O conceito de função em três livros didáticos de matemática do PNLD (2021): um olhar a partir da teoria dos registros das representações semióticas

Abstract

The aim of this thesis is to analyze, from the perspective of the Theory of Semiotic Representation Registers (TSRR), the approach to the concept of function in three high school mathematics textbooks. These textbooks were approved by the National Textbook Program (PNLD) (BRASIL, 2021). The methodological procedures used consisted of analyzing the concept of function approach, based on TSRR elements: representations, transformations (treatment and conversion), graph construction procedures, semantic congruence phenomenon, referential equivalence, and heterogeneity in both directions. The analyses indicated that there are varieties in the records in the three books analyzed, namely: natural language; and algebraic, graphic, tabular and figural language. Many activities with transformation of treatment are observed in the books, but the conversions were in greater number with emphasis on the representations of the register in natural language for the algebraic register and of the representations of this register for the graphic register. However with few proposals of activities with inverse conversions from the representation of the graphical record to the algebraic record. The procedure for the construction of graphs prioritized by the authors was of the point by point. In relation to the phenomenon of congruence, the analyses indicated that there are more activities with low and medium degrees of noncongruence and that with high degree there was a balanced distribution in the activities. From the analyses, it was considered that the approach to the concept of function is rich in terms of representations, treatment and conversions with different degrees of difficulty. However, based on the results of this study it was concluded that the three textbooks provide limited support for the students to understand the different function representations and that more than moving among the records they know how to coordinate them.