Aspectos epistemológicos a luz da teoria antropológica do didático subjacentes ao tema transformação linear

Abstract

Our purpose in this article was to reveal the epistemological aspects in the light of the anthropological theory of the Didactics are underlying the theme linear transformation in the textbook adopted for the teaching of Linear Algebra at the Federal Institute of Pará, revealing evidence of the dominant epistemological model, analyzing two types of tasks. The analysis of the didactic book is a reference for the elaboration of conjectures regarding the type of teaching that is being developed of a certain knowledge, in a certain institution. The Theory helped us to discuss Mathematical Organization and Didactics of the book in terms of the gender of tasks and task types, techniques and justifications of the rationale of mathematical object linear transformation. The reason for being to teach this object is given by the direct application of the definition, because the students should ask themselves when reading the proposals of the tasks enunciated by the authors, so that and why to study this subject? Some tasks are solved with the contents seen in high school, as a function as technology, not making it clear to the reader that it is a transformation from one vector space to another. We conclude that in the types of tasks discussed it was possible to give evidence of the dominant epistemological model, which we consider the direct use of the definition of linear transformation.