3D geometric thinking skills of preschool children

3D geometric thinking skills


  • Tugba Ocal
  • Medera Halmatov


Early childhood mathematics education takes attention for decades. The effect of qualified mathematics education during early years has an impact on children’s future academic success. Main purposes of the present study are twofold; to examine children’s current 3D geometry thinking skills and to investigate the development of children’s 3D geometry thinking skills after a 3D training program developed by researchers and named as 3D in Early Childhood (3DinEC). A qualitative study with conveniently sampled preschool students was done. The age range of participant children varied from 60 months to 72 months; three girls and four boys. A semi-structured interview form, which included six abilities Pittalis and Christou (2010) determined, has totally 15 questions. Descriptive and content analysis methods were used. Findings of the present study indicated that participant children had a limited understanding regarding 3D geometric thinking. However, some of these thinking skills like identification of 3D geometric shapes and recognition of these shapes’ properties, etc. could be enhanced through various activities.


Adelman, C. (2006) The toolbox revisited: Paths to degree completion from high school through college. Washington, D.C.: U.S. Department of Education.

Aktaş-Arnas, Y., & Aslan, D. (2004). The development of geometrical thinking in 3 to 6 years old children group. In O. Ramazan, K. Efe, & G. Güven (Eds.), 1st International Pre-School Education Conference (Vol. I, pp. 475–494). İstanbul: Ya-Pa Yayıncılık.

Battista M. & Clements, D. H. (1996). Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4(5), 258-264.

Berthelot, R. & Salin, M. H. (1998). The role of pupils’ spatial knowledge in the elementary teaching of geometry. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 71–78). Dordrecht: Kluwer.

Caldera, Y. M., Culp, A. M., O’Brien, M., Truglio, R. T., Alvarez, M., & Huston, A. C. (1999). Children’s play preferences, construction play with blocks, and visual – spatial skills: Are they related?. International Journal of Behavioral Development, 23(4), 855-872. https://doi.org/10.1080/016502599383577

Casey, B. M., Andrews, N., Schindler, H., Kersh, J. E., Samper, A. & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26, 269–309. https://doi.org/10.1080/07370000802177177

Charalambos, L. (1997). A few remarks regarding the teaching of Geometry, through a theoretical analysis of the geometrical figure. Nonlinear Analysis: theory, Methods & applications, 30(4), 2087-2095. https://doi.org/10.1016/S0362-546X(97)00294-0

Clements, D. H. (1998). Geometric and spatial thinking in young children. https://files.eric.ed.gov/fulltext/ED436232.pdf

Clements, D. H. (1992). Elaboraciones sobre los niveles de pensamiento geometrico [Elaborations on the levels of geometric thinking]. In A. Gutiérrez (Ed.), memorias del tercer simposio internacional sobre investigatcion en educacion matematica (pp. 16–43). València, Spain: Universitat De València.

Clements, D. H., Sarama, J., Baroody, A. J., Joswick, C., & Wolfe, C. B. (2019). Evaluating the efficacy of a learning trajectory for early shape composition. American Educational Research Journal, 56(6), 2509-2530. https://doi.org/10.3102/0002831219842788

Clements, D. H., Swaminathan, S., Hannibal, M., & Sarama, J. (1999). Young children's concepts of shape. Journal for Research in Mathematics Education, 30(2), 192-212.

Colom, R., Contreras, M. J., Botella, J., & Santacreu, J. (2001). Vehicles of spatial ability. Personality and Individual Differences, 32, 903–912.

Couto, A., & Vale, I. (2014). Pre-service teachers' knowledge on elementary geometry concepts. Journal of the European Teacher Education Network, 9, 57-73.

Davis, B., & The Spatial Reasoning Study Group, (2015). Spatial reasoning in the early years: Principles, assertions, and speculations. New York: Routledge.

Denizli, Z. A., & Erdoğan, A. (2018). Development of a three dimensional geometric thinking test for early graders. Journal on Mathematics Education, 9(2), 213-226.

Derȩgowski, J. B., & Bentley, A. M. (1987). Seeing the impossible and building the likely. British Journal of Psychology, 78(1), 91-97.

Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.), Proceedings of the 15th Conference of the International Group for the Psychology of Mathematics Education (PME) (pp. 33-48). Assisi, Italy.

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428

Duval, R. (1998). Geometry from a cognitive point of view. New Icmi Studies Series, 5, 37-51.

Eryaman, Z. (2009). A study on sixth grade students’ spatial reasoning regarding 2d representations of 3D objects [Unpublished master’s thesis]. Middle East Technical University, Ankara.

Ferrara, K., Hirsh‐Pasek, K., Newcombe, N. S., Golinkoff, R. M., & Lam, W. S. (2011). Block talk: Spatial language during block play. Mind, Brain, and Education, 5, 143–151. https://doi.org/10.1111/j.1751-228X.2011.01122.x

Ginsburg, H. P. (1997). Entering the child's mind: The clinical interview in psychological research and practice. New York: Cambridge University Press.

Ginsburg, H., Lee, J., & Boyd, J. (2008). Mathematics education for young children: what it is and how to promote it. Society for Research in Child Development, XXII(1), 3-24.

Gutierrez, A. (1992). Exploring the links between van Hiele levels and 3-dimensional geometry. Structural Topology, 18, 31-48.

Halpern, D. (2000). Sex Differences in Cognitive Abilities (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.

Hannibal, M. A. Z., & Clements, D. H. (2000). Young children’s understanding of basic geometric shapes. National Science Foundation. Grant No: ESI-8954644.

Heraud, B. (1987). Conceptions of area units by 8-9 year old children. In PME XI (Vol. III, pp. 299-304). Montreal, Canada.

Hershkowitz, R., Ben-Chaim, D., Hoyles, C., Lappan, G., Mitchelmore, M., & Vinner, S. (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 (pp. 70–95). Cambridge, MA: Cambridge University Press.

Jones, K. (2002). Issues in the teaching and learning of geometry. In L. Haggarty (Ed.), Aspects of teaching secondary mathematics: Perspectives on practice (pp. 121-139). London: Routledge Falmer.

Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850–867. https://doi.org/10.1037/a0014939

Kimura, D. (1999). Sex and cognition. Cambridge: MIT.

Levine, S. C., Ratliff, K. R., Huttenlocher, J., & Cannon, J. (2012). Early puzzle play: A predictor of preschoolers’ spatial transformation skill. Developmental Psychology, 48, 530–542. https://doi.org/10.1037/a0025913

Lohman, D. (1996). Spatial ability and g. In I. Dennis, & P. Tapsfield (Eds.), Human abilities: Their nature and assessment (pp. 97-116). Hillsdale, NJ: Erlbaum.

Lohman, D. F. (1988). Spatial abilities as traits, processes, and knowledge. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 4, pp. 181-248). Hillsdale, NJ: Lawrence Erlbaum Associates).

Love, E. (1995). The functions of visualization in learning geometry. In R. Sutherland, & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp.125-141). Berlin: Springer.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed). California: Sage Publications.

Murphy, C. M., & Wood, D. J. (1981). Learning from pictures: The use of pictorial information by young children. Journal of Experimental Child Psychology, 32(2), 279-297.

National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 34, 29–43.

Nieuwoudt, H. D., & van Niekerk, R. (1997). The spatial competence of young children through the development of solids. Chicago: American Educational Research Association.

Owens, K., & Outhred, L. (2006). The complexity of learning geometry and measurement. In A. Gutierrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 83-115). Rotterdam/Taipei: Sense Publishers.

Parzysz, B. (1988). ‘Knowing’ vs. ‘seeing’: Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79–92.

Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191-212.

Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205-235). Rotterdam: Sense Publications.

Ramani, G. B., Zippert, E., Schweitzer, S., & Pan, S. (2014). Preschool children’s joint block building during a guided play activity. Journal of Applied Developmental Psychology, 35(4), 326-336. https://doi.org/10.1016/j.appdev.2014.05.005

Reyna, V. F., Nelson, W. L., Han, P. K., & Dieckmann, N. F. (2009). How numeracy influences risk comprehension and medical decision making. Psychological Bulletin, 135, 943–973. http://dx.doi.org/10.1037/a0017327

Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2018). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46(1), 166-178. https://doi.org/10.1016/j.ecresq.2018.03.006

Sarama, J., & Clements, D. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge: Taylor & Francis Group.

Satlow, E., & Newcombe, N. S. (1998). When is a triangle not a triangle? Young children’s developing concepts of geometric shape. Cognitive Development, 13, 547–559.

Siew-Yin, H. (2003). Young children's concept of shape: van Hiele visualization level of geometric thinking. The Mathematics Educator, 7(2), 71-85.

Tsamir, P. Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81-95.

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139, 352–402. http://dx.doi.org/10.1037/a0028446

van Hiele, P. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310 - 316.

Van Klinken, E. (2010). Utilizing year three NAPLAN results to improve queensland teachers' mathematical pedagogical content knowledge. In L.

Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the mathematics education research group of Australasia (pp. 297-304). Fremantle: MERGA.

Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education, 3, 7–13. http://dx.doi.org/10.1016/j.tine.2014.02.005

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 (pp. 690-697). Melbourne: Mathematics Education Research Group of Australasia Inc.

Yıldırım, A., & Şimsek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.