Problemas presentes em livros didáticos de matemática envolvendo conteúdos de geometria: uma análise a partir da matriz de continuidade de problemas

Abstract

Problem solving is a powerful tool that can be used in the process of teaching and learning mathematics. To Know how to work with the various types of problems in the classroom context, from closed to open, means providing better productivity in this process, both for the teacher and for the student. In this understanding, this research aimed to analyze problems present in High School Mathematics Textbooks (LDs), involving the Geometry contents. For this purpose, we used a mathematics textbooks collection used for high school classes in a school in the Goiás state. The focus of the study was to verify the types of problems present in the chosen collection based on the Problem Continuity Matrix proposed by Schiever and Maker (2003). Theorists such as Gontijo et al (2019), Fonseca and Gontijo (2020, 2021), Schiever and Maker (2003), Polya (1995), among others, were used. This study presented a qualitative research approach, verified mathematical problems present in a collection of textbooks, focused on the Geometry discipline, it was verified if in the analyzed collection, the problems met the requirements in the Base Nacional Curricular Comum (BNCC) and also measured the proportion in which the types of problems are used. In this methodological development, the following steps were carried out: 1) Selection of the textbooks collection; 2nd) Selection of the content of the Geometry discipline; 3) Catalogue of the problems selected in the collection and; 4th) Analysis of all collected material. The results showed that there are signs that mathematics teachers, who are using the textbook collection as the only source of problems, may be using problems only of the "closed" type, which makes the process of stimulating Critical and Creative Thinking in students more difficult. Because, at the level of mathematical problems, the aforementioned theorists argue that the use of "open" problems is more effective in the teaching and learning process, in order to stimulate creativity in mathematics in students. Finally, only closed problems were identified in the analyzed collection, realizing that the majority are Type I and II, no Type III problems were found, as well as no type “open” problems (ranging from Type IV to VI) were identified. Therefore, it was suggested the inclusion of problems that are open type in mathematics textbooks and that the process of teacher training be rethought, so that they are able to stimulate in students Critical and Creative Thinking in mathematics.