The Surface Area of Plane Figures in Textbooks throughout Elementary School

Background: The studies emphasise the importance of a kind of teaching that contributes to understanding the concept and the calculus of the area of plane figures, considering the textbooks that are often the main resource teachers use to prepare classes. Objective: To investigate how the topic area of flat figures is introduced and guided in elementary school textbooks and to verify the potential and limitations of the proposals to mobilise the figural apprehensions and acquire knowledge. Design: This is a documentary research with a methodology based on the content analysis proposed by Bardin. Setting and participants: Four collections approved by the PNLD in 2019 and 2020 were selected. Data collection and analysis: In these collections, the volumes and units that addressed the topic in question were identified. The data analysis, carried out in light of Duval’s figural apprehensions and the four stages suggested by Clements and Stephan for constructing the concept of plane figure areas, seeks to identify whether the mathematical skills described by the BNCC can be favoured. Results: the proposals of the collections show the importance of using the grid for introducing the concept and calculation of the area of plane figures at the different levels of education; however, few activities mobilise reconfiguration processes. Conclusions: It is essential to propose activities that allow students to understand the area equivalence between the modified figures and lead them to understand the rectangular configuration and the formulas for area calculation.