Application of the ontosemiotic approach and its impact on the study of the Collatz conjecture
DOI:
https://doi.org/10.70939/revistadiged.v2i2.39Keywords:
Collatz conjecture, ontosemiotic approach, mathematics educationAbstract
OBJECTIVE: To evaluate the impact of applying the ontosemiotic approach in the teaching of the Collatz Conjecture to students in the Bachelor's Degree in Mathematics and Physics Education, with the goal of improving their understanding and skills in handling complex mathematical concepts. METHOD: A mixed-method approach was adopted, integrating quantitative and experimental methods, using cognitive epistemic configurations for data collection and analysis. This approach enabled a deep integration of the principles of the ontosemiotic approach with complexity sciences, facilitating a detailed assessment of the learning process. RESULTS: The analyzed data show a significant improvement in the students' ability to interact with mathematical symbols, interpret semiotic representations, and evolve in their understanding of abstract concepts. This evidence supports the effectiveness of the ontosemiotic approach in constructing solid mathematical knowledge. CONCLUSION: The study concludes that the ontosemiotic approach is a powerful tool for addressing complex mathematical problems, providing new insights into the construction of mathematical knowledge and cognitive interaction. It is recommended to integrate this approach more extensively into mathematics curricula to maximize its educational benefits and explore its applicability in other academic contexts.
References
Gleick, J. (1987). Caos: La creación de una ciencia. Penguin Books.
Gil, A. (2022, febrero 13). La conjetura de Collatz. https://temat.es/article/download/2022-p65/2022-p65-pdf/176
Godino, J. D., Batanero, C., Burgos, M., & Gea, M. M. (2021). Una perspectiva ontosemiótica de los problemas y métodos de investigación en educación matemática. Revemop, 3, e202107. https://doi.org/10.33532/revemop.e202107 DOI: https://doi.org/10.33532/revemop.e202107
Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema, 31(57), 90–113. https://doi.org/10.1590/1980-4415v31n57a05 DOI: https://doi.org/10.1590/1980-4415v31n57a05
Guerrero, L., & Falk, M. (2023). Una mirada a la teoría de representaciones semióticas de Duval desde el pensamiento manifestado por participantes de olimpiadas colombianas de Matemáticas. South Florida Journal of Development, 4(5), 2640–2653. DOI: https://doi.org/10.46932/sfjdv4n3-030
https://ojs.southfloridapublishing.com/ojs/index.php/jdev/article/download/2640/2062/5747
Ruiz, J. (2022). La aplicación de herramientas digitales con el enfoque ontosemiótico y su influencia en el aprendizaje de funciones exponenciales y logarítmicas [Tesis de maestría, Universidad de San Carlos de Guatemala]. https://doi.org/10.36958/sep.v5i1.92 DOI: https://doi.org/10.36958/sep.v5i1.92
Ruiz, J. (2023). Compuertas lógicas con la teoría socioepistemológica. Revista InUMES, 34–43.
https://drive.google.com/file/d/1-GkzRLXZw19v9PsHClxVOCT4Vd-A6Agd/view
Ruiz, J., Solórzano, L., & Boj, H. (2023). La enseñanza de la geometría en Guatemala. Libros Fahusac.
https://doi.org/10.46954/librosfahusac.30.c65 DOI: https://doi.org/10.46954/librosfahusac.30.c65
Ruiz, J. (2024). Pitagorismo: Contribuciones y decadencia de una escuela filosófica y matemática. Revista InUMES.
Ruiz Castillo, J. C. (2024). La filosofía de las matemáticas: Desde la ontología y epistemología hasta la pedagogía escolar. Revista Científica Avances en Ciencia y Docencia, 1(1), 37–41. https://doi.org/10.70939/revistadiged.v1i1.4 DOI: https://doi.org/10.70939/revistadiged.v1i1.4
Ruiz, J. (2025). Aplicación del enfoque ontosemiótico y la incidencia en el estudio de la conjetura de Collatz desde las ciencias de la complejidad [Tesis doctoral, CUNORI]. https://drive.google.com/file/d/1LZck3ra227nzbIpJVSk8v4ByM6WcHKjd/view?usp=sharing
Ruiz, J. (2025). Aplicación de las representaciones semióticas en cálculo multivariable mediante la construcción de una montaña rusa física y virtual. Revista Cuadernos de Investigación y Formación en Educación Matemática, 18(2), 85–98. https://doi.org/10.15517/5shh5h27 DOI: https://doi.org/10.15517/5shh5h27
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Juan Carlos Ruiz Castillo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- 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.
