How do students determine the convergence of a numerical series? An analysis of their arguments

Authors

DOI:

https://doi.org/10.31637/epsir-2025-1197

Keywords:

argumentation, Toulmin's argumentative model, infinite numerical series, convergence, divergence, convergence criterion, comparison table, warrant and backing

Abstract

Introduction: The purpose of this work was to analyze the characteristics of students' arguments while solving mathematical tasks about the convergence or divergence of infinite numerical series.  Studying students' arguments allows us to review their reasoning and understanding of numerical series. Methodology: To study the students' arguments, Toulmin's argumentative model was used, which has been used in the study of different forms of argumentation and in multiple contexts. The research is qualitative in nature, for which comparison tables were built to analyze the structure of the arguments and characterize them. Results: Two activities of 3 infinite numerical series were applied for students to determine their convergence or divergence, written and audio data were collected with the answers and justifications. Discussions: The arguments include different elements than those established by Toulmin's model. Conclusions: Among the conclusions obtained, it was found that students base their argument on the criteria of convergence of the series, this constitutes their starting point to develop their argumentative process without considering, in many cases, the data present in the mathematical activity or task.

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Author Biographies

Alejandro Miguel Rosas Mendoza, Instituto Politécnico Nacional/CICATA-Legaria

Research professor at CICATA-Legaria of the IPN since 2004. Graduate in Mathematics from the Universidad Veracruzana. Master of Science from CINVESTAV-IPN. Doctor in Educational Mathematics from the CICATA-Legaria of the IPN. Teaching experience since 1990 as a mathematics teacher in institutions such as the National Polytechnic Institute, the Technological Institute of Higher Studies of Monterrey, the Metropolitan Autonomous University, the Veracruzana University, and the College of High School Students of the State of Veracruz. He has directed research projects for the National Polytechnic Institute, ITESM, CFE, CONAHCYT, Iusacell.

Luis Fernando Ramírez Oviedo, Distance State University

Academic and researcher at the Universidad Estatal a Distancia, with more than 12 years of experience in university teaching. Currently chair coordinator for the Mathematics Teaching career. Member of the Costa Rican Mathematics Olympiad Commission. With studies in Mathematics Teaching from the University of Costa Rica, Master in Education and New Technologies from UDIMA, Spain. Master's Degree in Educational Mathematics at the Research Center for Applied Science and Advanced Technology of the National Polytechnic Institute of Mexico. He has presented presentations and workshops at national and international events. Author of university texts, articles in academic journals, articles in international conference proceedings and author of chapters in international books

Juan Gabriel Molina Zavaleta, Instituto Politécnico Nacional/CICATA-Legaria

Master of Science with Specialization in Educational Mathematics from the Center for Research and Advanced Studies of the IPN (CINVESTAV-IPN). He has been a professor-researcher in the Master of Science in Educational Mathematics Program belonging to CICATA-IPN from 2004 to date. He is the author of articles and book chapters published in various magazines and publishing houses

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Published

2025-01-30

How to Cite

Rosas Mendoza, A. M., Ramírez Oviedo, L. F., & Molina Zavaleta, J. G. (2025). How do students determine the convergence of a numerical series? An analysis of their arguments. European Public & Social Innovation Review, 10, 1–18. https://doi.org/10.31637/epsir-2025-1197

Issue

Vol. 10 (2025)

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Copyright (c) 2025 Alejandro Miguel Rosas Mendoza, Luis Fernando Ramírez Oviedo, Juan Gabriel Molina Zavaleta

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