LEARNING GEOMETRY IN KINDERGARTEN STUDENTS: AN EMPIRICAL STUDY INVESTIGATING THE RELATIONSHIP BETWEEN MATHEMATICAL ABILITY AND MATHEMATICAL CREATIVITY

Panagiotis Gridos

Abstract


One of the most important goals of contemporary education is the liberation of thinking and the development of students’ creativity. The cultivation of creative thinking should begin at a very early age during the teaching process. The aim of the present study is to examine how the mathematical ability and mathematical creative thinking (fluency, flexibility, originality) of kindergarten students change following a three-month intervention program that focuses on the development of students’ spatial reasoning, their ways of perceiving geometric shapes and to develop the ability to identify different solution strategies for a given problem. Data were collected from 14 students in a kindergarten classroom, who were assessed before, during, and after the intervention program. The analysis of the results reveals interesting associations among the variables of the study.

 

Article visualizations:

Hit counter


Keywords


kindergarten, learning geometry, mathematical ability, mathematical creativity, spatial reasoning

Full Text:

PDF

References


Beghetto, R. A., & Kaufman, J. C. (2014). Classroom contexts for creativity. High Ability Studies, 25(1), 53–69. https://doi.org/10.1080/13598139.2014.905247

Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers. Retrieved from https://link.springer.com/book/10.1007/978-94-009-2657-8

Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass. Retrieved from https://psycnet.apa.org/record/2016-07883-000

Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York, NY: Macmillan. https://doi.org/10.1108/978-1-60752-874-620251022

Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 136-163. https://doi.org/10.2307/30034954

Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children's concepts of shape. Journal for Research in Mathematics Education, 30(2), 192-212. https://doi.org/10.2307/749610

Deliyianni, E., Elia, I., Gagatsis, A., Monoyiou, A., & Panaoura, A. (2010). A theoretical model of students’ geometrical figure understanding. Proceedings of the 6th Conference of the European Society for Research in Mathematics Education (CERME 6), Lyon, France. Retrieved from https://ife.ens-lyon.fr/publications/edition-electronique/cerme6/wg5-03-deliyianni-et-al.pdf

Department for Education and Employment (DfEE) (2000). Investing in our future curriculum guidance for the foundation stage.

Duval, R. (1995). Geometrical Pictures: Kinds of Representation and Specific Processings. In R. Sutherland & J. Mason (Εds.), Exploiting Mental Imagery with Computers in Mathematics Education, (p. 142-157). Germany: Springer. Retrieved from https://link.springer.com/chapter/10.1007/978-3-642-57771-0_10

Duval, R. (2005). Understanding the mathematical way of thinking – The registers of semiotic representations. New York, NY: Springer. Retrieved from https://link.springer.com/book/10.1007/978-3-319-56910-9

Duval, R. (2014). The first crucial point in geometry learning: Visualization. Mediterranean Journal for Research in Mathematics Education, 13(1-2), 1-28.

Duval, R. (2017). Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations. London: Springer. Retrieved from https://www.cymsjournal.com/wp-content/uploads/2020/11/journal-Vol13Year2014.pdf

Elia, I., Deliyianni, E., Gagatsis, A., Avgerinos, E., & Gridos, P. (2022). Tracing creativity in geometry: Figural, instrumental and discursive geneses of reasoning in a geometry multiple-solution task. Proceedings of the 7th ETM Symposium Mathematical Working Space. Strasbourg, France: INSPÉ of the academy of Strasbourg.

Elia, I., Gagatsis, A., (2003). Young children’s understanding of geometric shapes: The role of geometric models. Eur. Early Child. Educ. Res. J. , 11, 43–61.

Elia, I., Gagatsis, Α., Deliyianni, Ε., Monoyiou, Α., & Michael, S. (2009). A structural model of primary school students’ operative apprehension of geometrical figures. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (PME), Thessaloniki, Greece. Retrieved from https://www.researchgate.net/publication/327721389_A_structural_model_of_primary_school_students'_operative_apprehension_of_geometrical_figures

Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605–618. https://doi.org/10.1007/s11858-009-0184-6

Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht, Netherlands: Kluwer. https://doi.org/10.1016/j.sbspro.2011.12.056

Gagatsis, A., Elia, I., Geitona, Z., Deliyianni, E. & Gridos, P. (2022). How could the Presentation of a Geometrical Task Influence Student Creativity? Journal of Research in Science, Mathematics and Technology Education, 5(1), 93-116. https://doi.org/10.31756/jrsmte.514

Gagné, F. (2008). Building gifts into talents: Overview of the DMGT. Gifted Child Quarterly, 52(3), 199–215. https://doi.org/10.1177/0016986208317756

Gogou, V., Gagatsis, A., Gridos, P., Elia, I. & Deliyianni, E. (2020). The double nature of geometrical figure: Insights from empirical data. Mediterranean Journal for Research in Mathematics Education, Vol. 17, 7-23.

Gridos, P., Gagatsis, A., Elia, I. & Deliyianni, E. (2019). Mathematical creativity and geometry: the influence of geometrical figure apprehension on the production of multiple solutions. Proceedings of the 11th Conference of the European Society for Research in Mathematics Education: Working Group 4 (pp. 789-796). Utrecht, Netherlands. https://hal.science/hal-02402180/document

Gridos, P., Avgerinos, E., Mamona-Downs, J. & Vlachou, R. (2021). Geometrical Figure Apprehension, Construction of Auxiliary Lines, and Multiple Solutions in Problem Solving: Aspects of Mathematical Creativity in School Geometry. International Journal of Science and Mathematics Education, 20(3), pp. 619-636. https://doi.org/10.1007/s10763-021-10155-4

Gridos, P., Avgerinos, E., Deliyianni, E., Elia, I., Gagatsis, A. & Geitona, Z. (2021). Unpacking The Relation Between Spatial Ability and Creativity in Geometry. The European Educational Researcher, 4 (3), 307 – 328. https://doi.org/10.31757/euer.433

Haylock, D. W. (1987). A framework for assessing mathematical creativity in school

children. Education Studies in Mathematics, 18(1), 59–74. https://doi.org/10.1007/BF00367914

Howse, T. D., & Howse, M. E. (2015). Linking the Van Hiele Theory to Instruction. Teaching Children Mathematics, 21(5), 304-313. Retrieved from https://mavenofmath.wordpress.com/wp-content/uploads/2017/01/van-hiele-levels.pdf

Kapur, M. (2014). Productive failure in learning math. Cognition and Instruction, 32(3), 215–248. https://doi.org/10.1080/07370008.2014.886684

Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: Prototypicality and inclusion. ZDM Mathematics Education, 47, 407–420.

Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Netherlands: Sense Publisher. https://doi.org/10.1163/9789087909352_010

Leikin, R., & Lev, D. (2013). Creativity in mathematics education: Processes and outcomes. ZDM – Mathematics Education, 45(2), 159–166. https://doi.org/10.1007/s11858-013-0490-5

Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM - The International Journal on Mathematics Education, 45, 159-166. https://doi.org/10.1007/s11858-012-0459-1

Levenson, E., Tirosh, D., & Tsamir, P. (2011). Preschool geometry: Theory, research, and practical perspectives. Rotterdam: Sense. Retrieved from https://books.google.ro/books/about/Preschool_Geometry.html?id=tlHzRvpX45YC&redir_esc=y

Mann, E. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260. Retrieved from https://files.eric.ed.gov/fulltext/EJ750778.pdf

Michael, S., Gagatsis, A., Elia, I., Deliyianni, E., & Monoyiou, A. (2009). Operative apprehension of geometrical figures of primary and secondary school students. In A. Gagatsis & S. Grozdev (Eds.), Proceedings of the 6th Mediterranean Conference on Mathematics Education (pp.67-78). Plovdiv, Bulgaria: University of Plovdiv, CMS. Retrieved from https://fmi-plovdiv.org/GetResource?id=535

National Council of Teachers of Mathematics (2010). Program for the research presession. 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(2), 29–43. Retrieved from https://www.aft.org/sites/default/files/Newcombe_1.pdf

Petridou, A. (2018). Development of Geometric Thinking in Early Childhood: A Theoretical Model. PhD Thesis. University of Cyprus.

Renzulli, J. S. (2016). The three-ring conception of giftedness: A developmental model for promoting creative productivity. In S. M. Reis (Ed.), Reflections on gifted education (pp. 55–86). Waco, TX: Prufrock Press. https://doi.org/10.1017/CBO9780511610455.015

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge. Retrieved from https://doi.org/10.4324/9780203883785

Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 3, 75–80. https://doi.org/10.1007/s11858-997-0003-x

Torrance, E.P. (1994). Creativity: Just wanting to know. Pretoria, South Africa: Benedic books. Retrieved from https://books.google.ro/books/about/Creativity.html?id=gABBAAAACAAJ&redir_esc=y

Tsamir, P., Tirosh, D., Tabach, M., & Levenson, E. (2010). Multiple solution methods and multiple outcomes— Is it a task for kindergarten children? Educational Studies in Mathematics, 73(3), 217–231. https://doi.org/10.1007/s10649-009-9215-z

Usiskin, Z. (1997). The implications of "Geometry for all". Journal of Mathematics Education Leadership, 1, 5-16.

Uttal, D. H., & Cohen, C. A. (2012). Spatial thinking and education: When, why and how? In B. Ross (Ed.), Psychology of learning and motivation (Vol. 57). New York, NY: Academic Press. https://doi.org/10.1016/B978-0-12-394293-7.00004-2

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. https://doi.org/10.2307/j.ctvjf9vz4




DOI: http://dx.doi.org/10.46827/ejes.v13i1.6460

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Panagiotis Gridos

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2026. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).