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Sociedad Española de Investigación
en Educación Matemática
Tesis Doctorales en Educación Matemática

Exploring the combination of GeoGebra and Paper Folding to Foster Geometrical Thinking in Secondary School.

  • Autora: Giovanna Valori.
  • Directoras: Dra. Veronica Albanese, Dra. Natividad Adamuz Povedano.
  • Fecha y lugar de defensa: 8 de junio de 2022. Departamento de Matemáticas. Universidad de Córdoba.
  • Tribunal:
    • Presidenta: Dra. María Burgos Navarro.
    • Secretaria: Dra. Elvira Fernández de Ahumada.
    • Vocal: Dr. Rafael Ramírez Uclés.
  • Calificación: Sobresaliente cum Laude.


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.