A study on the representations and generalization strategies of numerical sequences among secondary school students

Yasmin Cruz Hernández; José Antonio Juárez López; Carolina Napp Avelli; Lizzet Morales García

doi:10.29333/ejmste/17830

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Yasmin Cruz Hernández ¹ ^* , José Antonio Juárez López ¹ , Carolina Napp Avelli ² , Lizzet Morales García ¹

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¹ Meritorious Autonomous University of Puebla, Puebla, MEXICO² University of Maryland, College Park, MD, USA^* Corresponding Author

Abstract

Algebraic thinking in secondary education has been widely studied through the exploration of patterns. This study aimed to identify the representations developed by secondary school students to express a numerical sequence and to describe the strategies they employed for its generalization. To this end, a questionnaire was administered to 25 students aged 14 to 15, who were asked to represent four different numerical sequences. The results revealed four levels of representation: pre-structural, emerging, partially structured, and fully structured. Similarly, it was found that the strategies varied according to the type of task. In immediate and near generalization, students primarily relied on counting and additive operations, whereas in distant generalization, the strategies diversified, with the correspondence strategy being the most frequently used. Finally, it was evident that the representations produced by the students themselves served as an essential resource that facilitated the construction of their generalizations.

Keywords

figurative patterns
numerical sequences
generalization
strategies

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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 22, Issue 2, February 2026, Article No: em2776

https://doi.org/10.29333/ejmste/17830

Publication date: 03 Feb 2026

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Article Downloads: 11

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APA

Cruz Hernández, Y., Juárez López, J. A., Napp Avelli, C., & Morales García, L. (2026). A study on the representations and generalization strategies of numerical sequences among secondary school students. Eurasia Journal of Mathematics, Science and Technology Education, 22(2), em2776. https://doi.org/10.29333/ejmste/17830

Vancouver

Cruz Hernández Y, Juárez López JA, Napp Avelli C, Morales García L. A study on the representations and generalization strategies of numerical sequences among secondary school students. EURASIA J Math Sci Tech Ed. 2026;22(2):em2776. https://doi.org/10.29333/ejmste/17830

AMA

Cruz Hernández Y, Juárez López JA, Napp Avelli C, Morales García L. A study on the representations and generalization strategies of numerical sequences among secondary school students. EURASIA J Math Sci Tech Ed. 2026;22(2), em2776. https://doi.org/10.29333/ejmste/17830

Chicago

Cruz Hernández, Yasmin, José Antonio Juárez López, Carolina Napp Avelli, and Lizzet Morales García. "A study on the representations and generalization strategies of numerical sequences among secondary school students". Eurasia Journal of Mathematics, Science and Technology Education 2026 22 no. 2 (2026): em2776. https://doi.org/10.29333/ejmste/17830

Harvard

Cruz Hernández, Y., Juárez López, J. A., Napp Avelli, C., and Morales García, L. (2026). A study on the representations and generalization strategies of numerical sequences among secondary school students. Eurasia Journal of Mathematics, Science and Technology Education, 22(2), em2776. https://doi.org/10.29333/ejmste/17830

MLA

Cruz Hernández, Yasmin et al. "A study on the representations and generalization strategies of numerical sequences among secondary school students". Eurasia Journal of Mathematics, Science and Technology Education, vol. 22, no. 2, 2026, em2776. https://doi.org/10.29333/ejmste/17830