Introdução do conceito de número negativo: uma proposta de tarefas no contexto do ensino desenvolvimental

Abstract

The present study aimed to analyze, in light of the Developmental Teaching proposal (Elkonin- Davídov system), possibilities of organizing the teaching of negative integers based on proposed tasks that enable advances in attempts to overcome those recognized as traditional. It is understood that this mathematical concept, formally introduced in the seventh year of Elementary School, constitutes a complex concept for students and teachers, which requires the transition from empirical thinking to theoretical thinking, an indispensable condition for progress in later content. As a methodology, qualitative research was used, in the bibliographic modality, based on authors, among which Vygotsky (2001; 2014), Davídov (1982; 1987; 1988), Búrigo (2015), Freitas (2016) and Búrigo and Damazio (2016). This option allowed us to bring together different perspectives on the organization of teaching, with an emphasis on teaching and study activities, the role of schools and teacher training, as well as the limits of pedagogical approaches that, despite being disseminated as innovative, often do not favor the effective appropriation of the concept of negative numbers. The results of the analysis indicated that the predominance of everyday and fragmented examples leads to restricted and superficial learning, which hinders the development of abstract mathematical reasoning. The influence of curricular choices, teacher training and manipulable teaching materials in maintaining these difficulties was also highlighted. It is concluded that the objective was achieved, by problematizing the teaching of negative numbers, pointing out the need for proposals that interrelate, in the context of teaching activity, concrete situations to theoretical systematization and the elaboration of particular tasks that can help in the introduction of this concept. As a limitation, the lack of empirical research in the proposed tasks stands out, which suggests future research of a practical nature that tests, in the classroom, the effectiveness of these tasks and their ability to promote learning.