Conteúdos de Álgebra Linear Ensinados na Educação Básica: uma Análise de Livros do Ensino Superior

Abstract

This work aims to analyze the referrals given by Linear Algebra books, present in the basic bibliography of Mathematics Degree courses of the Brazilian institutions of Higher Education, regarding the teaching of Linear Systems, Matrices and Determinants. The theory behind this work is that of the Semiotic Representation Registers. We also adopt assumptions of the qualitative research and the Content Analysis, having as data source two textbooks of Linear Algebra. The textbooks were chosen by analyzing the bibliographic references of Brazilian Mathematics Degree courses. Data analysis allowed us to conclude that the relations, connections and situations-problems are little explored in both books, as well as the relations of the concepts of linear systems, matrices and determinants with other areas of knowledge. None of the books addresses the use of software as a tool for the resolution of linear systems, with a view to programming the resolution methods. With regard to methods of resolution, the book that explored more methods was book B. In addition the record of semiotic representation that had more emphasis in both books was the matrix record. The cognitive transformation of conversion was verified in both books. Finally, it should be highlighted that this research can be expanded from the analysis of other textbooks of Linear Algebra present in a significant way in the basic bibliographies of Brazilian institutions of Higher Education. As well, to investigate, compare and emphasize the advantages of using each of the methods for solving linear systems, regarding the computational programming of these methods, as well as to analyze the connections between the methods studied in Linear Algebra and revisited in Calculus Numerical linking these two compulsory curricular components in the graduation in Mathematics.