Advances in education are increasingly important, and it is necessary to look for methodological strategies that enhance the value of mathematics in society and promote integrated training that helps students reason critically and rigorously. In this sense, math trails with a focus on STEM and sustainable development are a good resource to connect mathematics with the environment in a transversal way with other disciplines. A total of 35 postgraduate students in secondary education and 30 undergraduate students in primary education participated in this research and received a training course from experts in mathematics teaching. During the experience, the graduate students designed trails that were tested by the undergraduate students after a prior review by three in-service primary teachers. Likert scale questionnaires and open questions were asked of the students to evaluate the training received and the execution of the experience. Likewise, it was also decided to hold a debate with the participants and a guided interview with in-service teachers to assess the possible application of the resource in primary education courses. The results show a very positive assessment of the experience and allow us to support this approach to promote a change in the teaching–learning of mathematics in the last years of primary education.

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.

In this paper, we describe an educational experience in the context of the Master’s degree that is compulsory in Spain to become a secondary education mathematics teacher. Master’s students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason’s reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students’ answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context.

INTRODUCCIÓN. La formación inicial del profesorado es un elemento básico para garantizar un sistema educativo de calidad. Los programas de formación, en cualquiera de sus etapas, deben asegurar las competencias del futuro profesor en materia de conocimientos, tanto teóricos como prácticos, y estar actualizados en metodologías educativas innovadoras y en tecnología. MÉTODO. En este trabajo se presenta una experiencia en la que se acerca a los alumnos del Máster en Formación del Profesorado de Educación Secundaria la realidad del aula en la que ejercerán su profesión en un futuro: los alumnos de la especialidad de Matemáticas del máster se transforman en docentes realizando los vídeos necesarios para aplicar la metodología del Aula Invertida (Flipped Learning) en un centro educativo real. RESULTADOS. Los estudiantes del máster aprendieron de un modo significativo a implementar una metodología innovadora, la Clase Invertida, formándose además en la grabación y edición de vídeos educativos. La actividad se complementó con la retroalimentación que se generó desde el centro educativo, enriqueciendo de este modo la experiencia. Para analizar el impacto de la actividad se realizó una encuesta a los estudiantes del máster y una entrevista semiestructurada a una muestra de ellos. DISCUSIÓN. Llevar la práctica real a los profesores en formación es un elemento esencial para su capacitación como docentes. Los estudiantes valoran como muy positivas este tipo de iniciativas, que los formadores de profesores conciben como necesarias para poder enseñar a aplicar los conocimientos teóricos que se imparten en el entorno universitario.

We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery.

El objetivo de este estudio es caracterizar las emociones que moviliza y declara sentir una formadora de maestros durante algunas sesiones impartiendo la asignatura de “Matemáticas y su Didáctica I”. A través de un estudio de caso instrumental y desde una perspectiva interpretativa se explora y analiza cómo influye en ellas el cambio de docencia a un contexto online debido al COVID-19. El modelo OCC de la estructura cognitiva de las emociones permite identificarlas y clasificarlas en base a la situación desencadenante y su valoración interna (sistema propio de metas, normas y actitudes). El análisis muestra las formas de procesamiento de información de la formadora y sus estrategias de afrontamiento ante las realidades que se le presentan. El estudio proporciona herramientas de conocimiento de los objetivos, actitudes y concepciones del docente a través de sus emociones, un primer paso para mejorar su gestión en el futuro.