RESOLUTION, ANALYSIS, AND ELABORATION OF DYNAMIC GEOMETRY INVESTIGATIVE TASKS: TEACHER KNOWLEDGE IN A TEACHER EDUCATION CONTEXT
The research reported in this thesis has as its object of study the professional knowledge that is mobilized in contexts of continuing education of teachers who teach mathematics, oriented to the resolution, analysis and elaboration of investigative tasks of dynamic geometry (TIGD) for the teaching of geometry in basic education. With regard to this object of study, the following research question was formulated: how a group of teachers who teach mathematics, in a context of continuing education, mobilize knowledge linked to the resolution, analysis and elaboration of TIGD for teaching geometry in basic education? To answer this question, it was established as a research objective to analyze the way in which a group of teachers who teach mathematics, in a context of continuing education, mobilize knowledge linked to the resolution, analysis and elaboration of TIGD for teaching geometry in basic education. The dissertation, written in multipaper format, is structured in three main parts. The first part concerns the introduction, in which the necessary elements are brought to place the reader in the research, such as the academic and professional trajectory of the author, the research guiding question and its construction process, the relevance, the objectives and the context of the research, as well as the methodological procedures adopted to answer the research question. In the second part, three chapters are presented, corresponding to articles submitted to scientific journals in the field of mathematical education. Chapter I describes the literature review carried out to know the state of knowledge of the object of study. In this regard, a review was developed according to the meta-synthesis modality, which consisted of the analysis and confrontation of 21 scientific articles obtained after a search process in three databases. In chapter II, written in Spanish (native language of the author of the dissertation), the theoretical framework that was used to analyze the research data is considered. For the constitution of this framework, the concepts of knowledge and joint work provided by the Theory of Objectification (TO) were adopted, and adapted to the context of the continuing education of teachers who teach mathematics, oriented to the resolution, analysis and elaboration of TIGD for the geometry teaching. Chapter III describes the empirical research carried out in order to answer the research question. For this, a methodological procedure was used that allowed to identify and examine seven critical events that provided information on how the knowledge of interest in the research was mobilized by ten teachers who teach mathematics in a situation of continuing education, while interacting with each other and with the trainer to solve a set of proposed tasks. Finally, the third and last part of the dissertation is dedicated to some final reflections, in which a retrospective look at the development of the research is carried out. Thus, the research objectives and research results are resumed, and based on that, possible future research is pointed out.