Argumentación en geometría por maestros en formación inicial en práctica pedagógica: un estudio de caso

This research is conducted in the doctoral program in Mathematics Education, in the School of Education, Universidad de Antioquia (Medellin, Colombia). This doctoral dissertation memoire documents and informs the research question: ?How argument, in geometry, preservice teachers during the teaching practice? A theoretical „integral‟ model for argumentation is proposed in order to answer the question. This model includes dialog, rhetoric resources and argumentative features that were used by the three preservice teachers while discussing geometry tasks with both, colleagues and students. The discussions held with the auditorium of their colleagues took place in the Teaching Seminar, while those held with the auditorium of the students, took place in the classroom. The research method corresponds to a case study, with a phenomelogical- hermeneutical approach, while it obeys to the argumentation particularities of Carlos, Helena and Maria, who were the preservice teachers who participated in the research. The analysis and the data interpretation, is carried out proposing by argumentative theoretic integral model that accounts for logic, dialectic and rhetoric features, which is achieve by two strategies put into play to investigate the singularities in the participants „argumentations‟: direct interpretation of examples and categoric sum up of individual examples. The more outstanding results allow concluding that the arguments used by the preservice teachers with their colleagues are, sometimes, monologic; while those used with their students are dialogic. The rhetoric resources used are models, 4 examples, illustrations and metaphors; and the argumentative features that outstand in the arguments used by the three preservice teachers are related to diverse warrants and modals qualifiers. The requested warrants, both to their colleagues and to their students, are respectively: a priori-epistemic, epistemic-institutional and a priori-epistemic and empiric-personals; and the modal qualifiers are provisional or absolute. In addition, their arguments‟ intentions are: validate, justify, refute, defend, explain or persuade with viewpoints o with geometric knowledge to the participants in both auditoriums.