Equação Polinomial do 2º Grau: abordagem em materiais curriculares, prática de ensino e de aprendizagem para o 8º e 9º anos do Ensino Fundamental

Abstract

The research presented in this dissertation was guided by the objective of understanding the approach given to the quadratic equation in curriculum materials for the 8th and 9th grades of Middle School and its learning process by students. Using a qualitative approach, it is a documentary analysis of eight Teacher's Manuals for the 8th and 9th grades, guided by the specific objectives of analyzing task-solving strategies and the roles of teachers and students in the approach given to the quadratic equation in Teacher's Manuals for the 8th and 9th grades, and examining the cognitive demands underlying the approach given to the quadratic equation in curriculum materials for the 8th and 9th grades; and also a case study that aimed to problematize the learning process of 9th-grade students regarding the quadratic equation based on proposals incorporated in curriculum materials. The studies developed in correspondence to each of these objectives are reported in three articles that comprise this dissertation. For the document analysis, tasks related to quadratic equations and their corresponding teaching guidelines were mapped and analyzed in light of theories on levels of cognitive demands, teaching approaches, and the expected roles of teachers and students in Mathematics classes. For the case study, learning processes were problematized based on a set of tasks with different levels of cognition and that envision varied student roles. The results show a predominance of low-level cognitive tasks, such as unconnected procedures, which may imply learning based on techniques and strategies that do little to mobilize mathematical reasoning; they also highlight the predominantly responsive role attributed to the student in the interaction with the tasks, which may result in learning centered on the reproduction of facts devoid of meaning; and, finally, the reproductive role attributed to teachers in teaching practices, which may limit their performance as agents of knowledge capable of mobilizing knowledge in the creation of learning opportunities. Regarding the implemented tasks, the results indicate that those with a low level of cognition were solved in a way that maintained the originally proposed cognitive level, showing a higher level of comprehension on the part of the students. Conversely, tasks requiring more complex reasoning and demanding higher levels of cognition were not well understood, resulting in unsatisfactory student performance. This highlights the importance of considering the cognitive levels of the tasks and adopting balanced approaches in curriculum materials, since these aspects can favor teaching and learning processes. The difficulties presented by students in solving high-level cognitive tasks are associated with reading and interpreting mathematical texts, as well as a lack of prior knowledge in Arithmetic and Algebra