21.
Erdoğan, A., Özdemir Erdoğan, E., Garan, Ö., & Güler., M. (2012). Assessing an environment designed for the popularization of mathematics. Elementary Education Online, 11(1), 51-74, 2012.
Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9. Mathematics Education Research Journal, 32, 235–255.
Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 8(3) 211–215.
Gutiérrez, A. (1992). Exploring the links between van Hiele Levels and 3-dimensional geometry. Structural Topology, 18, 31-48.
Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In the 20th International Group for the Psychology of Mathematics Education Conference, 8-12 July 1996 (p. 1, 3-19), Valencia: Universidad de Valencia.
Hallowell, D., Okamoto, Y, Romo, L., & LaJoy, J. (2015). First-grader’s spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM Mathematics Education, 47(3). 363-375 doi:10.1007/s11858-015-0664-9
Harris, J., Newscombe, N. S., & Hirsh-Pasek, K. (2013). A new twist on studying the development of dynamicspatial transformations: mental paper folding in young children. Mind, Brain and Education, 7(1), 49–55.
Heraud, B. (1987). Conceptions of area units by 8-9 year old children. In Eleventh International Conference of the International Group for the Psychology of Mathematics Education, 19–25 July (pp. 3, 229-304), Montreal.
Hirstein, J. J. (1981). The second national assessment in mathematics: area and volume. Mathematics Teacher, 74, 704-708.
Ibili, E., Çat, M., Resnyansky, D., Şahin, S., & Billinghurst, M. (2020). An assessment of geometry teaching supported with augmented reality teaching materials to enhance students’ 3D geometry thinking skills. International Journal of Mathematical Education in Science and Technology, 51(2), 224–246.
Karasar, N. (2009). Bilimsel araştırma yöntemi [Scientific research method]. Ankara: Nobel Publishing.
Kol, S. (2010). Okul öncesi dönemde kazanılan zaman ve mekân kavramlarının ölçülmesine yönelik başarı testi geliştirilmesi [Developing an achievement test to measure the concepts of time and space gained in the pre-school period]. In International Conference on New Trends in Education and Their Implications, 11-13 November 2010 (pp.894-902), Antalya.
Ministry of National Education [MoNE] (2013). İlköğretim 1-5. sınıflar matematik dersi öğretim programı [Elementary 1-5. grades math curriculum]. Ankara: Ministry of Education.
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: Primary and secondary school (1, 2, 3, 4, 5, 6, 7 and 8th Grades)]. Ankara: Ministry of Education.
Mitchelmore, M. C. (1980). Prediction of developmental stages in the representation of regular space figures. Journal of Research in Mathematics Education, March, 11(2), 83-93. https://doi.org/10.5951/jresematheduc.11.2.0083
Murphy, C. M., & Wood, D. J. (1981). Learning from pictures. The use of pictorial information by young children. Journal of Experimental And Child Psychology, 32, 279- 297.
National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston: NCTM.
Olkun, S. (1999). Stimulating children’s understanding of rectangular solids made of small cubes (Unpublished Doctorate Thesis). Arizona State University, USA.
Olkun, S. (2003a). When does the volume formula make sense to students? Hacettepe University Journal of Faculty of Education, 25, 160-165.
Olkun, S. (2003b). Making connections: Improving spatial abilities with engineering drawing activities. International journal of mathematics teaching and learning, 3(1), 1-10.
Olkun, S., & Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki [The relationship between primary school students' computer experiences and their spatial thinking and geometry achievements]. The Turkish Online Journal of Educational Technology , 2(4), 86-91.
Owens, K., & Outhred, L. (2006). The complexity of learning geometry and measurement. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the physchology of mathematics education: Past, present and future (pp. 83-111). Rotterdam/Taipei: Sence Publishers.
Parzysz, B. (1988). “Knowing" vs "seeing". Problems of the plane representation of space geometry. Educational Studies in Mathematics, 19(1988), 79-92.
Piaget, J., & Inhelder, B. (1956). The child's conception of space. London and New York: Routledge. 17 April 2015 retrieved from website
Piaget, J., İnhelder, B., & Szeminska, A. (1960). The child conception of geometry. Oxon: Routledge. 18 March 2015 retrieved from website
Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educ Stud Math, 75, 191-212.
Potari, D., & Spiliotopoulou, V. (2001). Patterns in children’s drawings and actions while constructing the nets of solids: the case of the conical surfaces. Focus on Learning Problems in Mathematics, 23(4), 41–62.
Sarama, J., & Clements, D. H. (2016). Physical and virtual manipulatives: What is “concrete?” In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (p. 71–93). Basel, Switzerland: Springer International.
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. USA: Pearson.
Van Hiele, P. M. (1986). Structure and insight. New York: Academic Press.
Van Hilele, P. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310-316. https://doi.org/10.5951/TCM.5.6.0310
Wolf, D. (1988). Drawing the boundary: the development of distinct systems for spatial representation in young children. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (p.231-245). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.
Wright, V., & Smith, K. (2017). Children’s schemes for anticipating the validity of nets for solids. Mathematics Education Research Journal, 29(3), 369–394.
Yeh, A., & Nason, R. (2004). Toward a semiotic framework for using technology in mathematics education: The case of learning 3d geometry. In International Conference on Computers in Education, 30 November-3 December 2004 (p.1191-1199), Melbourne, Australia: Common Ground Publishing Pty Ltd.
Yeh, A. (2013). Constructing a frame of cube: connecting 3D shapes with direction, location and movement. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (p. 690-697). Melbourne: Mathematics Education Research Group of Australasia Inc.
Yolcu, B., & Kurtuluş, A. (2010). A study on developing sixth-grade students’ spatial visualization ability elementary education. Elementary Education Online, 9(1), 256-274.
Copyright (c) 2022 International Online Journal of Primary Education (IOJPE) ISSN: 1300-915X
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright and permissions
The manuscripts submitted to International Online Journal of Primary Education (IOJPE) for publication should be original studies that were not published before or not submitted to anywhere else for publication.
Authors who submit their manuscript to International Online Journal of Primary Education (IOJPE) should acknowledge that they agree to transfer the copyright of their studies to IOJPE. All Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.
All articles published in International Online Journal of Primary Education (IOJPE) are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY 4.0).
Any further distribution or use of content published under CC BY 4.0 must contain the author(s) and the published article’s title, and journal citation. All articles published in IOJPE under a CC BY License may be used for Text and Data Mining purposes, subject to the conditions of the CC BY License terms. The license allows for commercial use. IOJPE allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator.
The journal’s objective is to disseminate articles published are free. Under the Creative Commons license (CC BY 4.00), the journal allows the user to permits unrestricted use, distribution, and reproduction in any medium, and even use the publication for commercial activities, provided that the original work is properly cited.
Open access is an approach that eases the interdisciplinary communication and encourages cooperation among different disciplines. IOJPE, therefore, contributes to its own field by providing more access to its articles and a more transparent review process.