The algebraic and geometric representations in the learning of change of basis
DOI:
https://doi.org/10.5007/1981-1322.2018v13n2p72Abstract
In the learning of linear algebra concepts, students in higher education tend to have difficulties due to their abstract nature, which can be minimized if the connection between the different representations of the same concept is explored. Based on a teaching that explored the algebraic and geometric representations of Linear Algebra concepts, we try to find out how students understand the transformations between the different representations, algebraic and geometric, of the concepts of coordinates and change of basis in the resolution of a task after the teaching. We adopt a qualitative and interpretative approach in order to understand how the students operationalize the concepts of coordinates and change of basis in these representations. The analysis of the students' answers to the proposed task indicates better performance in the transition from the algebraic to the geometric representation than in the transformations performed within the algebraic representation itself. The greatest difficulties are related to the misinterpretation of the concepts involved, the symbolic language and the inappropriate use of concepts and procedures derived from analytical geometry or already addressed in linear algebra.
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