Tarefas matemáticas e desenvolvimento do conhecimento matemático no 5.º ano de escolaridade

 

Regina Bispo (*)

Glória Ramalho (*)

Nuno Henriques (*)

 

RESUMO

As tarefas matemáticas providenciam o contexto no qual os estudantes aprendem matemática. Embora sejam muitos os factores que influenciam o processo de aprendizagem da matemática, as tarefas propostas aos estudantes são determinantes na medida em que actuam como “causas próximais” da aprendizagem.

O nível de exigência cognitiva e a promoção do processo de matematização são características fundamentais nas tarefas propostas aos alunos.

Este estudo incide sobre a análise das tarefas matemáticas propostas por professores a alunos do 5.º ano de escolaridade. Os itens foram analisados de acordo com e estrutura teórica desenvolvida no âmbito do programa PISA da OECD.

Os níveis de exigência cognitiva mais elevados foram encontrados no desenvolvimento das competências matemáticas Comunicação e Pensamento e Raciocínio, sendo estes significativamente maiores que os associados às competências Argumentação, Colocação e Resolução de problemas, Modelação e Uso de auxiliares e instrumentos. A competência matemática menos trabalhada nos itens analisados é o Uso de linguagem simbólica, formal e técnica.

A análise dos dados mostrou que a maioria das tarefas incluem-se no grupo das tarefas de Reprodução.

Em conclusão, o estudo evidencia que a grande maioria das tarefas não usam contextos realistas e, predominantemente, conduzem os estudantes a seleccionar procedimentos e algoritmos de resolução pré-definidos.

Palavras-chave: Tarefas matemáticas, ensino da matemática, competências matemáticas, níveis de exigência cognitiva.

 

ABSTRACT

Mathematical tasks provide the context in which students learn mathematics. Although many factors also determine the learning process, instructional tasks operate as the “proximal causes” of students’ learning from teaching.

Their characterization can therefore help to understand the link between teaching and learning mathematics.

Different mathematical tasks can be associated with different cognitive processes and so induce different kinds of learning. Cognitive demand and the ability to promote mathematisation are key characteristics of instructional tasks.

This study focused on the analysis of mathematical tasks proposed to 5th grade students by their teachers. The instructional tasks were analyzed according to the OECD/PISA framework.

Higher cognitive demands appear associated with the Communication and Thinking and Reasoning mathematical competencies. Competencies such as Argumentation, Problem posing and Solving, Modeling and Use of Aids and Tools are worked at a significant lower cognitive level. The mathematical competency less worked was the Use of symbolic, formal and technical language and operations.

Data analysis also showed that most of the tasks are included in a reproduction cluster.

In conclusion, the analysis showed that in most cases instructional tasks do not have a real-world context and only lead students, predominantly, to select routine procedures and/or apply standard algorithms.

Key words: Mathematical tasks, mathematical competencies, levels of cognitive demande.

 

Texto completo disponível apenas em PDF.

Full text only available in PDF format.

 

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(*) Unidade de Investigação em Psicologia Cognitiva, Instituto Superior de Psicologia Aplicada, Lisboa.