Dynamic Hypermedial Aids (DHA) in Teaching Notable Products
Abstract
This study proposes a novel pedagogical framework based on Dynamic Hypermedial Aids (DHA), integrating socioconstructivist principles, the Van Hiele model of geometric reasoning, and information and communication technologies (ICT) to enhance the teaching of notable algebraic products. The main contribution of the study lies in the development of a structured DHA-based instructional model that extends beyond conventional ICT-supported approaches by combining geometric visualization, variational thinking, and adaptive learning sequences.
The research adopts a qualitative analytical–interpretive design involving a purposive sample of 32 eighth-grade students. Data were collected through participant observation, video recordings, and activity logs, and analyzed using thematic coding and methodological triangulation.
The findings indicate improvements in students’ conceptual understanding of algebraic–geometric relationships, particularly in interpreting binomial squares through geometric representations. Additionally, increased levels of student engagement and the emergence of more autonomous learning behaviors were observed.
Overall, the study highlights the potential of DHA as an effective pedagogical tool for fostering deeper mathematical understanding and supporting active learning processes in algebra education.
Keywords: Dynamic Hypermedial Aids (DHA); Mathematics Education; Algebraic Thinking; Geometric Reasoning; Variational Thinking; ICT in Education; Instructional Design; Secondary Education.
Full Text:
PDFReferences
J. Onrubia, "Enseñar: crear Zonas de Desarrollo Próximo e intervenir en ellas," in El constructivismo en el aula, C. Coll et al., Eds. Barcelona: Graó, 2002, pp. 101-124.
Ministerio de Educación Nacional (MEN), Derechos Básicos de Aprendizaje: Matemáticas Versión 2. Bogotá, Colombia, 2016. [Online]. Available: https://www.colombiaaprende.edu.co/sites/default/files/files_public/2022-06/DBA_Matematicas-min.pdf
L. F. Gómez, "La enseñanza de las matemáticas desde la perspectiva sociocultural del desarrollo cognoscitivo," ITESO, Jalisco, México, 1994.
J. Amador, J. Rojas, H. Sánchez, and E. Duque, Las ayudas Hipermediales dinámicas AHD en los proyectos de aula con TIC, otra forma de enseñar y aprender conjuntamente. Pereira, Colombia: Universidad Tecnológica de Pereira, 2013.
B. Crispín et al., "Aprendizaje Autónomo," in Aprendizaje Autónomo orientaciones para la docencia. Ciudad de México: Dirección de Publicaciones de la Universidad Iberoamericana, 2011.
L. Morales, "El aprendizaje autónomo en la enseñanza de la matemática," 2016.
M. Cabrera, "El aprendizaje colaborativo en entornos virtuales," 2008.
C. Ricce, L. Díaz, and T. López, "El aprendizaje colaborativo en la enseñanza de las matemáticas: revisión sistemática," Acción y Reflexión Educativa, no. 46, pp. 1-18, 2021. doi: 10.48204/j.are.n46a1
P. Alvarado and Y. Molina, "Aprendizaje colaborativo en la resolución de problemas matemáticos," 2018.
H. S. Barrows, "A taxonomy of problem-based learning methods," Medical Education, vol. 20, no. 6, pp. 481-486, 1986. doi: 10.1111/j.1365-2923.1986.tb01386.x
J. H. C. Moust, P. A. J. Bouhuijs, and H. G. Schmidt, El aprendizaje basado en problemas: guía del estudiante. 2007.
F. Fouz and D. Berritzegune, "Modelo Van Hiele para la didáctica de la Geometría," in Un paseo por la geometría, pp. 67-82, 2013.
G. Vargas and A. Gamboa, "EL MODELO DE VAN HIELE Y LA ENSEÑANZA DE LA GEOMETRIA," Uniciencia, vol. 27, no. 1, pp. 74-93, 2013. [Online]. Available: https://www.revistas.una.ac.cr/index.php/uniciencia/article/view/4979
T. Rowland, "The Knowledge Quartet: The genesis and application of a framework for analysing mathematics teaching and deepening teachers' mathematics knowledge," Journal of Education, no. 1, pp. 15-33, 2013.
H. C. Hill, D. L. Ball, and S. G. Schilling, "Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students," Journal for Research in Mathematics Education, vol. 39, no. 4, pp. 372-400, 2008. doi: 10.5951/jresematheduc.39.4.0372
A. J. Bishop, "Space and geometry," in Acquisition of mathematics concepts and processes, R. Lesh and M. Landau, Eds. New York: Academic Press, 1983, pp. 175-203.
S. García and O. López, La enseñanza de la geometría. México: Instituto Nacional para la Evaluación de la Educación, 2008.
A. Mojica, Aprende a aprender Matemáticas 8. Libro de contenidos. Bogotá: Norma, 2019.
A. Baldor, Álgebra. 1941.
D. L. Ball, M. H. Thames, and G. Phelps, "Content knowledge for teaching: What makes it special?" Journal of Teacher Education, vol. 59, no. 5, pp. 389-407, 2008. doi: 10.1177/0022487108324554
M. J. Koehler and P. Mishra, "What is technological pedagogical content knowledge (TPACK)?" Contemporary Issues in Technology and Teacher Education, vol. 9, no. 1, pp. 60-70, 2009. [Online]. Available: https://citejournal.org/volume-9/issue-1-09/general/what-is-technological-pedagogicalcontent-knowledge
L. S. Shulman, "Those who understand: Knowledge growth in teaching," Educational Researcher, vol. 15, no. 2, pp. 4–14, 1986. doi: 10.3102/0013189X015002004
Refbacks
- There are currently no refbacks.
