Processos de Raciocínio Matemático Mobilizados por Estudantes de Cálculo em Tarefas Envolvendo Representações Gráficas

Abstract

Acknowledging the importance of reasoning development as a basic competence in learning Differential and Integral Calculus, this work is aimed at understanding the mathematical reasoning processes of students in this discipline, in the process involving the investigation of task resolution that contains the coordinated analysis of changes that happen in two interdependent variables. Adoptin a qualitative perspective of an interpretative nature, with the principles of Design-Based Research, we use the written protocol and audio recordings of the work of three groups of students when solving task involving the creation, interpretation, and reflection about graphics. As a result, we highlight a process construction of conjectures supported by mathematical knowledge that they already had, in the perception of relationships present in the task or, still, in common sense. In addition, we emphasize the search for reasons for validation or refutation, at which time students recovered knowledge they already had or * Doutor em Ensino de Ciências e Educação Matemática pela Universidade Estadual de Londrina (UEL). Professor do Departamento de Matemática da Universidade Tecnológica Federal do Paraná (UTFPR), Londrina, Paraná, Brasil. E-mail: andrelt@utfpr.edu.br. ** Doutora em Ensino de Ciências e Educação Matemática pela Universidade Estadual de Londrina (UEL). Professora do Departamento de Matemática da Universidade Tecnológica Federal do Paraná (UTFPR), Cornélio Procópio, Paraná, Brasil. E-mail: elianearaman@utfpr.edu.br. ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980-4415v35n69a08 Bolema, Rio Claro (SP), v. 35, n. 69, p. 158-178, abr. 2021 159 built new mathematical knowledge, with the elaboration of new conjectures or improvement of an already elaborated on, new investigations and attempts to justify. Finally, we highlight the role played by the discussion among students, as well the potential and limitations of the tasks.