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Construindo desafios: A Formulação de problemas matemáticos num 3º ano de escolaridade
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Abstract(s)
A presente investigação, realizada no âmbito do Mestrado de Qualificação para a Docência em Educação Pré-Escolar e Ensino do 1.º CEB, foi conduzida na formulação e resolução de problemas matemáticos numa turma do 3.º ano do 1.º Ciclo do Ensino Básico, composta por 20 alunos.
A resolução e a formulação de problemas em Matemática no 1.º Ciclo do Ensino Básico são fundamentais para o desenvolvimento de capacidades e competências essenciais dos alunos, ajudando-os a compreender os conceitos matemáticos de forma concreta e a promover o raciocínio lógico e o pensamento crítico. A resolução de problemas assume um papel especial no ensino e aprendizagem em Matemática, destacado nos documentos curriculares da Matemática, desde os primeiros anos, pois ajuda a atribuir significado aos conceitos e a estabelecer conexões dentro e fora da disciplina. Em relação à formulação de problemas é-lhe dada, ainda, pouca relevância, no entanto, este processo permite que os alunos apliquem os conhecimentos em situações práticas, compreendendo profundamente os conceitos matemáticos. Além disso, a prática de formular e resolver problemas contribui para o desenvolvimento de capacidades de resolução de problemas, fundamentais tanto na matemática como noutras áreas do conhecimento e na vida quotidiana.
O principal objetivo foi analisar as potencialidades e fragilidades dos alunos, considerando a tipologia das tarefas e as representações utilizadas nas suas resoluções, no que respeita à formulação de problemas. Assim, foram formuladas as seguintes questões orientadoras: 1) De que forma os alunos formulam problemas em Matemática? 2) Quais as potencialidades e as fragilidades evidenciadas pelos alunos na formulação de problemas em Matemática? 3) Quais as estratégias a que os alunos recorrem na resolução de problemas em Matemática?
Tendo isso em conta, para este estudo, desenvolveu-se uma proposta didática com a seleção criteriosa de treze tarefas, sendo quatro de resolução de problemas e nove de formulação de problemas. Ao longo da investigação, utilizou-se uma metodologia qualitativa, seguindo o design de investigação-ação, do paradigma interpretativo. A recolha de dados foi realizada por meio de observação participante, gravações de áudio, diário de bordo e documentos das tarefas propostas aos alunos. Para a análise dos dados, foram definidas categorias e indicadores que permitiram avaliar as estratégias de resolução e formulação de problemas.
A análise dos dados possibilitou concluir que os alunos demonstraram grande empenho, interesse e motivação neste tipo de tarefas. Contudo, os alunos demonstraram pouca criatividade na formulação dos problemas, com a maioria a permanecer fiel às expressões fornecidas e encontradas nos manuais escolares.
The present investigation, conducted within the scope of the master’s degree in Teacher Qualification for Preschool Education and 1º CEB on the formulation and resolution of mathematical problems in a 3rd grade class of the 1st Cycle of Basic Education, consisting of 20 students. The solving and formulation of Mathematical problems in the 1st Cycle of Basic Education are fundamentals for the students’ development of competencies and essential skills, helping them understand the mathematical concepts in a concrete way and promoting logic thought process and critical thinking. Problem solving plays a special role in Mathematical teaching and learning, highlighted in the Mathematics curricular documents, since the first years, as it helps give meaning to the concepts and establish connections inside and outside the subject. When it comes to problem formulation, it is given, still, little relevance. However, this process allows the students to apply their knowledge in practical situations, deeply understanding the mathematical concepts. Besides that, the practice of formulating and solving problems contributes to the development of problem-solving skills, fundamental in mathematics and also other areas of knowledge and everyday life. The main objective was to analyze the strengths and weaknesses of the students, considering the types of tasks and representations used in their solutions. This way, the following guiding questions were formulated: 1) How do students formulate problems in Mathematics? 2) What strengths and weaknesses are shown by the students during the formulation of Mathematical problems? 3) What resolution strategies do the students use when solving Mathematical problems? Whit this in mind, for this study, a didactic proposal was developed with the careful selection of thirteen tasks, where four were problem solving tasks and nine were problem formulation tasks. Throughout the investigation, a qualitative methodology was used, following the investigation-action design, from the interpretative paradigm. Data collection was carried out through participant observation, audio recordings, a logbook and documents with the tasks proposed to the students. For the data analysis, categories and indicators, which allowed for the evaluation of the strategies of problem solving and formulation, were defined. The data analysis allowed us to conclude that the students showed great effort, interest and motivation. However, it is concluded that the students showed lack of creativity in problem formulation, with the majority staying loyal to the given expressions, found in schoolbooks.
The present investigation, conducted within the scope of the master’s degree in Teacher Qualification for Preschool Education and 1º CEB on the formulation and resolution of mathematical problems in a 3rd grade class of the 1st Cycle of Basic Education, consisting of 20 students. The solving and formulation of Mathematical problems in the 1st Cycle of Basic Education are fundamentals for the students’ development of competencies and essential skills, helping them understand the mathematical concepts in a concrete way and promoting logic thought process and critical thinking. Problem solving plays a special role in Mathematical teaching and learning, highlighted in the Mathematics curricular documents, since the first years, as it helps give meaning to the concepts and establish connections inside and outside the subject. When it comes to problem formulation, it is given, still, little relevance. However, this process allows the students to apply their knowledge in practical situations, deeply understanding the mathematical concepts. Besides that, the practice of formulating and solving problems contributes to the development of problem-solving skills, fundamental in mathematics and also other areas of knowledge and everyday life. The main objective was to analyze the strengths and weaknesses of the students, considering the types of tasks and representations used in their solutions. This way, the following guiding questions were formulated: 1) How do students formulate problems in Mathematics? 2) What strengths and weaknesses are shown by the students during the formulation of Mathematical problems? 3) What resolution strategies do the students use when solving Mathematical problems? Whit this in mind, for this study, a didactic proposal was developed with the careful selection of thirteen tasks, where four were problem solving tasks and nine were problem formulation tasks. Throughout the investigation, a qualitative methodology was used, following the investigation-action design, from the interpretative paradigm. Data collection was carried out through participant observation, audio recordings, a logbook and documents with the tasks proposed to the students. For the data analysis, categories and indicators, which allowed for the evaluation of the strategies of problem solving and formulation, were defined. The data analysis allowed us to conclude that the students showed great effort, interest and motivation. However, it is concluded that the students showed lack of creativity in problem formulation, with the majority staying loyal to the given expressions, found in schoolbooks.
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Keywords
Matemática; 1.º CEB; Formulação e resolução de problemas matemáticos. Mathematics, 1º CEB, Mathematical problem formulation and resolution