Navegando por Assunto "Anthropological Theory of Didactics"

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Alterações e recombinações praxeológicas reveladas por professores de matemática do ensino básico em formação continuada: a partir de um modelo epistemológico alternativo para o ensino da álgebra escolar
(Universidade Federal do Pará, 2017-04-05) PEREIRA, José Carlos de Souza; Nunes, José Messildo Viana; http://lattes.cnpq.br/5188612973174798; https://orcid.org/0000-0001-9492-4914
This research aims to develop a course of study and research with teachers of basic mathematics, aiming to promote possible changes and praxeological recombinations in the praxeological equipment objectified of these teachers submitted to the study of an alternative epistemological model for school algebra. The Anthropological Theory of Didactics (ATD) is the main theoretical model that bases the structural basis of the research. The theoretical elements of the ATD guarantee a consistent methodological path and, mainly, the methodological praxeology of the Parcours d'Ètude et de Recherche (PER), presented by Chevallard. The continuous training process was carried out, initially, with twelve teachers of basic mathematics and finished with seven teachers. The PER methodology guided this training process, consisting of eleven sessions. These sessions were filmed and recorded in audios and parts of those recordings were transcribed in the textual form. The analysis of the material obtained in these sessions reveals the ostensible didactic memories and the objectification of the praxeological equipment of the math teachers who participated fully in the process of continuous formation. The consistency of the objectification of the praxeological equipment of the teachers who elaborated and presented their proposals of classes to teach polynomials in the eighth year of elementary school revealed the possible praxeological alterations and recombination that the study of the Alternative Epistemological Model promoted in praxeological equipment and practices Teachers of these math teachers. The formulation of the answer to the guiding question of the thesis, followed the praxeology that we propose in a minimal model for the formulation of answers, in the context of the research praxeology of the ATD.The results of the research show that our two hypotheses were confirmed by the analysis that we made of the transcripts of the statements of the six teachers who presented their class proposals, as well as the written preparation of these same proposals.The confirmation of both hypotheses guarantees the proof of the thesis. In the conclusions and perspectives are the outcomes of all process of the methodological praxeology employed in this research.
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Praxeologias e modelos praxeológicos institucionais: o caso da álgebra linear
(Universidade Federal do Pará, 2017-04-04) MATOS, Fernando Cardoso de; NUNES, José Messildo Viana; http://lattes.cnpq.br/5188612973174798; https://orcid.org/0000-0001-9492-4914
This research deals with our concern to teach the Linear Algebra discipline in a Mathematics Degree Course, due to the students' difficulty in understanding the objects studied. The objects linear systems, matrices, vector spaces, vector subspaces, linear combinations, base and dimension were studied from the qualitative study of linear systems, since our idea was to make content less abstraction. National and international studies have already approached the subject using theories, others proposing ways that demonstrate the actions and functionalities of their approaches. Thus, this paper answers the following questions: What characteristics do mathematical and didactic organizations assume as institutional praxeologies, referring to the teaching of Linear Algebra and What conditions can we establish in a higher institution to make certain mathematical and didactic organizations with specific characteristics? In response, we propose an epistemological model of reference, composed of a task system constituted from a historical epistemological study in original works, which we had access, besides the constitution of a course of study and research, that was used as teaching methodology In a course of Mathematics undergraduates, lasting for 5 months between the years 2014 and 2015. The theoretical basis was based on the Anthropological Theory of Didactics. Starting from a concrete problem, we compared our model proposal with textbook adopted to teach the discipline under analysis and use the categories of analysis supported in the Theory, in addition to comparing the model with the text of the knowledge of a teacher who minister this Discipline in the course of Mathematics. In our analyzes we verified that the mathematical object linear systems comes as an appendix at the end of the book, and the tasks are not articulated with arrays, vector spaces and sub spaces, but that linear combinations is a technology that justifies the study of linear dependencies and independence , Base and size of space. The dominant epistemological model of the textbook analyzed and the teacher was to present the definition, with direct applications in the tasks. In order to develop the study, we created three didactic systems: the first was the creation of the mathematical and didactic organization of the reference model, the second was the study course with 14 undergraduate students and the last one was the mathematical and didactic organization presented through Of the groups on Linear Algebra objects studied. The study course proved that studying linear systems is to study Linear Algebra itself. From the study, our thesis was based on a proposal for an Epistemological Model of Reference on Linear Algebra, focused on basic education, with a direct impact on teacher training, becoming an alternative epistemological model for the undergraduate course In Mathematics of the Federal Institute of Pará.