Research Activities With Irrational Numbers in Classes With Principles of Lesson Study
DOI:
https://doi.org/10.35763/aiem30.7928Keywords:
Class study, Irrational number, Mathematics teaching, Research activities, Teacher trainingAbstract
The research focuses on identifying the contributions of Lesson Study (LS) to the conceptualization of irrational numbers among eighth-grade students aged between 13 and 15 years. The activity is carried out within a Semillero group, an extracurricular academic space in which research activities are conducted as part of the initial and ongoing training of mathematics teachers. The methodology adopts an interpretative approach, based on the analysis of experiences and meanings constructed by the participants. The results show that LS promotes collective reflection on lesson planning as well as negotiation and support in the design of investigative tasks that generate collaborative learning environments through argumentation and problem solving. These investigative tasks, being open-ended, non-directive, and challenging, change the dynamics of the mathematics classroom, fostering the learning of abstract concepts such as irrational numbers.
References
Assis, A. (2012). A produção de significados matemáticos em um contexto de aulas exploratório-investigativas [Teses de doutorado, Universidade Federal de Minas]. https://repositorio.ufmg.br/handle/1843/BUOS-96CGHT
Baldin, Y. (2009). O significado da introdução da metodologia japonesa de lesson study nos cursos de capacitação de professores de matemática no Brasil [Ponencia de congresso]. XVIII Encontro Anual da SBPN e Simpósio Brasil-Japão. SBPN.
Becerra, H. M. y Font, V. (2019). Las problemáticas semióticas y la metáfora en las representaciones de los conjuntos infinitos. Acta Latinoamericana de Matemática Educativa, 32(1), 531–540.
Breda, A., Font, V., Lima, V. M. R. y Pereira, M. V. (2018). Componentes e indicadores de los criterios de idoneidad didáctica desde la perspectiva del enfoque ontosemiótico. Transformación, 14(2), 162–176.
Breda, A., Hummes, V., Silva, R. y Sánchez, A. (2021). El papel de la fase de observación de la implementación en la metodología estudio de clases. Bolema, 35(69), 263–288, https://doi.org/10.1590/1980-4415v35n69a13
Cavalcanti Moreira, P. (2004). O conhecimento matemático do professor: Formação na licenciatura e prática docente na escola básica [Tese de Doutorado, Universidade Federal de Minas Gerais]. https://repositorio.ufmg.br/bitstream/1843/EABA-6ABMUH/1/2000000078.pdf
Corbetta, P. (2010). Metodología y técnicas de investigación social. McGraw-Hill.
D’Amore, B. (2006). Didáctica de la Matemática. Editorial Magisterio.
Elliot, J. (2015). Lesson y learning study y la idea del docente como investigador. Revista Interuniversitaria de Formación del Profesorado, 29(3), 29–46. https://www.redalyc.org/pdf/274/27443871003.pdf
Ernest, P. (1991). The philosophy of mathematics education. Routledge Falmer – Taylor & Francis Group.
Ferraz, A. y Sasseron, L. (2017). Propósitos epistêmicos para a promoção da argumentação em aulas investigativas. Investigações em Ensino de Ciências, 22(1), 42–60. https://doi.org/10.22600/1518-8795.ienci2017v22n1p42
Font, V., Calle, E. y Breda, A. (2023). Uso de los criterios de idoneidad didáctica y la metodología lesson study en la formación del profesorado de matemáticas en España y Ecuador. Paradigma, 44, 376–397.
Glaser, B. y Strauss, A. (1967). Strategies for qualitative research. Aldine.
Gómez, L. E., Mueriel, L. E. y Londoño, D. A. (2019). El papel del docente para el logro de un aprendizaje significativo apoyado en las TIC. Encuentros, 17(2), 118–131. https://www.redalyc.org/journal/4766/476661510011/html/
Hummes, V., Breda, A., Seckel, M. y Font, V. (2020). Criterios de idoneidad didáctica en una clase basada en el lesson study. Praxis y Saber, 11(26), 1–14. https://doi.org/10.19053/22160159.v11.n26.2020.10667
Jiménez, A. (2002). Quando professores de matemática da escola e da universidade se encontram: (Re)significação e reciprocidade de saberes [Tesis doctoral, Universidade Estadual de Campinas]. http://repositorio.unicamp.br/jspui/handle/REPOSIP/253213
Jiménez, A., Font, V., Suárez, Z., Díaz, M., Leguizamón, J., Álvarez, A., Calle, E., Sánchez, A., Breda, A. y Morales, L. (2022). Hacia la transformación de la clase de matemáticas: Algunas perspectivas. UPTC. https://doi.org/10.19053/9789586606608
Lee, L. H. J. y Tan, S. C. (2020). Teacher learning in lesson study: Affordances, disturbances, contradictions, and implications. Teaching and Teacher Education, 89, 102986. https://doi.org/10.1016/j.tate.2019.102986
Limas, L. y Jiménez, A. (2017). Actividades exploratorio investigativas en clase de matemáticas. Eco matemático, 8(1), 93–105.
Lourido, D. M. (2020). Análisis exploratorio de los elementos semiótico-cognitivos vinculados a la enseñanza de los números irracionales [Trabajo de Maestría, Universidad Nacional de Colombia]. https://repositorio.unal.edu.co/handle/unal/78934
Maulana, R., Bruscato, A. M., Helms-Lorenz, M., Irnidayanti, Y., de Jager, T., Galindev, U., Adiyasuren, A., Shahzad, A., Fadhilah, N., Chun, S., Lee, O., Coetzee, T. y Moorer, P. (2023). Secondary education teachers’ effective teaching behaviour across five countries: Does it change over time? En R. Maulana, M. Helms-Lorenz y R. M. Klassen (Eds.), Effective teaching around the world (pp. 361–398). Springer. https://doi.org/10.1007/978-3-031-31678-4_17
Melo, N. (2020). Investigações matemáticas na sala de aula dos autores: João Pedro da Ponte; Joana Brocardo e Helia Oliveira. Ensino da Matemática em Debate, 7(2), 303–307. https://doi.org/10.23925/2358-4122.2020v7i2p261-265
Ministerio de Educación Nacional. (2006). Estándares básicos de competencias en matemáticas.
Murata, A. (2011). Introduction: Conceptual overview of lesson study. En L. C. Hart, A. S. Alston y A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 1–12). Springer.
Oliveira, T. y Fiorentini, D. (2009). Explorando o sentido de número irracional no ensino fundamental. En D. L. Carvalho y K. C. Conti (Orgs.), Histórias de colaboração e investigação na prática pedagógica em matemática: Ultrapassando os limites da sala de aula (1.ª ed., pp. 131–148). Alínea.
Pereira, S., Miranda, S. y Carvalho, P. (2018). O ensino de ciências por investigação: Abordagem em publicações recentes. Revista Sapiência: Sociedade, Saberes e Práticas Educacionais, 7(2), 288–304.
Ponte, J. P. (2010). Explorar e investigar em matemática: Uma atividade fundamental no ensino e na aprendizagem. Revista Iberoamericana de Educación Matemática, 21, 13–30. https://www.revistaunion.org/index.php/UNION/article/view/1034/730
Ponte, J. P. (2022). Estudos de aula na formação de professores de Matemática [Conferencia]. III Congreso Internacional de Educaciones, Pedagogías y Didácticas. Universidad Pedagógica y Tecnológica de Colombia.
Ponte, J. P., Quaresma, M. y Mata-Pereira, J. (2023). Prospective mathematics teachers’ views of their learning in a lesson study. PNA, 17(2), 117–136. https://doi.org/10.30827/pna.v17i2.23896
Reina, L. y Wilhelmi, M. (2021). El problema didáctico del reconocimiento de los números irracionales en educación secundaria. En A. Y. Soto Lazcano y L. Suárez Téllez (Coords.), Repensar las didácticas específicas. Una aportación multidisciplinaria a la enseñanza especializada (pp. 79–103). Red de Investigadores Educativos Chihuahua.
Salas-Solano, B. y Valverde-Soto, G. (2025). Articulación del modelo del conocimiento especializado del docente de matemática (MTSK) y el estudio de clase (lesson study): Oportunidades para la formación del profesorado de matemáticas. Revista Actualidades Investigativas en Educación, 25(1), 1–27. https://doi.org/10.15517/aie.v25i1.60756
Schön, D. (1992). La formación de profesionales reflexivos. Hacia un nuevo diseño de la enseñanza y el aprendizaje en las profesiones. Paidós.
Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. En D. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 495–511). MacMillan.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Alfonso Jiménez Espinosa, Leidy Johana Limas Berrio, Yudy Alexandra Molina Hurtado

This work is licensed under a Creative Commons Attribution 4.0 International License.
The articles published in this journal are under a license Creative Commons: By 4.0 España from number 21 (2022).
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and keep the acknowledgement of authorship.
- The texts published in this journal are – unless indicated otherwise – covered by the Creative Commons Attribution 4.0 international licence. You may copy, distribute, transmit and adapt the work, provided you attribute it (authorship, journal name, publisher) in the manner specified by the author(s) or licensor(s). The full text of the licence can be consulted here: http://creativecommons.org/licenses/by-nc/4.0.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).


