MODELAGEM MATEMÁTICA NO ENSINO DE EQUAÇÕES POLINOMIAIS DE 1º GRAU: uma abordagem no 7º ano do ensino fundamental

Abstract

The aim of this research was to investigate the contributions of mathematical modeling as a didactic strategy for teaching first-degree polynomial equations to a 7th-grade class at a municipal public elementary school in Elesbão Veloso, Piauí, Brazil. The study is based on the diagnosis that traditional teaching of this content, grounded in the memorization of procedures and the mechanical resolution of decontextualized exercises, contributes to students’ lack of motivation and low performance in internal and external assessments. The research adopts the mathematical modeling cycle as its central methodological framework, articulating the stages of interaction, mathematization, and validation with the teaching of introductory algebra. The pedagogical intervention was organized into eight sessions, structured around two thematic cycles: the first focused on modeling the electricity bill from Equatorial Piauí, and the second on modeling the water bill from Águas do Piauí. Sixteen students participated in the research and collectively constructed mathematical models representing real tariff structures, validating them through residential consumption bills from their own families. The study adopts a qualitative, quantitative, exploratory, and action research approach, using pre-test and post-test assessments, participant observations recorded in a field diary, students’ productions, and photographic records as data collection instruments. The results revealed substantial and widespread improvement in the class’s performance, with a significant increase in the total number of correct answers and a considerable reduction in the total number of errors between the two assessment moments. The individual mean number of correct answers increased substantially, with the vast majority of students demonstrating positive progress throughout the intervention. All ten questions in the assessment instrument showed positive growth, with particularly notable improvement in the questions that had the lowest rates of correct answers in the initial diagnostic assessment. The results indicate that mathematical modeling, by connecting algebraic content to real-life situations that are meaningful to students, promotes more contextualized learning, develops critical thinking and investigative autonomy, and contributes to students’ civic education, in full alignment with the guidelines of the Brazilian National Common Curricular Base (BNCC). It is concluded that the approach proved effective and meaningful, with potential for replication in the teaching of first-degree polynomial equations in the context of 7th-grade public elementary education in the interior of Piauí.