A álgebra nos livros didáticos: um estudo dos usos das variáveis, segundo o Modelo 3UV

Abstract

Based on my students difficulties and by the fact of Algebra be a Mathematic area that occupies an important place in the scholar curriculum, the aim of this work is to investigate if the introduction to Algebra study proposed on text books is characterized by the use of variable in agreement to the 3UV model of Ursini et al. (2005) to the Algebra teaching. This is important as long as the text books are an instrument of work of teachers of the basic teaching network. The 3UV model considers essentially three distinct uses of the variable: the unknown terms (unknowns), the general number and the functional relation. The Mathematic text books analysis is the subject present in studies and researches connected to Mathematical Education. In this way their analysis can contribute to the comprehension of one part of the complex school system. To analyze if the algebraic contents mentioned in the book such as its exercises and problem situations show the use of variable regarding the 3UV model, we have chosen issues of the 7th grade of the Fundamental Teaching, from the three most distributed collections by PNLD 2008 in São Paulo State. We have chosen these issues because it is in this grade that the Algebra studies have been frequently started in the current school units. For analysis, some rules were established in order to observe if 3UV model can be identified in the analyzed text books and if the algebraic contents, such as their exercises and problem situations proposed, show these uses. The conclusion is that the 3UV model can be identified in the analyzed text books, but their exercises and problem situations do not show all the variable uses specially the use of unknown variable. From the three analyzed books, the first shows the uses of the variable as a generic number. The second book shows the variable only as an unknown term and only the third text book shows the three variable uses