[en] The doctoral thesis 'Contribution to the study of teaching and learning of isometries through whole group discussions with technology' constitutes a progress to the area of mathematics education research under the tradition of socio-cognitive approaches. For the analysis of learning and teaching processes in secondary school mathematics, the discursive and instrumental dimensions have been considered. The practical interpretation of these dimensions corresponds, respectively, with the development of discussions in whole group and the use of dynamic geometry software. The key question of our research is the following: How can the relationships between learning and teaching isometries be optimized by means of whole group discussions and technology? To answer this question, two goals have been posed: 1) Analysing the planning, implementation and evaluation of a systematic for a didactic sequence with whole group discussions and dynamic geometry software; 2) Detecting learning opportunities and how they are taken advantage of in relation to the didactic sequence created within the systematic. To attain the goals, an experimental situation was designed with a group of 14 and 15-year-old students in a school of Barcelona. In accordance with the theoretical foundation, the research question and the scientific goals, we have created a methodological design with two primary components. For the achievement of the first goal and inspired by concrete literature, the phases of planning, implementation and evaluation are integrated in an unprecedented method, which we call systematic. We have elaborated a didactic sequence for the resolution of isometry problems, in adjustment to the orientations given by the systematic. Through the classroom development of the sequence of problems, an external instrument has been used to prove the effectiveness of such systematic in regard to the application of the sequence. The accomplishment of the second goal may be understood as a validation of the systematic. To this end, an analytical instrument has been designed to detect the learning opportunities generated throughout the implementation of the sequence. The next step to validating the systematic has been to verify whether the students have taken advantage of any of the opportunities. Their capitalization has been explored through the comparison of the students' protocols -before and after whole group discussion- to underline changes that point to evidence of learning. The methodological tools created ad hoc have been proved particularly useful to carry out the planning, implementation and evaluation of the sequence of problems. The didactic tool 'Problem tree' becomes a backbone for the teacher's participation in several phases of the scheme: anticipation, mode of operation, monitoring, and sequencing the didactic implementation. The instrument 'Stages of discussion' becomes a useful tool aimed at organising data analysis, while helping to prepare the precise procedure to detect learning opportunities. The instrument 'Learning opportunities detector' is mainly used in the analysis aimed at characterising the concept of learning within whole group discussions with technology. There is general consensus on the need to prepare the development of classroom mathematical practices. However, there are no specific instruments involving teaching tools designed to carefully manage whole group discussions with technology. Thus, the current investigation is expected to contribute to the introduction of certain changes likely to improve the teaching and learning of mathematics. From our perspective, such improvement is the ultimate goal of the research in mathematics education research.

[es] Este trabajo de tesis doctoral contribuye al estudio de la enseñanza y aprendizaje de las isometrías mediante discusiones en gran grupo con tecnología. Para dar respuesta a cómo potenciar las relaciones entre enseñanza y aprendizaje de las isometrías en dicho entorno, se plantean dos objetivos: 1) Analizar una sistemática de planificación, implementación y evaluación de una secuencia didáctica con discusiones en gran grupo bajo el soporte de un software de geometría dinámica; 2) Detectar oportunidades de aprendizaje de las isometrías y su aprovechamiento en el contexto de la secuencia didáctica creada a partir de la sistemática anterior. Para el análisis de los procesos de enseñanza y aprendizaje en el aula de matemáticas de secundaria se consideran las dimensiones discursiva e instrumental. Se elabora una secuencia didáctica de resolución de problemas de isometrías, que se ajusta a las orientaciones dadas por la sistemática y se diseña un instrumento de análisis inédito a fin de detectar oportunidades de aprendizaje que se hayan generado durante la implementación de la secuencia. Luego se comprueba si algunas de estas oportunidades han sido aprovechadas por los alumnos desde la perspectiva de su progreso matemático. Tanto el diseño de instrumentos inéditos como su aplicación y validación son parte sustancial del trabajo. La consecución del primer objetivo lleva a resultados de tipo metodológico en torno al análisis de la sistemática. Estos se corresponden con los instrumentos didácticos 'Árbol del problema' y 'Estadios de la discusión'. Por un lado, el árbol deviene un instrumento vertebrador de la participación del profesor en varias situaciones de clase. Por otro, los estadios son una herramienta útil para organizar parte del análisis de datos y preparar el procedimiento de detección de oportunidades de aprendizaje. La consecución del segundo objetivo supone en sí mismo una forma de validar la sistemática mediante el instrumento 'Detector de oportunidades de aprendizaje'. La estrecha relación entre enseñanza y aprendizaje que se establece a lo largo del estudio, junto con el interés por mejorar las prácticas de educación matemática, proporcionan recomendaciones para el aula. Al respecto, este trabajo de tesis tiene que contribuir a introducir cambios susceptibles de reforzar la enseñanza y el aprendizaje de las matemáticas, que es el fin último de la investigación en el área y la motivación primera que origina todo el proceso que aquí se relata.