Mathematical Knowledge for Teaching the Area of Plane Surfaces: A Literature Review on Professional Noticing

Mathematics teaching is a social practice, shaped by distinct ways of recognizing, interpreting, and responding to situations that emerge in the classroom. This professional noticing, however, requires a kind of mathematical knowledge that is specific to teaching. This study aims to identify discussions have taken place in Brazil regarding the mathematical knowledge necessary for teaching the concept of area of plane surfaces in Basic Education, based on a literature review conducted through the CAPES Theses and Dissertations Catalog. The theoretical framework is grounded in Moreira’s distinctions between school mathematics and academic mathematics, as well as in the body of literature concerning the concept of professional noticing. The analysis of the 17 selected studies revealed, among other aspects, that by understanding area as a magnitude through the lens of the Game with Frames—originally developed by Douady and Perrin-Glorian in the 1980s and later expanded by Brazilian researchers—it is possible to infer mathematical knowledge relevant to teaching the area of plane surfaces in Basic Education. This perspective supports the development of professional noticing of students’ errors, difficulties, and misconceptions observed both in classrooms and in teacher education contexts. Some elements of this knowledge are discussed in the present article.