Tasks for teaching and learning first-degree polynomial equation in the 6th grade elementary school

Abstract

This article aimed to analyze how the teacher's specialized knowledge to work with mathematical tasks on first-degree polynomies equations can promote possible learning situations of 6th grade elementary school students. For this, three tasks were analyzed: one of the types of exercise, another of the problem type and a third of the investigative type, selected from the Matemática: compreensão e prática, by Ênio Silveira and Convergências matemáticas, by Eduardo Chavante (PNLD 2020). The classification of the tasks was performed based on Ponte (2005) and analyzed based on the task markers proposed by Barbosa (2013) and Costa, Oliveira e Silva (2017). For the analysis of the possible knowledge mobilized by the teacher for the implementation of such tasks, the theoretical model Mathematics Teacher's Specialized Knowledge (MTSK) elaborated by Carrillo et al (2013) was used. The results show that mathematical tasks are a fundamental segment in the teaching and learning process, constituting a guiding thread of the teacher's pedagogical work and students' learning. The knowledge of the teacher as the main transforming element of students' learning and that one should prioritize work with challenging tasks, which has a high level of cognitive requirement, that leads the student to think through mathematical relationships and connections, to the detriment of the mechanical use of memorized and unconnected rules and procedures.