Didactic transposition as a field in the arithmetic-algebra transition: A systematic review
DOI:
https://doi.org/10.15359/ree.30-1.20123Keywords:
Mathematical education, field approach, didactic transposition, arithmetic-algebra transition, SDG 4, quality education, educational processAbstract
Objective. To analyze the academic production related to the transition from arithmetic to algebra in primary and secondary schools from the perspective of didactic transposition. Methodology. To achieve this objective, a systematic literature mapping was developed to obtain a structured overview of the academic production related to the object of study. The search was conducted in Scopus, Web of Science, and ScienceDirect, considering the period 2014–2024. Inclusion and exclusion criteria were applied, and qualitative techniques such as coding and thematic categorization were used. The documents were systematized using a Structured Analysis Grid (SAG) for subsequent synthesis and interpretation. Results. A diversity of pedagogical and didactic approaches aimed at facilitating the transition from arithmetic to algebra through didactic transposition was identified. However, a significant gap was evident in the conceptualization of didactic transposition as a structured field of power relations, knowledge, and discourse within the educational sphere. Discussion and conclusions. Recognizing didactic transposition as a field allows us to understand how teaching discourses and practices shape educational dynamics in different contexts. This approach broadens our understanding of educational transitions and opens lines of research focused on the critical analysis of pedagogical practices and teacher training.
Downloads
References
*Barallobres, G. (2017). Ciertos fenómenos didácticos que caracterizan las dificultades de aprendizaje en la transición de la aritmética al álgebra en la escuela secundaria. Unión. Revista Iberoamericana de Educación Matemática, (51), 27-47. https://www.revistaunion.org/index.php/UNION/article/view/384/197
*Bazzul, J. & Carter, L. (2017). (Re)considering Foucault for science education research: Considerations of truth, power and governance. Cultural Studies of Science Education, 12(2), 435-452. https://doi.org/10.1007/s11422-016-9800-2
*Beltrán Véliz, J., Navarro Aburto, B., & Peña Troncoso, S. (2018). Prácticas que obstaculizan los procesos de transposición didáctica en escuelas asentadas en contextos vulnerables: Desafíos para una transposición didáctica contextualizada. Revista Educación, 42(2), 1-19. https://doi.org/10.15517/revedu.v42i2.27571
*Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I., Gardiner, A. M., Stroud, R., Stylianou, N., Fonger, N. L., & Stylianou, D. (2018). Implementing a framework for early Aalgebra Implementing a Framework for Early Algebra 1. En C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds. The global evolution of an emerging field of research and practice (pp. 27-49). Springer. https://doi.org/10.1007/978-3-319-68351-5_2
Bordieu, P. & Passeron, J.-C. (1979). La reproducción. Elementos para una teoría del sistema de enseñanza. Editorial Laia.
Bourdieu, P. (1969). Campo de poder, campo intelectual. Montressor Jungla Simbólica.
*Castellanos, M. T., Flores, P., & Moreno, A. (2017). Reflexión de futuros profesores de matemáticas sobre problemas profesionales relacionados con la enseñanza del álgebra escolar. Bolema: Boletim de Educação Matemática, 31(57), 408-429. https://doi.org/10.1590/1980-4415V31N57A20
Chevallard, Y. (1997). La transposición didáctica: Del saber sabio al saber enseñado. Aique.
*Cortés-Tujano, L. O. & Toro-Uribe, J. A. (2024). Álgebra y argumentación: Desafíos para la investigación en educación matemática. Pedagogía y Saberes, (60), 192-206. https://doi.org/10.17227/PYS.NUM60-18627
Foucault, M. (1970). La arqueologia del saber. Siglo XXI. https://monoskop.org/images/b/b2/Foucault_Michel_La_arqueologia_del_saber.pdf
Foucault, M. (2005). El orden del discurso. Fabula TusQuets Editores.
*Furman, C. E. (2020). Interruptions: Cultivating Truth-Telling as resistance with pre-service teachers. Studies in Philosophy and Education, 39(1), 1-17. https://doi.org/10.1007/s11217-019-09681-0
*González, J. R. & Hidalgo-Herrero, M. (2022). Transposição didática no ensino da geometria em Espanha durante a década de 1960. Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 24(2), 433-464. https://doi.org/10.23925/1983-3156.2022V24I2P433-464
*Guzmán Valeta, A. M., Torres Díaz, G. A., Mendoza, Y. F., & de la Hoz Escorcia, S. M. (2021). Transposición didáctica y la perspectiva crítica de Pablo Freire. Encuentros, 13, 168-176. https://doi.org/10.5281/ZENODO.4395248
*Hallworth, D. J. (2024). Deconstructing the problematisation of challenging behaviour in primary schools. Education 3-13, 52(3), 313-327. https://doi.org/10.1080/03004279.2022.2089712
*Hausberger, T. (2018). Structuralist praxeologies as a research program on the teaching and learning of abstract algebra. International Journal of Research in Undergraduate Mathematics Education, 4, 74-93. https://doi.org/10.1007/s40753-017-0063-4
*Hausberger, T. & Jovignot, J. (2024). The challenge of structuralist thinking in abstract algebra: A transition problem. International Journal of Mathematical Education in Science and Technology, 1-23. https://doi.org/10.1080/0020739X.2024.2311284
*Hitt, F., Quiroz, S., Saboya, M. & Lupiáñez, J. L. (2023). Une approche socioculturelle pour la construction d'habiletés de généralisation arithmético-algébriques dans les écoles québécoises et mexicaines. Educación MatEMática, 35(3), 112-150. https://doi.org/10.24844/EM3503.04
Kaput, J. J. (2008). What Is algebra? What is algebraic reasoning? En J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds), Algebra in the Early Grades (pp. 5-17). Taylor & Francis. https://doi.org/10.4324/9781315097435-2
*Knijnik, G. (2023). Numeracy, vulnerability, ethics and social justice. Adults Learning Mathematics, 17(1), 59-69. https://files.eric.ed.gov/fulltext/EJ1410160.pdf
La Madriz, J. J. (2010). Discusión reflexiva: Entre las concepciones del saber docente, y el proceso de transposición didáctica. SAPIENS, 11(1), 79-96. http://ve.scielo.org/scielo.php?script=sci_arttext&pid=S1317-58152010000100006&lng=es&nrm=iso&tlng=es
*Martínez Suárez, M. D. & Romero Díaz, T. (2019). Transición de la aritmética al álgebra: Un estudio con estudiantes universitarios de Nicaragua. Revista Electrónica de Conocimientos, Saberes y Prácticas, 2(2), 29-39. file:///Users/liana/Downloads/william_flores,+Transicio%CC%81n.pdf
*Mejía Osorio, G. (2021). Representaciones semióticas de objetos matemáticos y articulación de sentidos en situaciones de tratamiento. El caso de los profesores de matemáticas [Tesis doctoral, Universidad Distrital Francisco José de Caldas]. http://enfoqueontosemiotico.ugr.es/tesis/Mejia_2021_Tesis.pdf
*Montecino, A. & Andrade-Molina, M. (2024). Unpacking discourses about the transition from school to university mathematics: An intensive reading. En Educational Studies in Mathematics (Vol. 117, 341-356). https://doi.org/10.1007/s10649-023-10288-z
*Mutodi, P. & Mosimege, M. (2021). Learning mathematical symbolization: Conceptual challenges and instructional strategies in secondary schools. Bolema: Boletim de Educação Matemática, 35(70), 1180-1199. https://doi.org/10.1590/1980-4415v35n70a29
*Peñaloza Tello, M. L. & Quiceno Castrillón, H. (2016). El campo de la evaluación en Colombia. Editorial Bonaventuriana.
*Perafán Echeverri, G. A. (2013). La transposición didáctica como estatuto epistemológico fundante de los saberes académicos del profesor. Folios, (37), 83-93. https://doi.org/10.17227/01234870.37folios83.93
*Pereira, J. C. S. de, Nunes, J. M. V., Matos, F. C. de, & Almouloud, S. A. (2023). Transición de la aritmética al álgebra a la luz de las ideas de Yves Chevallard. Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 25(1), 430-454. https://revistas.pucsp.br/index.php/emp/article/view/61669/42091
*Pereira, J. C, S. de, Silva, F. H. S. de, & Nunes, J. M. V. (2017). Análise de narrativas praxeológicas de conexões entre aritmética e álgebra. Amazônia: Revista de Educação em Ciências e Matemáticas, 13(27), 87-106. https://doi.org/10.18542/amazrecm.v13i27.4228
Petersen, K., Feldt, R., Mujtaba, S., & Mattsson, M. (2008). (PDF) Systematic mapping studies in software engineering. 12th International Conference on Evaluation and Assessment in Software Engineering (EASE). https://doi.org/10.14236/ewic/EASE2008.8
*Planas, N. & Alfonso, J. M. (2023). Secondary-school teachers’ noticing of aspects of mathematics teaching talk in the context of one-day workshops. The Journal of Mathematical Behavior, 71, 101084. https://doi.org/10.1016/j.jmathb.2023.101084
*Pliego-Pastrana, P., Rondero-Guerrero, C., Tetlalmatzi-Montiel, M., & Castillo-Gálvez, A. M. (2022). Articulación de saberes matemáticos en el álgebra: Transición de lo concreto a lo abstracto., 10, 127-133. Pädi Boletín Científico de Ciencias Básicas e Ingenierías del ICBI 10(Especial), 127-133. https://repository.uaeh.edu.mx/revistas/index.php/icbi/article/view/8324/8798
*Ramos Palacios, L. A., Guifarro, M. I,, & Casas García, L. M. (2021). Dificultades en el aprendizaje del álgebra, un estudio con pruebas estandarizadas. Bolema: Boletim de Educação Matemática, 35(70), 1016-1033. https://doi.org/10.1590/1980-4415v35n70a21
*Rytzler, J. (2019). Turning the gaze to the self and away from the self – Foucault and Weil on the matter of education as attention formation. Ethics and Education, 14(3), 285-297. https://doi.org/10.1080/17449642.2019.1617452
*Scheiner, T., Godino, J. D., Montes, M. A., Pino-Fan, L. R., & Climent, N. (2022). On metaphors in thinking about preparing mathematics for teaching: In memory of José (“Pepe”) Carrillo Yáñez (1959-2021). Educational Studies in Mathematics, 111(2), 253-270. https://doi.org/10.1007/s10649-022-10154-4
*Silveira, M. R. A. da (2017). Compreensão da matemática no uso de símbolos e da gramática. Revista Guillermo de Ockham, 15(1), 51-57. https://doi.org/10.21500/22563202.3190
*Sousa, R. T. de, Alves, F. R. V., & Souza, M. J. A. (2022). Geogebra 3D en la enseñanza de las cuadráticas: Posibilidades de transposición didáctica a través de la visualización geométrica. Revista Electrónica de Investigación en Educación en Ciencias, 17(1), 22-34. https://doi.org/10.54343/REIEC.V17I1.297
*Valenzuela García, J. & Gutiérrez Marfileño, V. E. (2018). Desarrollo del pensamiento algebraico en estudiantes de bachillerato a través de la generalización visual de sucesiones de figuras. Educación Matemática, 30(2), 49-72. https://doi.org/10.24844/EM3002.03
*Valiero, E., Barrionuevo, M., & Villenas, F. (2021). Ordenamiento de los regisros semióticos en la didáctica del álgebra en la escuela secundaria. Correspondencia con la enseñanza de expresiones algebraicas racionales. Educación Matemática, 33(2), 173-204. https://doi.org/10.24844/EM3302.07
*Valverde-Riascos, O. O. & Díaz-Castellar, A. A. (2021). Tendencias de estudios sobre los saberes previos, las estrategias metacognitivas y la transformación semiótica en la resolución de problemas algebraicos. Revista UNIMAR, 39(2), 206-230. https://dialnet.unirioja.es/ejemplar/592166
*Yepes Montoya, A. M. & Mosquera Suárez, C. J. (2020). La formación de profesores de matemáticas a partir del desarrollo del conocimiento didáctico del contenido matemático: Experiencia para la innovación en la enseñanza del concepto de variable en el álgebra escolar. Asociación Colombiana Para La Investigación En Educación En Ciencias y Tecnología. EDUCyt, 11(Extra), 1317-1328. https://die.udistrital.edu.co/revistas/index.php/educyt/article/view/133/126
*Zapata Zapata, V., Quintriqueo Millán, S., & Valdebenito Zambrano, V. (2022). Kimeltuwün en la transposición didáctica como marcode análisis de prácticas pedagógicas en microcentros rurales de la Araucanía. Diálogo Andino, (67), 42-54. https://www.scielo.cl/pdf/rda/n67/0719-2681-rda-67-42.pdf
*Zapatera Linares, A. (2022). La generalización de patrones como herramienta para introducir el pensamiento algebraico en educación primaria. Educación Matemática, 34(2), 134-152. https://doi.org/10.24844/em3402.05
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2026 Victoria Alejandra García-Fajardo, Diana Carolina Burbano-González
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License.
1. In case the submitted paper is accepted for publication, the author(s) FREELY, COSTLESS, EXCLUSIVELY AND FOR AN INDEFINITE TERM transfer copyrights and patrimonial rights to Universidad Nacional (UNA, Costa Rica). For more details check the Originality Statement and Copyright Transfer Agreement
2. REUTILIZATION RIGHTS: UNA authorizes authors to use, for any purpose (among them selfarchiving or autoarchiving) and to publish in the Internet in any electronic site, the paper´'s final version, both approved and published (post print), as long as it is done with a non commercial purpose, does not generate derivates without previous consentment and recognizes both publisher's name and authorship.
3. The submission and possible publication of the paper in the Educare Electronic Journal is ruled by the Journal’s editorial policies, the institutional rules of Universidad Nacional and the laws of the Republic of Costa Rica. Additionally, any possible difference of opinion or future dispute shall be settled in accordance with the mechanisms of Alternative Dispute Resolution and the Costa Rican Jurisdiction.
4. In all cases, it is understood that the opinions issued are those of the authors and do not necessarily reflect the position and opinion of Educare, CIDE or Universidad Nacional, Costa Rica. It is also understood that, in the exercise of academic freedom, the authors have carried out a rogorous scientific-academic process of research, reflection and argumentation thar lays within the thematic scope of interest of the Journal.
5. The papers published by Educare Electronic Journal use a Creative Commons License:
The articles published by Educare Electronic Journal can be shared with a Creative Commons License: 
