STEAM stained-glass window: Integrating the arts, mathematics and technology into a maker experience
DOI:
https://doi.org/10.48489/quadrante.42179Keywords:
GeoGebra, irregular polygon, stained-glass window, aperiodic tiling, STEAM education, teacher educationAbstract
This article is based on an experiment conducted within the context of STEAM Education and Maker Culture, starting with the creation of an artistic stained glass window based on a newly discovered aperiodic tiling pattern, using a single irregular 13-sided piece. Combining digital (GeoGebra) and physical resources (laser-cut acrylic pieces), two undergraduate mathematics students faced geometric construction challenges and explored symmetries, patterns, and visual properties in light of Gestalt principles – unification, segregation, symmetry, and simplification. In this scenario, the guiding question of this qualitative and exploratory research was: how can the geometric construction process of an irregular figure, motivated by a contextualized problem, evolve with the aid of technology and from the perspective of form perception (Gestalt Theory)? The task was conceived as an open-ended activity, valuing autonomy, creativity, and interdisciplinarity between Mathematics, Arts, and Technology. Throughout four construction cycles, an evolution was observed in the participants' geometric reasoning, technological proficiency in using the tools, and visual perception. The final result not only solved a practical problem but also solidified as an artistic and pedagogical product, reinforcing the transformative potential of STEAM practices in mathematics education.
References
Amaral, C. A. N., Mariano, J. C. F., & Wrobel, J. S. (2014). Oficina de pavimentação com triângulos equiláteros. Anais do Encontro Internacional de Ensino de Matemática, 2(1), 1-12.
André, M. E. D. A. (2005). Etnografia da prática escolar. Papirus.
Arnal-Palacián, M. (2021). Mathematical flexibility of degree of primary education students in solving an area problem: Pick’s theorem. Mathematics Teaching Research Journal, 12(4), 21–35. http://www.hostos.cuny.edu/mtrj/
Barros, F. C. (2016). Pavimentações do Plano: Propostas lúdicas de aula. Trabalhando com Ângulos Internos, Simetrias, Isometrias, Obras de Artes e Mediatrizes [Dissertação de Mestrado, Instituto de Matemática Pura e Aplicada]. Repositório do IMPA. https://impa.br/wp-content/uploads/2016/12/TCC_Felipe_de_Carvalho_Barros.pdf .
Batista, L. S, Souza, M. D. O, Nobrega, M. R. A., & Silva, M. F. (2017). Atividades matemáticas à luz da teoria da Gestalt. Anais Conedu (pp. 1-9). CEMEP/UEPB.
Berry, R. Q., & Larson, M. R. (2019). The need to catalyze change in high school mathematics. Phi Delta Kappan, 100(6), 39–44. https://doi.org/10.1177/0031721719834027 .
Blanco, T. F., González-Roel, V., Diego-Mantecón, J. M., & Ortiz-Laso, Z. (2021). Análisis de la conexión arte-matemáticas en los libros de texto de Educación Primaria. Educación matemática, 33(3), 67-93. https://doi.org/10.24844/EM3303.03
Bogdan, R. C., & Biklen, S. K. (1994). Investigação qualitativa em educação: uma introdução à teoria e aos métodos. Porto Editora.
Borba, M. C., Silva, R. R. S., & Gadanidis, G. (2020). Fases das tecnologias digitais em educação matemática: Sala de aula e internet em movimento. Autêntica Editora.
Borba, M. C., & Villarreal, M. E. (2005). Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modeling, Experimentation and Visualization. Springer.
Burow, O-A., & Scherpp, K. (1985). GestaltPedagogia: Um Caminho para a Escola e a Educação. Summus.
Carniel, M., Lieban, D. E., & Deconti, G. S. (2023). Um vitral como perspectiva STEAM combinando arte, matemática e tecnologia. In MTC- Mostra Técnico -Científica 2023- Campus Bento Gonçalves (p. 1). IFRS.
Chen, S. Y., & Lin, S. W. A. (2019). Cross-cultural study of mathematical achievement: From the perspectives of one’s motivation and problem-solving style. International Journal of Science and Mathematics Education, 18, 1149–1167. https://doi.org/10.1007/s10763-019-10011-6 .
Diego-Mantecón, J. M., Blanco, T. F., Búa, J. B., & Sequeiros, P. G. (2019). Is the relationship between art and mathematics addressed thoroughly in Spanish secondary school textbooks? Journal of Mathematics and the Arts, 13(1–2), 25–47. https://doi.org/10.1080/17513472.2018.1552068 .
Diego-Mantecón, J. M., Ortiz-Laso, Z., & Blanco, T. F. (2022). Implementing STEM projects through the EDP to learn mathematics: the importance of teachers’ specialization. In P. R. Richard, M. P. Vélez, & S. Van Vaerenbergh (Eds.), Mathematics education in the age of artificial intelligence (pp. 399-415). Springer. https://doi.org/10.1007/978-3-030-86909-0_17
Doorman, M., Bos, R., de Haan, D., Jonker, V., Mol, A., & Wijers, M. (2019). Making and implementing a mathematics day challenge as a makerspace for teams of students. International Journal of Science and Mathematics Education, 17, 149–165. https://doi.org/10.1007/s10763-019-09995-y .
English, L. D. (2020). Facilitating STEM Integration Through Design. In J. Anderson & Y. Li (Eds.), Integrated Approaches to STEM Education: An International Perspective (pp. 45-66). Springer. https://doi.org/10.1007/978-3-030-52229-2_4 .
Gomes Filho, J. (2009). Gestalt do objeto: sistema de leitura visual da forma. Escrituras.
Gómez-Gálvez, P., Vicente-Munuera, P., Tagua, A., Forja, C., Castro, A. M., Letrán, M., ... & Escudero, L. M. (2018). Scutoids are a geometrical solution to three dimensional packing of epithelia. Nature Communications, 9(1), 2960. https://doi.org/10.1038/s41467-018-05376-1
Harron, J. R., Jin, Y., Hillen, A., Mason, L., & Siegel, L. (2022). Maker math: Exploring mathematics through digitally fabricated tools with K–12 in-service teachers. Mathematics, 10(17), 3069. https://doi.org/10.3390/math10173069.
Healy, L., & Sinclair, N. (2007). If this is our mathematics, what are our stories?. International Journal of Computers for Mathematical Learning, 12(1), 3-21. https://doi.org/ 10.1007/s10758-006-9109-4
Hsu, P. S., Lee, E. M., Ginting, S., Smith, T. J., & Kraft, C. (2019). A case study exploring non-dominant youths’ attitudes toward science through making and scientific argumentation. International Journal of Science and Mathematics Education, 17, 185–207. https://doi.org/10.1007/s10763-019-09997-w .
Kurti, R. S., Kurti, D. L., & Fleming, L. (2014). The philosophy of educational makerspaces part 1 of making an educational makerspace. Teacher Librarian, 41(5), 8-11. https://newblankets.org/worth_a_look/philosophy_of_makerspace.pdf
Kus, M., & Newcombe, N. S. (2025). Facilitation of students’ disembedding in an online visual arts and mathematics education program. International Journal of STEM Education, 12(8), 1-29. https://doi.org/10.1186/s40594-024-00524-0 .
Lefrançois, G. R. (2008). Teorias da aprendizagem. Cengage Learning.
Lévy, P. (1997). As tecnologias da inteligência. Editora 34.
Namukasa, I. K., Gecu-Parmaksiz, Z., Hughes, J., & Scucuglia, R. (2023). Technology maker practices in mathematics learning in STEM contexts: A case in Brazil and two cases in Canada. ZDM – Mathematics Education, 55(7), 1331–1350. https://doi.org/10.1007/s11858-023-01534-y .
Neto, A., Loss, C., Silva, M., Maria, S., & Dal Col, A. (2023). Tesselações: Ladrilhos de Penrose e sua construção com o GeoGebra. Professor de Matemática Online (PMO), 11(6), 81-96. https://doi.org/10.21711/2319023x2023/pmo1106 .
Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Kluwer Academic Publishers.
Ortiz-Laso, Z. (2023). El enfoque integrado STEAM y su impacto en la enseñanza de las matemáticas en educación secundaria: un estudio experimental [Tese de doutoramento, Universidad de Cantabria]. Repositorio Abierto de la Universidad de Cantabria. https://hdl.handle.net/10902/30200
Ortiz-Laso, Z., Diego-Mantecón, J. M., Lavicza, Z., & Blanco, T. F. (2023). Teacher growth in exploiting mathematics competencies through STEAM projects. ZDM – Mathematics Education, 55(7), 1283-1297. https://doi.org/10.1007/s11858-023-01528-w
Paganelli, A., Cribbs, J. D., Huang, X. S., Pereira, N., Huss, J., & Chandler, W. (2016). The makerspace experience and teacher professional development. Professional Development in Education, 43(2), 232-235. https://doi.org/10.1080/19415257.2016.1166448
Santos Neto, A., Barbosa, S. M., & Dal Col, A. (2023). Fundamentos para a Construção no GeoGebra de Tesselações Aperiódicas usando um Único Polígono. arXiv, 1, 1-13. https://doi.org/10.48550/arXiv.2311.14753 .
Smith, D., Myers, J. S., Kaplan, C. S., & Goodman-Strauss, C. (2024). An aperiodic monotile. Combinatorial Theory, 4(1), 1-91. https://doi.org/10.5070/C64163843.
Stake, R. E. (2010). Qualitative research: Studying how things work. The Guilford Press.
Stewart, I. (2012). Uma história da Simetria na Matemática. Zahar.
Stohlmann, M. (2018). A vision for future work to focus on the “M” in integrated STEM. School Science and Mathematics, 118(7), 310-319. https://doi.org/10.1111/ssm.12301
Sullivan, P. (2018). Challenging mathematical tasks: Unlocking the potential of all students. Oxford University Press.
Yin, Y., Hadad, R., Tang, X., & Lin, Q. (2020). Improving and assessing computational thinking in maker activities: The integration with physics and engineering learning. Journal of Science Education and Technology, 29, 189–214. https://doi.org/10.1007/s10763-019-09995-y.
Zulatto, R. B. A. (2002). Professores de Matemática que Utilizam Softwares de Geometria Dinâmica: suas características e perspectivas. [Dissertação de Mestrado, Universidade Estadual Paulista]. Repositório da UNESP. http://hdl.handle.net/11449/91012
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Quadrante

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) belongs to Quadrante. Nevertheless, we encourage articles to be published in institutional or personal repositories as long as their original publication in Quadrante is identified and a link to the journal's website is included.








