Uma caracterização sobre resolução de problemas como competência a partir de orientações propostas na coleção A conquista matemática (PNLD 2024)

Abstract

The aim of the research was to characterize the author's guidelines for the collection A Conquista Matemática (PNLD 2024) in relation to problem-solving skills. The choice of this collection, authored by Giovanni Júnior (2022), was the result of a survey carried out, by federative unit, based on the data available on the Ministry of Education (MEC) website, in the section referring to the National Book and Teaching Material Program (PNLD). This revealed that copies of the aforementioned collection had been significantly acquired by schools linked to the municipal and state spheres in most federal units - in other words, in 19 and 20 federal units, respectively. As theoretical support for the investigation, we adopted the understandings of Schroeder and Lester (1989), Stanic and Kilpatrick (1989), Onuchic et al (2021), Dante (2005) and Polya (2006), regarding teaching approaches and the roles of problem solving, problem typification and solution stages, as well as the provisions present in the BNCC, and Perrenoud (1999) regarding the concept of competence. In order to process the data extracted from the research source, stages were developed that dialog with the content analysis proposed by Bardin (2016). The expression Problem Solving as a Competency emerged as a result of an initial exercise, the aim of which was to define a way of referring to the set of specific competencies investigated, namely: competencies three, five, six and eight, which refer, respectively, to understanding the relationship between areas of knowledge and seeking solutions; using mathematical processes and tools to model and solve various problems; facing problem situations and using different registers and languages to express answers and conclusions; and seeking solutions through collective work (Brasil, 2018). However, as the research developed, this theme came to be understood as an objective of the teaching and learning of mathematics to be carried out at the Elementary School - Final Years stage, in view of the proposals of the BNCC. Regarding the distribution of the competences investigated, it was possible to see in the collection examined that the author arranged them in isolation from each other or in an articulated way. The competence that was mentioned the most, in isolation, was the third competence (31), followed by the sixth competence (29), out of a total of 101 isolated mentions identified. On the other hand, the most frequent combination in the book brings together competences three and six, and was identified in seven of the 20 mentions in the combination format present in the material examined. With regard to the content of the guidelines covered in the research, three categories were established: teaching approach, resource potential and student action. Among these, the teaching approach category stands out for covering 47% of the guidelines characterized. Thus, based on the teaching procedures identified among the clippings analyzed, it was possible to see that in order to encourage the development of skills related to problem solving, the teaching to solve problems approach is more evident in the collection, as opposed to the teaching through problem solving approach which, according to the author of the work, is the one that most dialogues with the propositions of the BNCC. This finding corroborates the inference that the theme of problem solving as a skill - intrinsic to the concept of Problem Solving as a Competence - is related to the approach of teaching to solve problems.