Walking to learn: reflections on the teaching of geometry from a social perspective.
DOI:
https://doi.org/10.65598/rps.6240Keywords:
School geometry Situated learning Urban environment Visual culture Critical pedagogy Teacher mediation City as classroom Visual literacy Contextualized teaching Mathematics educationAbstract
This article offers a theoretical reflection on the teaching of geometry from a situated and socially committed perspective, moving away from traditional approaches focused on content transmission. It outlines a didactic proposal that connects mathematical knowledge with the urban environment, visual culture, and students’ everyday experiences, recognizing the city as a pedagogical space and the teacher as a cultural mediator. The study integrates theoretical foundations from cognitive psychology, the semiotics of mathematical knowledge, and critical pedagogy to envision scenarios in which geometric learning is constructed through aesthetic sensitivity, cultural diversity, and critical reading of space. Organizational elements of the proposal are presented, along with expected outcomes that highlight the formative potential of a contextualized and inclusive geometry. This reflection positions itself as a starting point for future educational experiences that acknowledge the city as a living classroom and geometry as a cultural tool for critically inhabiting the world.
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References
Ayala García, E. T. (2017). La ciudad como espacio habitado y fuente de socialización. Ánfora, 24(42), 189–216. https://redalyc.org/journal/3578/357851475008/html
Barrantes, M.& Blanco, L. (2003). Concepciones de los estudiantes para maestro en España sobre la geometría escolar y su enseñanza-aprendizaje. Revista Latinoamericana de Investigación en Matemática Educativa, RELIME, 6(2), 107-132. https://www.redalyc.org/pdf/335/33560202.pdf
Barrantes, M., Balletbo, I., & Fernández, M. A. (2013). La enseñanza-aprendizaje de la Matemática (Geometría) en Educación Secundaria en la última década. Revista de la Sociedad Argentina de Educación Matemática, 56, 41-50. https://funes.uniandes.edu.co/wp-content/uploads/tainacan-items/32454/1181177/Barrantes2013La.pdf#
Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education (Vol. 6). Springer Science & Business Media. https://books.google.com.br/books
Boyer, C. B., & Merzbach, U. C. (2011). A history of mathematics. John Wiley & Sons. https://books.google.com.br/
Cordero, F. (2015). La ciencia desde el niñ@. Porque el conocimiento también se siente. Primera Edición. Barcelona, España: Gedisa. www.gedisa.com/ficha.aspx?aut=Cordero,%20Francisco&idcol=860&cod=869011
Cordero, F., Flores, R., & Rodríguez, M. (2019). Saberes cotidianos y matemática escolar: tensiones y posibilidades. Revista Latinoamericana de Investigación en Matemática Educativa, 22(1), 67–89. https://doi.org/10.12802/relime.19.2211
Cruz-Pichardo, I. M., & Cabero-Almenara, J. (2020). Una experiencia gamificada en el aprendizaje de los triángulos en geometría: grado de aceptación de la tecnología. Revista Prisma Social, (30), 65–87. https://revistaprismasocial.es/article/view/3566
D’Ambrosio, U. (2001). Etnomatemática: elo entre las tradiciones y la modernidad. Belo Horizonte: Autêntica. https://www.amazon.com.br/Etnomatem%C3%A1tica-Elo-Entre-Tradi%C3%A7%C3%B5es-Modernidade/dp/8575260197
Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3–26). Cuernavaca: PME-NA. https://pat-thompson.net/PDFversions/1999Duval.pdf
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Suny Press. https://books.google.com.br/
Escobar, B. R. P., Rimachi, J. M., Bejarano, D. G. C., & Zuta, J. C. M. (2025). Entrenamiento de Ciudadanos del Futuro a través de Recursos Audiovisuales: Formación Socioeducativa y Responsabilidad Social de Estudiantes en el Norte del Perú. VISUAL REVIEW. International Visual Culture Review/Revista Internacional de Cultura Visual, 17(3), 317-329. https://visualcompublications.es/revVISUAL/article/view/5904
Fernández González, J., Moreno Jiménez, T., & González, G. (2003). Las analogías como modelo y como recurso en la enseñanza de las ciencias. Alambique, 35, 82-89. https://www.grupoblascabrera.org/webs/ficheros/08%20Bibliograf%C3%ADa/01%20Analogias/21%20Analogias%20modelo%20y%20recurso.pdf
Gilligan, K. A. (2020). Make space: the importance of spatial thinking for learning mathematics. Frontiers for young minds, 8(5). frym-08-00050%20.pdf
Gilligan-Lee, K. A., Hawes, Z. C. K., & Mix, K. S. (2022). Spatial thinking as the missing piece in mathematics curricula. npj Science of Learning, 7(10). https://doi.org/10.1038/s41539-022-00128-9
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education, 39(1–2), 127–135. https://doi.org/10.1007/s11858-006-0004-1
González-Tejero, J. M. S., Parra, R. M. P., & Padilla, M. O. (2011). El desarrollo del conocimiento matemático. Psicogente, 14(26), 269–293. https://dialnet.unirioja.es/servlet/articulo?codigo=6113733
Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26. https://doi.org/10.1037/0003-066X.53.1.5
Gutiérrez, A. (2013). Visualization in geometry education. In B. Ubuz (Ed.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 1–10). Antalya: ERME. https://1library.org/article/visualiza%C3%A7%C3%A3o-em-geometria-sob-a-perspectiva-de-guti%C3%A9rrez.q7r496dy
Hoyles, C., & Lagrange, J. B. (2010). Mathematics Education and Technology—Rethinking the Terrain. New York: Springer. https://doi.org/10.1007/978-1-4419-0146-0 https://link.springer.com/book/10.1007/978-1-4419-0146-0 https://doi.org/10.62161/revvisual.v17.5904
Johnson-Laird, P. N. (1983). Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness. Cambridge: Cambridge University Press. https://books.google.com.br/books/about/Mental_Models.html?id=FS3zSKAfLGMC&redir_esc=y
Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. https://academic.oup.com/book/54990
Lakatos, I. (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press. https://www.amazon.com.br/Proofs-Refutations-Logic-Mathematical-Discovery/dp/052121078X
Lerman, S. (2000). The social turn in mathematics education research. Educational Studies in Mathematics, 39(1–3), 19–44. https://www.researchgate.net/profile/Stephen-Lerman/publication/268513889_The_social_turn_in_mathematics_education_research/links/624ea0e24f88c3119ce6588b/
Medina Herrera, L. M., Juárez Ordóñez, S., & Ruiz-Loza, S. (2024). Enhancing mathematical education with spatial visualization tools. Frontiers in Education, 9. https://doi.org/10.3389/feduc.2024.1229126
Napa Vileta, Z. A. (2023). Los recursos didácticos como apoyo en el proceso de enseñanza-aprendizaje de los estudiantes. MQRInvestigar, 7(3), 4078–4105. https://www.investigarmqr.com/ojs/index.php/mqr/article/view/663 https://doi.org/10.56048/MQR20225.7.3.2023.4078-4105
Nelsen, R. B. (2016). Geometry & Algebra. In Proofs Without Words III: Further Exercises in Visual Thinking (pp. 1–2). Washington, DC: Mathematical Association of America. https://www.cambridge.org/core/books/abs/proofs-without-words-iii/geometric-series-v/D8D01BB665550977CE8DD4B85CA7DADA
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. Journal of Mathematics Teacher Education, 6(2), 115–141. https://forskning.ruc.dk/en/publications/mathematical-competencies-and-the-learning-of-mathematics-the-dan/
OEI (2015). Cosas de la educación. Costa Rica: Universia. https://oei.int/oficinas/secretaria-general/noticias/numero-221-junio-2015/
Padúa, G. J. D., & Casanueva, M. C. (2021). La imagen mental situada en un entorno o contexto dinámico. Ludus Vitalis, 29(55), 73–94. https://ludus-vitalis.org/ojs/index.php/ludus/article/view/948
Putri, A. A. A., Wajid, A., Irawan, R., & Usmiyatun, U. (2026). Development of RME-Based E-Modules with Ethnomathematics Integration to Improve Graphic to Symbolic Transformation Skills in Junior High School Mathematics. AL-ISHLAH: Jurnal Pendidikan, 18(2). https://journal.staihubbulwathan.id/index.php/alishlah/article/view/7546
Radford, L. (2008). The cultural-epistemological conditions of the emergence of algebraic symbolism. Educational Studies in Mathematics, 69(3), 215–233. https://www.researchgate.net/publication/251865870_THE_CULTURAL-EPISTEMOLOGICAL_CONDITIONS_OF_THE_EMERGENCE_OF_ALGEBRAIC_SYMBOLISM_1
Roque, V., Raposo, R., de Morais, N. S. N., & Roque, F. (2021). Enseñanza y aprendizaje en línea durante la pandemia de Covid-19: El caso de la educación superior pública portuguesa. Revista Prisma Social, (35), 221-248. https://revistaprismasocial.es/ps/article/view/4334
Ruamba, M. Y., Sukestiyarno, Y. L., Rochmad, & Asih, T. S. N. (2025). The Impact of Visual and Multimodal Representations in Mathematics on Cognitive Load and Problem-Solving Skills. International Journal of Advanced and Applied Sciences, 12(4), 164–172. https://doi.org/10.21833/ijaas.2025.04.018 https://www.science-gate.com/IJAAS/Articles/2025/2025-12-04/1021833ijaas202504018.pdf
Sagástegui, D. (2004). Una apuesta por la cultura: el aprendizaje situado. Sinéctica, Revista Electrónica de Educación, (24), 30–39. https://www.redalyc.org/pdf/998/99815918005.pdf
Schenck, K. E., & Nathan, M. J. (2024). Navigating spatial ability for mathematics education: A review and roadmap. Educational Psychology Review. https://doi.org/10.1007/s10648-024-09935-5
Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13. https://journals.sagepub.com/doi/10.3102/0013189X027002004
Urban Mathematics Education Journal of Urban Mathematics Education, Vol. 17(2), 2025. https://doi.org/10.21423/jume-v17i2 https://jume-ojs-tamu.tdl.org/jume/issue/view/39
Veschi, B. (2019). Etimología de Geometría. https://etimologia.com/geometria/
Weigand, H. G., Hollebrands, K., & Maschietto, M. (2025). Geometry education at secondary level–a systematic literature review. ZDM–Mathematics Education, 57(4), 829-843. https://link.springer.com/article/10.1007/s11858-025-01703-1
Yang, Y., Du, W., Mavrikis, M., & Geraniou, E. (2025). Spatial skill development through augmented reality in mathematics education: A scoping review. Digital Experiences in Mathematics Education, 1-34. https://link.springer.com/article/10.1007/s40751-025-00187-8
Zuazua, Y., & Rodríguez, R. (2002). Enseñar y aprender Matemáticas. Revista de Educación, 329, 239–256. https://dialnet.unirioja.es/servlet/articulo?codigo=498779
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