Conocimiento especializado del profesor de matemáticas en contextos de formulación de problemas

Resumo

Problem posing as a school mathematical practice applied in childhood and primary education is of special interest from the point of view of the benefits that the literature reports on it. Research associated with the implementation of problem posing in the classroom concludes that it helps pupils to establish relationships between elementary and more complex mathematical content, as well as to gain in autonomy, detaching themselves from the influence of the teacher and textbooks. This leads them to improve their ability to configure mathematical situations through the creation of problems and also helps to foster creativity in students, among other benefits. On the teachers' side, problem posing can be used to evaluate a given content, to know the level of understanding of the students and to contribute to the development of the students from an autonomous point of view. Not only from the literature we identify potentialities through the implementation of tasks based on the formulation of problems, but also from the regulations, both state and autonomous, it is mentioned that the practice of formulating problems should be addressed in the classroom. Some authors conclude that, despite being a practice with educational potential, it does not play an important role in the classroom. Thus, this lack of implementation may be caused by the lack of training, as well as the lack of teachers' knowledge about problem posing. Thus, the present research focuses on the study of teachers' knowledge of problem posing as a school mathematical practice implemented in early childhood and primary education classrooms, through three subresearches that focus on the school practice of formulating problems from three different perspectives: the teacher as a problem formulator, the teacher as a designer and manager of a formulation session, and the knowledge that a teacher mobilises in a problem formulation session. In the first research developed, we analyse the answers to an evaluation task in a teacher training context, paying attention to how they formulate a multiplicative structure problem based on integers. This will allow us to know what specialised knowledge has been mobilised during the performance of the assessment task focused on problem posing. In the second investigation, we characterise the classroom activity based on the formulation of problems, through the emergence of categories that respond to criteria of design and management of the task. The analysis of this research in terms of MTSK is carried out by focusing on the categories identified, allowing us to extract elements of knowledge associated with each of these categories. Finally, the third research aims to understand the knowledge mobilised by a teacher in a problem posing session. This knowledge differs from the previous one in that, despite being a classroom session, in the previous one we analysed the implicit knowledge that can be linked to each of the categories, while in this one we analysed the knowledge that is put into play in the session. In order to identify the specialised knowledge in each of the investigations provided, we use a methodology based on content analysis. We will use the mathematics teacher specialised knowledge model (MTSK) as an analytical tool that will allow us to characterise teachers' problem formulation knowledge. The results of the research show that knowledge for the action of posing mathematical problems is different in nature from knowledge for formulating, managing and implementing problem posing tasks. Likewise, it is observed that there is specific knowledge about problem posing linked to knowledge about contents linked to the formulation process itself, taking into account the contents involved in the task. Therefore, not only does knowledge about problem posing seem to be relevant, but also knowledge of the topics on which a problem formulation task is to be formulated or managed is needed.