Exploring Approaches to the Concept of Area: An Analysis of High School Textbooks in the New High School Education

Abstract

The New High School (NEM) and the National Common Curricular Base stem from changes in Brazilian public curriculum policies, impacting the redesign of curricula and adaptation of teaching materials. The National Program of Textbooks and Teaching Materials (PNLD 2021), in accordance with the NEM, altered the Textbooks (LD), and it is within this context, in the scope of Mathematics Education, that this text aims to understand the different approaches to the concept of Area and the different deductions of the formulas presented by NEM LD authors. Using a qualitative approach and employing the Theorem System for LD’s analysis, we start from the theoretical foundation that comprehends working with Area in terms of geometric, magnitude, numeric, and algebraic/functional framesets, and with it, we discuss, in an analytical way, the data produced. As a result, it was possible to observe a diversity of approaches and strategies adopted by LD’s authors in the presentation of Area. The works demonstrated concerns in providing different concepts that can be mobilized in the treatment of areas of plane figures. However, we evidenced that the approach to Area often restricts itself to its definition as a numerical measure, leaving aside important aspects related to its geometric nature (shape) and its interpretation in different contexts. We hope that these results may invite teachers, and the community in general, to reflect on the teaching of Area presented in NEM LD’s, as well as to advance in the debate about it.

Geometry; Framesets; Plane figures; Deduction