Una profundización en la conceptualización de elementos del modelo de Conocimiento Especializado del Profesor de Matemáticas (MTSK)

Laburpena

This doctoral thesis is organized through the compendium of various publications in which I participated during my PhD studies. The line of research in which it is embedded is the "Initial training and professional development of teachers". Specifically, studies on the mathematics teacher's specialised knowledge are shown. We show a discussion about one of the models used internationally to study the knowledge of the teacher to teach mathematics (MKT) and how a deep analysis allowed us to detect some difficulties in its use for analytical purposes. Those difficulties gave rise to the formation of the model called Mathematics Teacher's Specialised Knowledge which is what we use as a theoretical reference in this thesis. It broadly describes each of its subdomains and some categories that we used to analyze the knowledge which supports the practice of a math teacher. The aims of the thesis focus on deepening specific aspects of some elements of the model in order to consolidate it as a powerful tool to analyze the knowledge of a math teacher. This deepening was made on four elements: a) Knowledge of the Features of learning mathematics: we carried out a study with two teachers who taught linear algebra in high school. We analyzed 15 classes of each teacher who worked on issues of matrices and determinants. Based on a review of the previous literature on the knowledge the teacher has about his students or their learning processes, we selected episodes in which appeared some features about it and drew out knowledge indicators for each episode. These indicators were categorized according to common characteristics, thus forming a series of categories. b) Knowledge of mathematics teaching: using the same data collected in the study described above, we analyzed those moments when teachers gave examples or provided help to their students. We obtained indicators on the knowledge teachers showed about didactic features of examples and scaffolding techniques used in the teaching of the subjects. c) Knowledge of practices in mathematics: we present a partial study which attempts to characterize the content of this subdomain. We used the characterizations that have been made about each of the practices identified in the specialised literature. With these we chose video clips of class which, with the data obtained from a semi¬structured interview, served to identify opportunities to delve into specific aspects of the knowledge of the practice. d) Relations between the mathematics teacher's specialised knowledge and her beliefs about teaching and learning mathematics: A study was done using online environments to analyze the designs of class of a teacher and deepen on aspects of their specialised knowledge by a semi-structured interview. We found implications on how traits of certain didactic tendency may condition the use a teacher makes on her knowledge to teach mathematics and to interpret and predict the productions of his students. Because the last two studies were made in online environments, we present a research about how the practice of researcher is modified regarding their actions in face-to-face researches. Finally, although it is not related to the research objectives, we present a proposal to use the theoretical model to analyze activities for the initial training of primary school teachers in the area of mathematics.