Specialized Knowledge of Prospective Secondary Mathematics Teachers in Developing Proof-Based Tasks

Authors

DOI:

https://doi.org/10.35763/aiem29.6735

Keywords:

Initial training, Mathematical proof, Secondary education, Specialized knowledge

Supporting Agencies

Universidad de Lima

Abstract

Proof is a fundamental activity in mathematics, and its integration across different educational levels, with appropriate approaches, is relevant. Engaging in proof-related activities enhances students’ mathematical understanding, making it crucial for prospective teachers to develop a deep knowledge of this practice. In this study, using a qualitative approach, we aim to understand the knowledge of three prospective secondary mathematics teachers as they engage in proof-related tasks. We identify their knowledge about specific proofs, proof as a mathematical practice, and the didactic aspects of proof. We highlight the recognition of proof as a practice that fosters mathematical learning by these future teachers and, in this regard, emphasize the importance of including proof in initial teacher education.

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References

Alfaro-Carvajal, C., Flores-Martínez, P., & Valverde-Soto, G. (2019). La demostración matemática: Significado, tipos, funciones atribuidas y relevancia en el conocimiento profesional de los profesores de matemáticas. Uniciencia, 33(2), 55–75. https://doi.org/10.15359/ru.33-2.5

Alfaro, C., Flores, P., & Valverde, G. (2020). Conocimiento especializado de profesores de matemática en formación inicial sobre aspectos lógicos y sintácticos de la demostración. PNA, 14(2), 85–117. https://doi.org/10.30827/pna.v14i2.9363

Alfaro-Carvajal, C., & Fonseca-Castro, J. (2024). Specialized knowledge of prospective mathematics teachers on the concept of mathematical proof. Uniciencia, 38(1), 1–16. https://doi.org/10.15359/ru.38-1.5

Balacheff, N. (2000). Procesos de prueba en los alumnos de matemáticas. Una empresa docente. https://hal.archives-ouvertes.fr/hal-00520133/document

Ball, D. L., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures. Paper presented at The 2009 Curtis Center Mathematics and Teaching Conference.

Bardin, L. (1998). L’analyse de contenu. Presses Universitaires de France.

Cabassut, R., Conner, A., İşçimen, F. A., Furinghetti, F., Jahnke, H. N., & Morselli, F. (2011). Conceptions of proof in research and teaching. En G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education (pp. 169–190). Springer. https://doi.org/10.1007/978-94-007-2129-6_7

Calle, E., Breda, A., & Font, V. (2023). Significados parciales del teorema de Pitágoras usados por docentes en la creación de tareas en el marco de un programa de formación continua. Uniciencia, 37(1), 1–23. https://doi.org/10.15359/ru.37-1.1

Carrillo, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., & Muñoz-Catalán, M. C. (2018). The mathematics teacher´s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–253. https://doi.org/10.1080/14794802.2018.1479981

Carrillo, J., Montes, M., & Climent, N. (2022). Investigación sobre el conocimiento especializado del profesor de matemáticas (MTSK): 10 años de camino. Dykinson.

Climent, N., & Montes, M. (2022). El modelo MTSK: Antecedentes y estructura. En J. Carrillo, M. A. Montes, & N. Climent (Eds.), Investigación sobre el conocimiento especializado del profesor de matemáticas (MTSK): 10 años de camino (pp. 27–34). Dykinson. https://doi.org/10.2307/j.ctv2zp4vp1.6

De Villiers, M. (1993). El papel y la función de la demostración en matemáticas. Épsilon: Revista de la Sociedad Andaluza de Educación Matemática “Thales”, 26, 15–30.

Delgado-Rebolledo, R., & Espinoza-Vásquez, G. (2019). El conocimiento del profesor de matemáticas sobre la demostración y sus roles en la enseñanza de las matemáticas. En J. M. Marbán, M. Arce, A. Maroto, J. M. Muñoz-Escolano, & Á. Alsina (Eds.), Investigación en Educación Matemática XXIII (pp. 253–262). SEIEM.

Duval, R. (2016). El funcionamiento cognitivo y la comprensión de los procesos matemáticos de la prueba. En R. Duval & A. Sáenz-Ludlow (Eds.), Comprensión y aprendizaje en matemáticas: perspectivas semióticas seleccionadas (pp. 95–125). Universidad Distrital Francisco José de Caldas.

Griffiths, P. A. (2000). Mathematics at the turn of the millennium. American Mathematical Monthly, 107(1), 1–14. https://doi.org/10.2307/2589372

Hanna, G., & De Villiers, M. (2008). ICMI Study 19: Proof and proving in mathematics education. ZDM, 40(2), 329–336. https://doi.org/10.1007/s11858-008-0073-4

Hanna, G., & De Villiers, M. (2011). Aspects of proof in mathematics education. En G. Hanna & M. De Villiers (Eds.), Proof and proving in mathematics education (pp. 1–10). Springer. https://doi.org/10.1007/978-94-007-2129-6_1

Lesseig, K. (2016). Investigating mathematical knowledge for teaching proof in professional development. International Journal of Research in Education and Science, 2(2), 253–270. https://doi.org/10.21890/ijres.13913

Martínez Recio, A. (2001). La demostración en matemática: Una aproximación epistemológica y didáctica. En M. F. Moreno, F. Gil, M. Socas, & J. D. Godino (Eds.), Investigación en educación matemática: Quinto Simposio de la Sociedad Española de Investigación en Educación Matemática (pp. 27–44). Autor.

Ministerio de Educación. (2016). Programa curricular de educación secundaria. http://www.minedu.gob.pe/curriculo/pdf/programa-curricular-educacion-secundaria.pdf

Morali, H. S., & Ahsen, F. (2023). Incorrect theorems and proofs: An analysis of pre-service mathematics teachers’ proof evaluation skills. Journal of Pedagogical Research, 7(3), 248–262. https://doi.org/10.33902/JPR.202318840

National Council of Teachers of Mathematics. (2003). Principios y estándares para la educación matemática (SAEM Thales, Trad.). SAEM Thales.

Schwarz, B., Leung, I. K. C., Buchholtz, N., Kaiser, G., Stillman, G., Brown, J., & Vale, C. (2008). Future teachers’ professional knowledge on argumentation and proof: A case study from universities in three countries. ZDM Mathematics Education, 40, 791–811. https://doi.org/10.1007/s11858-008-0150-8

Stake, R. E. (2005). Investigación con estudio de casos. Morata.

Stylianides, G. J., Stylianides, A. J., & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. En J. Cai (Ed.), Compendium for research in mathematics education (pp. 237–266). National Council of Teachers of Mathematics.

Stylianides, A. J., & Stylianides, G. J. (2022). Introducing students and prospective teachers to the notion of proof in mathematics. Journal of Mathematical Behavior, 66, Article 100957. https://doi.org/10.1016/j.jmathb.2022.100957

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Published

2026-04-30

How to Cite

Advíncula Clemente, E., Torres Cespedes, I., Delgado Rebolledo, R., & Hau Yon, F. (2026). Specialized Knowledge of Prospective Secondary Mathematics Teachers in Developing Proof-Based Tasks. Advances of Research in Mathematics Education, (29), 49–67. https://doi.org/10.35763/aiem29.6735

Issue

No. 29 (2026)

Section

Artículos

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Copyright (c) 2026 Elizabeth Advíncula Clemente, Isabel Torres Cespedes, Rosa Delgado Rebolledo, Flor Hau Yon

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