An Experience with Pre-Service Teachers, Using GeoGebra Discovery Automated Reasoning Tools for Outdoor Mathematics

This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this project is that the use of technological tools, such as mathematical modeling, visualization, automatic reasoning and artificial intelligence, significantly improves the teaching and learning of mathematics, in addition to fostering positive attitudes in students. With this hypothesis in mind, in this article, we describe an investigation that has been developed in initial training courses for mathematics teachers in several universities in Madrid, where students used GeoGebra Discovery automated reasoning tools to explore geometric properties in real objects through mathematical paths. Through these activities, future teachers modeled, conjectured and validated geometric relationships directly on photographs of their environment, with the essential concourse of the automated discovery and verification of geometric properties provided by GeoGebra Discovery. The feedback provided by the students’ answers to a questionnaire concerning this novel approach shows a positive evaluation of the experience, especially in terms of content learning and the practical use of technology. Although technological, pedagogical and disciplinary knowledge is well represented, the full integration of these components (according to the TPACK model) is still incipient. Finally, the formative potential of the approach behind this experience is highlighted in a context where Artificial Intelligence tools have an increasing presence in education, as well as the need to deepen these three kinds of knowledge in similar experiences that articulate them in a more integrated way.