A praxeological approach to the study of fractal geometry in high school textbooks

Abstract

This text is part of a larger research that characterized didactic and mathematical praxeologies related to how Fractal Geometry is approached in high school textbooks. The research aimed to analyze four collections containing three books each. The chosen books were the most adopted among the five most populous cities in the state of Paraná and were all approved by Plano Nacional do Livro Didático (PNLD) of 2018. The analysis of the produced data was carried out from the perspective of praxeological organizations - didactics and mathematics - with the Anthropological Theory of The Didactic (ATD) as a theoretical-methodological reference providing opportunities to investigate the mathematical and didactic choices made by the authors of the selected books. For this article, we will focus on the analyses of the four books adopted in the First Year of High School in the state of Paraná. As a result of the analyses, it was possible to point out that the object of knowledge Fractal Geometry is present in four out of the twelve textbooks analyzed, either theoretically or in the exercises. Such presentation occurs in association with other thematic units of Base Nacional Comum Curricular (BNCC) that are out of the scope of Geometry, such as Numbers and Algebra. With regard to the categorized Task Types, they are presented through explorations of fractals such as the snowflake and Koch curve, Sierpinski carpet and triangle, but in general, the proposals for the study of this theme were predominantly used as a means for teaching mathematics subjects other than Fractal Geometry itself.