The algebraic and geometric representations in the learning of change of basis

Authors

  • Graciela Moro Universidade do Estado de Santa Catarina
  • Floriano Viseu Universidade do Minho - Braga, Portugal
  • Ivanete Zuchi Siple Universidade do Estado de Santa Catarina

DOI:

https://doi.org/10.5007/1981-1322.2018v13n2p72

Abstract

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.

Author Biographies

Graciela Moro, Universidade do Estado de Santa Catarina

Doutoranda em Educação Matemática no Programa de Pós-Graduação em Ciência da Educação da Universidade do Minho, Braga, Portugal. Professora Assistente do Departamento de Matemática do Centro de Ciências Tecnológicas da UDESC, Joinville, Santa Catarina, Brasil.

Floriano Viseu, Universidade do Minho - Braga, Portugal

Doutor em Educação, Especialidade de Didática da Matemática. Professor Auxiliar do Instituto de Educação, Universidade do Minho, Campus de Gualtar, Braga, Portugal.

Ivanete Zuchi Siple, Universidade do Estado de Santa Catarina

Doutora em Engenharia de Produção pela Universidade Federal de Santa Catarina (UFSC), Brasil. Pós-Doutora em Didática da Matemática (INRP-FRANÇA). Professora Adjunta do Departamento de Matemática do Centro de Ciências Tecnológicas da UDESC, Joinville, Santa Catarina, Brasil.

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Published

2018-12-12

Issue

Vol. 13 No. 2 (2018)

Section

Artigos

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