Article Sidebar

Download
PDF
Statistic
Read Counter : 113 Download : 22

Downloads

Download data is not yet available.

Main Article Content

Abstract

The conceptual and procedural understanding of the derivative remains a persistent challenge in undergraduate engineering education, particularly in bridging symbolic, graphical, and applied interpretations. Despite advances in digital tools, few instructional designs systematically integrate interactive exploration with formal mathematical reasoning. This study addresses this gap by proposing an instructional framework that combines functional modeling with GeoGebra-based simulations, grounded in the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), specifically targeting first-year engineering students in Chile. A mixed exploratory–descriptive design was implemented, combining quantitative and qualitative analyses. A three-session intervention involved 102 students who engaged in tasks assessing derivative understanding across multiple representations, including graphical slopes, symbolic differentiation, and applied rate-of-change problems. Data were collected via performance questionnaires and written productions, with validity ensured through expert review and reliability confirmed via pilot testing. Students exhibited strong proficiency in graphical interpretation and procedural manipulation of derivatives, with success rates exceeding 85%. Conversely, tasks requiring formal argumentation, rigorous use of limit definitions, and theoretical justification showed reduced performance at 68%, highlighting the challenge of connecting exploratory simulations with formal mathematical reasoning. The findings demonstrate that integrating functional dependency analysis, interactive simulations, and OSA principles can strengthen comprehension of derivatives, particularly in geometric interpretations and formal rate-of-change reasoning. This research provides a replicable instructional design that enhances both conceptual insight and procedural competence, offering evidence-based strategies for technology-enhanced mathematics instruction in engineering curricula and contributing to broader curriculum development.

Keywords

Derivative Instructional Process Interactive Simulation Mathematical Modelling Ontosemiotic Approach

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Galindo Illanes, M. K., Chamorro Manríquez, D., Breda, A., & Sala-Sebastià, G. (2025). Instructional process for the construction of the derivative function: Modelling and simulation in GeoGebra from the Ontosemiotic Approach. Journal on Mathematics Education, 16(3), 1001–1022. https://doi.org/10.22342/jme.v16i3.pp1001-1022
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Aguilera, C., Manzano, A., Martínez, I., Lozano M., & Casiano, C. (2017). El modelo de aula invertida. Universidad de Almería. Revista Internacional de Psicología del Desarrollo y de la Educación, 4(1), 261-266. https://doi.org/10.17060/ijodaep.2017.n1.v4.1055
  2. Alarcón, A., Vázquez, A., & Marimón, C. (2019). Las tecnologías del aprendizaje y el conocimiento en la formación docente. Revista Conrado, 15(68), 180-186. http://scielo.sld.cu/scielo.php?script=sci_arttext&pid=S1990-86442019000300180
  3. Araya, D., Pino-Fan, L. R., Medrano, I., & Castro, W. F. (2021). Epistemic criteria for the design of tasks about limits on a real variable function. Bolema, 35(69), 179-205. https://doi.org/10.1590/1980-4415v35n69a09
  4. Ardina, G., Bautista, G., & Santos, M. S. D. (2025). GeoGebra integration in mathematics teaching: Bridging research and classroom practice. Journal of Interdisciplinary Perspectives, 3(8), 845-856. https://doi.org/10.69569/jip.2025.505
  5. Bedada, T. B., & Machaba, M. F. (2022). Investigation of student’s perception learning calculus with GeoGebra and cycle model. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), em2164. https://doi.org/10.29333/ejmste/12443
  6. Breda, A., Pochulu, M., Sánchez, A., & Font, V. (2021). Simulation of teacher interventions in a training course of mathematics teacher educators. Mathematics, 9(24), 3228. https://doi.org/10.3390/math9243228
  7. Burgos, M., & Godino, J. D. (2020). Modelo ontosemiótico de referencia de la proporcionalidad. Implicaciones para la pla-nificación curricular en primaria y secundaria. Avances De Investigación En Educación Matemática, 18, 1–20. https://doi.org/10.35763/aiem.v0i18.255
  8. Burgos, M., Bueno, S., Godino, J. D., & Pérez, O. (2021). Onto-semiotic complexity of the Definite Integral. Implications for teaching and learning Calculus. REDIMAT – Journal of Research in Mathematics Education, 10(1), 4-40. https://doi.org/10.17583/redimat.2021.6778
  9. Burgos, M., Castillo, M. J, Beltrán-Pellicer, P., Giacomone, B. Y., & Godino, J. D. (2020). Análisis didáctico de una lección sobre proporcionalidad en un libro de texto de primaria con herramientas del enfoque ontosemiótico. Bolema, 34(66), 40–68. https://doi.org/10.1590/1980-4415v34n66a03
  10. Colquepisco-Paucar, N. T. (2019). Aprendiendo el cálculo diferencial e integral con GeoGebra. Killkana Técnica, 3(2), 11–16. https://doi.org/10.26871/killkana_tecnica.v3i2.484
  11. Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). SAGE.
  12. Del Río, L. S. (2020). Recursos para la enseñanza del Cálculo basados en GeoGebra. Revista Do Instituto GeoGebra Internacional De São Paulo, 9(1), 120–131. https://doi.org/10.23925/2237-9657.2020.v9i1p120-131
  13. Drijvers, P., Kieran, C., Mariotti, M., Ainley, J., Andresen, M., Chan, Y. C., Dana-Picard, T., Gueudet, G., Kidron, I., Leung, A., & Meagher, M. (2009). Integrating technology into mathematics education: Theoretical perspectives. En New ICMI studies series (pp. 89-132). Springer. https://doi.org/10.1007/978-1-4419-0146-0_7
  14. Font, V. (2005). Una aproximación ontosemiótica a la didáctica de la derivada [An ontosemiotic approach
  15. Galindo Illanes, M. K., & Breda, A. (2023). Significados de la derivada en los libros de texto de las carreras de Ingeniería Comercial en Chile. Bolema, 37(75), 271–295. https://doi.org/10.1590/1980-4415v37n75a13
  16. Galindo Illanes, M. K., & Breda, A. (2024). Instructional process of the derivative applied in business engineering students in Chile. Uniciencia, 38(1), 1–23. https://doi.org/10.15359/ru.38-1.17
  17. Galindo Illanes, M. K., Breda, A., & Alvarado, H. A. (2023). Diseño de un proceso de enseñanza de la derivada para estudiantes de ingeniería comercial en Chile. Revista Paradigma, 44(4), 321–350. https://doi.org/10.37618/PARADIGMA.1011-2251.2023.p321-350.id1386
  18. Galindo Illanes, M. K., Breda, A., Alvarado, H. A., & Sala-Sebastià, G. (2025). Characterization of sub-fields of derivative problems in engineering textbooks. Eurasia Journal of Mathematics, Science and Technology Education, 21(3), em2591. https://doi.org/10.29333/ejmste/15987
  19. Galindo Illanes, M. K., Breda, A., Chamorro, D. D., & Alvarado, H. A. (2022). Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmste/12162
  20. Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111–132. https://enfoqueontosemiotico.ugr.es/documentos/Godino_2013_idoneidad_didactica.pdf
  21. Godino, J. D. (2016). La idoneidad didáctica como herramienta de análisis y reflexión sobre la práctica del profesor de matemáticas. [Videoconferencia]. Vimeo. https://vimeo.com/175426315
  22. Godino, J. D. (2022). Emergencia, estado actual y perspectivas del enfoque ontosemiótico en educación matemática. REVIEM, 2(2), 1–24. https://doi.org/10.54541/reviem.v2i2.25
  23. Godino, J. D. (2024). Enfoque ontosemiótico en educación matemática: Fundamentos, herramientas y aplicaciones. McGraw-Hill.
  24. Godino, J. D., & Burgos, M. (2020). ¿Cómo enseñar las matemáticas y ciencias experimentales? Resolviendo el dilema entre transmisión e indagación. Paradigma, XLI 80–106. https://doi.org/10.37618/PARADIGMA.1011-2251.2020.p80-106.id872
  25. Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 38-43. https://www.jstor.org/stable/26742011
  26. Godino, J. D., Batanero, C., & Burgos, M. (2024). Understanding the onto-semiotic approach in mathematics education through the lens of the cultural historical activity theory. ZDM Mathematics Education, 56, 1331–1344. https://doi.org/10.1007/s11858-024-01590-y
  27. Godino, J. D., Batanero, C., & Font, V. (2007). The ontosemiotic approach to research in mathematics education. ZDM, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  28. Godino, J. D., Batanero, C., & Font, V. (2020a). El enfoque ontosemiótico: Implicaciones sobre el carácter prescriptivo de la didáctica. Revista Chilena de Educación Matemática, 12(2), 47-59. https://doi.org/10.46219/rechiem.v12i2.25
  29. Godino, J. D., Batanero, C., Burgos, M., & Gea, M. M. (2021). Una perspectiva ontosemiótica sobre problemas y métodos de investigación en educación matemática. Revemop, 3, e202107. https://doi.org/10.33532/revemop.e202107
  30. Godino, J. D., Burgos, M., & Wilhelmi, M. R. (2020b). Papel de las situaciones adidácticas en el aprendizaje matemático. Una mirada crítica desde el enfoque ontosemiótico. Enseñanza de las Ciencias, 38(1), 147-164. https://doi.org/10.5565/rev/ensciencias.2906
  31. 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. http://dx.doi.org/10.1590/1980-4415v31n57a05
  32. Guilcapi, J. R., Martinez, J. M., Saavedra, M. C., & Guilcapi, L. E. (2019). Aplicación del software Matlab, como estrategia metodológica en la enseñanza-aprendizaje de cálculo de una variable a nivel superior de ingeniería de telecomunicaciones de la UTA. Explorador Digital, 3(3.1), 30-40. https://doi.org/10.33262/exploradordigital.v3i3.1.863
  33. Gusmão, T. C. R. S., & Font, V. (2022). Análisis metacognitivo de un aula de matemática sobre medida de superficies. Revista Latinoamericana De Investigación En Matemática Educativa, 25(2), 169–196. https://doi.org/10.12802/relime.22.2522
  34. Hohenwarter, M., & Preiner, J. (2007). Dynamic mathematics with GeoGebra. Journal of Online Mathematics and its Applications, 7(1), 2-12.
  35. Illescas, M. S., Illesca, T. L., Enriquez, M. del C., Riera Cartuche, D. R., Salazar, M. A., Hidalgo, L. E., & Bernal, A. P. (2024). Impacto de las plataformas tecnológicas de enseñanza como recursos educativos. Ciencia Latina Revista Científica Multidisciplinar, 8(4), 11401-11419. https://doi.org/10.37811/cl_rcm.v8i4.13307
  36. Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14–26. https://doi.org/10.3102/0013189X033007014
  37. Kado, K. (2021). Impact of GeoGebra on the students’ conceptual: Understanding of limit of a function in Bhutan. International Journal of Asian Education, 2(4), 539-548. https://doi.org/10.46966/ijae.v2i4.140
  38. Kaiser, G., Blum, W., Ferri, R. B., & Greefrath, G. (2015). Anwendungen und modellieren. En Springer eBooks (pp. 357-383). https://doi.org/10.1007/978-3-642-35119-8_13
  39. Ledezma, C. (2024). Mathematical modelling from a semiotic-cognitive approach. Journal of Research in Mathematics Education, 13(3), 268-292. https://doi.org/10.17583/redimat.15066
  40. Ledezma, C., Breda, A., & Font, V. (2023). Prospective teachers’ reflections on the inclusion of mathematical modelling during the transition period between the face-to-face and virtual teaching contexts. International Journal of Science and Mathematics Education, 22, 1057–1081. https://doi.org/10.1007/s10763-023-10412-8
  41. Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49, 937-949. https://doi.org/10.1007/s11858-017-0867-3
  42. López, R. R., & Hernández, M. W. (2016). Principios para elaborar un modelo pedagógico universitario basado en las TIC. Estado del arte. Episteme Uniandes. Revista digital de Ciencia, Tecnología e Innovación, 3(4), 575-593. https://www.redalyc.org/pdf/5646/564677242009.pdf
  43. Mora-Casasola, M. F. (2023). Implementación de recursos educativos digitales, una revisión sistemática desde la enseñanza del cálculo diferencial. Revista Digital Matemática, Educación e Internet, 24(1), 1-18. https://doi.org/10.18845/rdmei.v24i1.6709
  44. Pino-Fan, L. R., Parra-Urrea, Y. E., & Castro-Gordillo, W. F. (2019). Significados de la función pretendida por el currículo de matemáticas chileno. Magis. Revista Internacional de Investigación en Educación, 11(23), 201–220. https://doi.org/10.11144/Javeriana.m11-23.sfpc
  45. Rahman, M. A., Sook Ling, L., & Yin, O. S. (2024). Sistema de aprendizaje interactivo para el aprendizaje de cálculo. F1000Research, 11, 307. https://doi.org/10.12688/f1000research.73595.2
  46. Rezaei, J., & Asghary, N. (2024). Teaching differential equations through a mathematical modelling approach: The impact on problem-solving and the mathematical performance of engineering undergraduates. International Journal of Mathematical Education in Science and Technology, 56(5), 899–919. https://doi.org/10.1080/0020739X.2024.2307397
  47. Sepúlveda-Delgado, O., Suárez-Aguilar, Z. E., & Pino-Fan, L. R. (2021). Significados de referencia del objeto grupo. Revista de Investigación, Desarrollo e Innovación, 11(2), 297-318. https://doi.org/10.19053/20278306.v11.n2.2021.12757
  48. Spooner, K. (2023). Using mathematical modelling to provide students with a contextual learning experience of differential equations. International Journal of Mathematical Education in Science and Technology, 55(2), 565–573. https://doi.org/10.1080/0020739X.2023.2244472
  49. Torres-Peña, R. C., Peña-González, D., Chacuto-López, E., Ariza, E. A., & Vergara, D. (2024). Updating calculus teaching with AI: A classroom experience. Education Sciences, 14(9), 1019. https://doi.org/10.3390/educsci14091019
  50. Trouche, L. (2005). An instrumental approach to mathematics learning in symbolic calculator environments. In D. Guin, K. Ruthven, and L. Trouche. (eds.), The Didactical Challenge of Symbolic Calculators (pp. 137-162). Springer. https://doi.org/10.1007/0-387-23435-7_7
  51. Valarezo, J. W., & Santos, O. C. (2019). Technologies for learning and knowledge in teacher education. Revista Conrado, 15(68), 180-186. https://conrado.ucf.edu.cu/index.php/conrado/article/view/1003
  52. Verón, M. A., & Giacomone, B. (2021). Análise dos significados do conceito de diferencial de uma perspectiva ontosemiótica. Revemop, 3, e202109. https://doi.org/10.33532/revemop.e202109
  53. Weinhandl, R., & Lavicza, Z. (2021). Real-world modelling to increase mathematical creativity. Journal of Humanistic Mathematics, 11(1), 265–299. https://doi.org/10.5642/jhummath.202101.13
  54. Winkel, B. (2023). Using modelling to motivate and teach differential equations. International Journal of Mathematical Education in Science and Technology, 55(2), 193-197. https://doi.org/10.1080/0020739X.2023.2289794
  55. Zagoto, M. M., Musdi, E., Arnawa, I. M., Fauzan, A., Bentri, A., & Dakhi, O. (2025). Effectiveness of Geogebra-based learning on students’ cognitive and affective participation in mathematics. Salud Ciencia y Tecnología, 5, 2001. https://doi.org/10.56294/saludcyt20252001