Design and implementation of a task sequence for teaching homothety

Yenifer Aguilera Moraga; Paula Verdugo-Hernández; Jessica Gatica

doi:10.29333/ejmste/16540

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Yenifer Aguilera Moraga ¹ , Paula Verdugo-Hernández ² ^* , Jessica Gatica ³

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¹ Pedagogía en Educación Media en Matemática y Física, Universidad de Talca, Linares, CHILE² Escuela de Pedagogía en Ciencias Naturales y Exactas, Facultad de Ciencias de la Educación, Universidad de Talca, Linares, CHILE³ Instituto de Matemáticas, Universidad de Talca, Linares, CHILE^* Corresponding Author

Abstract

The teaching of geometry in Chile faces several challenges, as evidenced by the low performance of students in international assessments. In particular, the concept of homothety is impacted by teaching methodologies that emphasize rote memorization and procedural repetition rather than conceptual understanding. This study explores how a task sequence fosters mathematical work with the concept of homothety among 15- to 16-year-old students in a public high school in the Maule Region of Chile. Grounded in the mathematical working space (MWS) theory, this research provides a framework for analyzing how students engage with mathematical tasks. Employing a qualitative approach, specifically a case study, the findings reveal that the task sequence contributes to progressive mathematical reasoning. The study concludes that the designed activities align with the criteria for “emblematic tasks”, evidencing their fundamental role in supporting students’ conceptual understanding of homothety.

Keywords

teaching
task design
homothety
mathematical work
personal MWS

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 6, June 2025, Article No: em2656

https://doi.org/10.29333/ejmste/16540

Publication date: 24 Jun 2025

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Article Downloads: 12

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How to cite this article

APA

Aguilera Moraga, Y., Verdugo-Hernández, P., & Gatica, J. (2025). Design and implementation of a task sequence for teaching homothety. Eurasia Journal of Mathematics, Science and Technology Education, 21(6), em2656. https://doi.org/10.29333/ejmste/16540

Vancouver

Aguilera Moraga Y, Verdugo-Hernández P, Gatica J. Design and implementation of a task sequence for teaching homothety. EURASIA J Math Sci Tech Ed. 2025;21(6):em2656. https://doi.org/10.29333/ejmste/16540

AMA

Aguilera Moraga Y, Verdugo-Hernández P, Gatica J. Design and implementation of a task sequence for teaching homothety. EURASIA J Math Sci Tech Ed. 2025;21(6), em2656. https://doi.org/10.29333/ejmste/16540

Chicago

Aguilera Moraga, Yenifer, Paula Verdugo-Hernández, and Jessica Gatica. "Design and implementation of a task sequence for teaching homothety". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 6 (2025): em2656. https://doi.org/10.29333/ejmste/16540

Harvard

Aguilera Moraga, Y., Verdugo-Hernández, P., and Gatica, J. (2025). Design and implementation of a task sequence for teaching homothety. Eurasia Journal of Mathematics, Science and Technology Education, 21(6), em2656. https://doi.org/10.29333/ejmste/16540

MLA

Aguilera Moraga, Yenifer et al. "Design and implementation of a task sequence for teaching homothety". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 6, 2025, em2656. https://doi.org/10.29333/ejmste/16540