A elaboração de problemas envolvendo o princípio multiplicativo: um estudo documental de livros didáticos do 6º ano à luz da BNCC

Abstract

This research aims to analyze how three 6th-grade Elementary School Mathematics textbook collections approved by the PNLD 2024 address problem-posing involving the multiplicative principle, in accordance with the EF05MA09 skill of the BNCC (BRASIL, 2018). The study is grounded in Mathematics Education discussions regarding problem-solving and problem-posing, particularly drawing from the contributions of Pólya, Onuchic, Smole, Allevato, and Ponte, who highlight the importance of the tasks’ degree of openness and student protagonism in the learning process. Characterized as a qualitative, descriptive, and documentary research, its analytical corpus comprised the collections A Conquista Matemática, Teláris Essencial, and Matemática e Realidade. The selected activities were analyzed under two distinct categories: the tasks' degree of openness and cognitive demand (Categories A) and the level of alignment with the BNCC's EF05MA09 skill (Categories B). The results indicate that the collections exhibit different degrees of openness in problem-posing activities, demonstrating a predominance of authorial tasks in the A Conquista Matemática collection, whereas activities in the other collections presented a previously defined mathematical structure or operations. Furthermore, a predominance of activities failing to explicit counting contexts or other typical scenarios of the multiplicative principle was observed, which does not intentionally foster the development of combinatorial thinking as prescribed by the EF05MA09 skill. In conclusion, there is a clear need for greater pedagogical guidance in problem-posing tasks to strengthen both intellectual autonomy and conceptual understanding of the multiplicative principle in the 6th grade of Elementary School.