Resumen de Exploración de la combinación de geogebra y plegado de papel para fomentar el pensamiento geométrico en la escuela secundaria
This doctoral research explores through different studies the potential of the combined use of paper folding and dynamic geometry, GeoGebra, in high school plane geometry. The need for this combination arises from the individual potentials of the artefacts in play for the development of visuospatial skills and geometric reasoning that a joint use could reinforce. The first study uses the theoretical tools of the Onto-semiotic approach to mathematics education and Duval's theory of figural apprehensions. The interplay between physical and digital activity in a proving process is analysed through the practices and configurations of objects and processes that emerge in the student work. It highlights how multiple visual representations such as folded models and crease diagrams and their digital counterparts allow for better coordination of operative and discursive apprehensions during the problem-solving process, especially from conjecture generation to proof construction. The second study, with the theoretical tools of Geometric Working Spaces and Geometrical Paradigms and Duval’s approach to visualization, analyses how students approach a paper folding question involving the calculation of measurement of elements by experiencing folding physically and/or virtually in exploratory activity and constructing a digital diagram to model it. The duo of physical and digital tools helped students in the exploratory phase. In the calculation phase different relationships with the representations were noticed. In the third and final study quantitative methods are used, with a quasi-experiment design, to evaluate the didactic effectiveness of the integration of paper folding and GeoGebra tasks into the traditional geometry curriculum. Teaching effectiveness is assessed through the improvement of the van Hiele levels of geometric thinking and visuospatial skills.
The studies show some benefits of a joint practice of paper folding and GeoGebra in the study of plane geometry. Considering the absence of research on the use of geometric paper folding and dynamic geometry in high school, these results can be considered a first original contribution to research in this area.
Referencias Arıcı, S., & Aslan-Tutak, F. (2015). The effect of origami-based instruction on spatial visualization, geometry achievement, and geometric reasoning. International Journal of Science and Mathematics Education, 13(1), 179–200. https://doi.org/10.1007/s10763-013-9487-8 Duval, R. (1995). Geometrical pictures: kinds of representation and specific processings. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery with Computers in Mathematics Education (pp. 142–157). Springer-Verlag.
Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. Annales de Didactique et Sciences Cognitives, 10, 5–53.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39(1–2), 127–135. https://doi.org/10.1007/s11858-006-0004-1 Jones, K. (2002). Issues in the Teaching and Learning of Geometry. In L. Haggarty (Ed.), Aspects of Teaching Secondary Mathematics (pp. 121–139). RoutledgeFalmer. https://doi.org/10.4324/9780203165874 Kuzniak, A., Nechache, A., & Drouhard, J. P. (2016). Understanding the development of mathematical work in the context of the classroom. ZDM - Mathematics Education, 48(6), 861–874. https://doi.org/10.1007/s11858-016-0773-0
