Rotas de modelação matemática apoiadas pela tecnologia na aprendizagem da álgebra linear: um estudo com estudantes universitários da Costa Rica
DOI:
https://doi.org/10.48489/quadrante.23721Palavras-chave:
álgebra linear, estudantes universitários, rotas de modelação matemática, modelo computacional, folha de cálculoResumo
A modelação matemática é um contexto relevante e produtivo para o ensino da álgebra linear, favorecendo a aprendizagem de conceitos e competências de modelação dos estudantes, comumente negligenciadas na matemática universitária. Este estudo visa caracterizar rotas de modelação realizadas e competências postas em prática por estudantes universitários da Costa Rica, numa disciplina de álgebra linear, ao resolverem uma tarefa de modelação matemática envolvendo conceitos de conjunto gerador e base de um subespaço vetorial, usando uma folha de cálculo. A recolha de dados incluiu observação participante das discussões dos estudantes e suas resoluções escritas, bem como os ficheiros Excel produzidos. A análise revelou rotas de modelação dos estudantes incompletas e completas, nas quais utilizaram conceitos de combinação linear, subespaço gerado, base canónica e não canónica para construir modelos. O uso da tecnologia influenciou o modo como os alunos obtiveram resultados matemáticos e reais extraídos do seu modelo matemático. Nas rotas completas, o modelo computacional impulsionou transições no ciclo de modelação entre resultados computacionais, matemáticos e reais, melhorando os processos de modelação. Complementarmente, o Excel desempenhou duas funções principais, calcular e simular, permitindo aos grupos que o utilizaram avaliarem a eficácia dos seus modelos matemáticos e computacionais e validá-los no confronto com a situação real.
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