Pre-service teachers’ mathematical work on a calculus task that connects school and university

Romina Menares-Espinoza; Jorge Gaona; Carolina Henríquez-Rivas

doi:10.29333/ejmste/16861

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Romina Menares-Espinoza ¹ ^* , Jorge Gaona ² , Carolina Henríquez-Rivas ³

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¹ Facultad de Ciencias, Universidad de Valparaíso, Valparaíso, CHILE² Facultad de Ciencias de la Educación, Universidad de Playa Ancha, Valparaíso, CHILE³ Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca, CHILE^* Corresponding Author

Abstract

This paper addresses the issue of the gap that exists between the mathematics studied in initial teacher training and the school mathematics that the in-service teacher must teach. We present empirical results on how pre-service teachers (PTs) activate and coordinate cognitive processes and epistemological aspects when solving a university mathematic task that can be solved in the calculus domain. This task can likewise be adapted to the school level. This study is based on the theory of mathematical working spaces (MWS). The results examine the differentiation of the MWS of the participants according to the dynamics present between the problem-solving processes used in the task. The study’s conclusion explores the possibilities offered by the task in terms of enriching the MWS of PTs and contributing to the shrinking of the mathematical gap that exists between the university and the school.

Keywords

mathematical working spaces
initial teacher training
tasks design
calculus
university mathematics
school mathematics

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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 9, September 2025, Article No: em2702

https://doi.org/10.29333/ejmste/16861

Publication date: 03 Sep 2025

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APA

Menares-Espinoza, R., Gaona, J., & Henríquez-Rivas, C. (2025). Pre-service teachers’ mathematical work on a calculus task that connects school and university. Eurasia Journal of Mathematics, Science and Technology Education, 21(9), em2702. https://doi.org/10.29333/ejmste/16861

Vancouver

Menares-Espinoza R, Gaona J, Henríquez-Rivas C. Pre-service teachers’ mathematical work on a calculus task that connects school and university. EURASIA J Math Sci Tech Ed. 2025;21(9):em2702. https://doi.org/10.29333/ejmste/16861

AMA

Menares-Espinoza R, Gaona J, Henríquez-Rivas C. Pre-service teachers’ mathematical work on a calculus task that connects school and university. EURASIA J Math Sci Tech Ed. 2025;21(9), em2702. https://doi.org/10.29333/ejmste/16861

Chicago

Menares-Espinoza, Romina, Jorge Gaona, and Carolina Henríquez-Rivas. "Pre-service teachers’ mathematical work on a calculus task that connects school and university". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 9 (2025): em2702. https://doi.org/10.29333/ejmste/16861

Harvard

Menares-Espinoza, R., Gaona, J., and Henríquez-Rivas, C. (2025). Pre-service teachers’ mathematical work on a calculus task that connects school and university. Eurasia Journal of Mathematics, Science and Technology Education, 21(9), em2702. https://doi.org/10.29333/ejmste/16861

MLA

Menares-Espinoza, Romina et al. "Pre-service teachers’ mathematical work on a calculus task that connects school and university". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 9, 2025, em2702. https://doi.org/10.29333/ejmste/16861