The development of students’ mathematical reasoning in Calculus courses

• André Luis Trevisan ^[1] ; Eliane Maria de Oliveira Araman ^[1] ; Maria de Lurdes Serrazina ^[2]
  1. [1] Universidade Tecnológica Federal do Paraná

     Universidade Tecnológica Federal do Paraná

     Brasil

     
  2. [2] Instituto Politécnico de Lisboa

     Instituto Politécnico de Lisboa

     Socorro, Portugal

     
• Localización: Avances de investigación en educación matemática: AIEM, ISSN-e 2254-4313, Nº. 24, 2023, págs. 39-56
• Idioma: español
• DOI: 10.35763/aiem24.4326
• Títulos paralelos:
  • El desarrollo del razonamiento matemático de los estudiantes en los cursos de Cálculo
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El objetivo es comprender cómo la participación de los estudiantes en la resolución y discusión de tareas exploratorias, vinculada a las acciones del profesor, puede contribuir al desarrollo de su razona-miento matemático (RM) en el curso de Cálculo Diferencial e Integral. El estudio fue una investigación cua-litativa, y los participantes fueron estudiantes de ingeniería de educación superior. Los datos se componen de (a) protocolos que contienen registros escritos de las discusiones de estudiantes; (b) audios de estas discusiones; y (c) vídeo de la discusión plenaria mediada por el profesor. Discutimos los procesos de RM que movilizan los estudiantes, especialmente conjeturar, generalizar y justificar. Señalamos cuál de las acciones del docente puede contribuir al desarrollo del RM, en un movimiento continuo y creciente, rela-cionado esencialmente con la profundización de las discusiones a partir de elementos presentados por los propios estudiantes, y las oportunidades que se crean en ese proceso.

  • English

    The aim is to understand how the students’ involvement in solving and discussing exploratory tasks, combined with the teacher’s actions, can contribute to the development of their mathematical rea-soning (MR) in a Differential and Integral Calculus course. The study was qualitative, with an interpretive approach, and the participants were undergraduate engineering students. The data consists of (a) proto-cols containing written records of students’ discussions; (b) audio recordings of these discussions; and (c) video of the plenary discussion facilitated by the teacher. We discuss the MR processes that students mo-bilize, in particular conjecturing, generalizing, and justifying. We point out which of the teacher’s actions can contribute to the development of MR, in a continuous and growing movement, essentially related to the deepening of discussions based on elements presented by the students themselves, and the opportu-nities that are created in this process.

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