Una caracterización del conocimiento didáctico del contenido como parte del conocimiento especializado del profesor de matemáticas de secundaria

Resum

The work of criticism and reflection on the most widely models used to investigate the nature of the professional knowledge of the teacher and their effectiveness as tools for research yields as a result that the analysis made on the specificity of the knowledge of mathematics teacher required to propose a more specific model, interested in particular aspects of a mathematics teacher. This model would overcome the difficulties reported on previous models to use for empirical research, without neglecting the most powerful elements in each of the previous models as well as their basic elements in them. This work shows a piece of the development of a model that will serve to analyze the specific features of teacher's mathematical and pedagogical knowledge, which we call Mathematics Teacher's Specialised Knowledge - MTSK. This thesis is a sign of progress in the collective construction that our group has made on MTSK. The theoretical framework presents and explains the model, and a preliminary theoretical construction of the domains and subdomains is done that comprise it, especially as regards the domain of pedagogical content knowledge, based on the collection of data from the research literature on professional knowledge of the mathematics teacher. Besides being complemented by empirical work, analysis in which it tests the theoretical construction and reflections on the construction and structure of the model are made. The main objective is to describe and characterize the pedagogical content knowledge of mathematics teacher, understood as one of the two domains that form the MTSK model. We are especially interested in providing information about the characterization of the subdomains of knowledge of the features of learning mathematics (KFLM) and knowledge of mathematics teaching (KMT). The main intention of this description and characterization is to understand the nature of this knowledge, so that we can make theoretical and methodological contributions to the development of MTSK and in turn to the body of research on the professional knowledge of the mathematics teacher. This research is framed in the line of professional development, particularly in relation to professional knowledge the teacher has and uses in a context of continuous training; it also has the distinction of being a virtual environment interaction. It is a qualitative study conducted through an instrumental case study with an interpretative approach. The findings of this study show the potential of the model as an analytical tool for understanding mathematics teacher's knowledge and advances in, mainly, the characterization of the KMT and KFLM subdomains. Results are given about the need to include and differentiate these subdomains as part of MTSK. Also offer clarification of the definition of each subdomain as well as the generation of categories and subcategories, powerful examples that illustrate each of the categories, information on the way in which the researcher can approach to this knowledge, the type of interactions with other subdomains of MTSK and possible ways of development of each subdomain.