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RESOLUÇÃO DE PROBLEMAS EM CONTEXTO REAL UMA ABORDAGEM ÀS INEQUAÇÕES NO 9.º ANO
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O presente relatório desenvolveu-se no âmbito do Mestrado em Ensino de matemática no 3.º ciclo do Ensino Básico e no Secundário e tem como objetivo descrever e refletir sobre o trabalho realizado na prática de ensino supervisionada, no ano letivo 2021/2022, bem como o trabalho de investigação com alguns alunos da turma do 9.º ano que a professora estagiária acompanhou.
A prática de ensino supervisionada compreende uma descrição e análise do trabalho pe-dagógico desenvolvido durante o ano letivo. Por um lado, a prática letiva descreve a observa-ção, planificação e lecionação de aulas e, por outro lado, contempla a dinamização de atividades não letivas, assim como a participação em reuniões e termina com uma reflexão sobre a prática de ensino.
O trabalho de investigação teve como objetivo compreender o raciocínio demonstrado pelos alunos do 9.º ano relativamente à diversidade na resolução de problemas em contexto da vida real. Neste sentido, foram analisadas as resoluções dos alunos a problemas do quotidiano com base na explicação dos próprios, em entrevistas. A intenção subjacente ao estabelecimento deste objetivo era responder às seguintes questões de investigação:
1. De que forma os alunos interpretam o enunciado de problemas da vida real e o traduzem algebricamente?
2. Quais as etapas por que os alunos passam durante a resolução de problemas?
3. De que modo os problemas da vida real contribuem para a compreensão das inequações?
4. Qual a análise que os alunos fazem entre a solução obtida e a resposta adequada ao pro-blema?
A realização do estudo seguiu uma metodologia qualitativa com base em três estudos de caso. As técnicas de recolha de dados foram a observação participante, a observação não parti-cipante, a recolha documental e a entrevista semiestruturada.
As conclusões do estudo sugerem que os alunos apresentam capacidades na tradução dos enunciados dos problemas algebricamente. As etapas de resolução dos problemas seguidas co-adunam-se com a heurística proposta por Pólya. Destaca-se o facto de os alunos terem analisado e refletido sobre a solução obtida, sendo que mesmo em casos de sucesso de resolução dos problemas seria pertinente, num estudo futuro, ponderar sobre a suscetibilidade de generaliza-ção. A proposta de problemas com contexto real, envolvendo inequações, parece contribuir positivamente para a aprendizagem dos alunos, ao promover um envolvimento mais profundo.
The present report is a result of a Master's Degree in Mathematics Teaching in Secondary Education and it aims to describe and reflect on the work done in the supervised teaching prac-tice, in the school year 2021/2022, as well as the research conducted with some students of a 9𝑡ℎ grade class that the student teacher has accompanied. The first part of the report focus on the supervised teaching practice and includes a de-scription and analysis of the pedagogical work developed during the school year. On one hand, the teaching practice, including observation, planning and classes teaching and, on the other hand, the non-teaching practice, including the dynamization of a diversified set of activities promoted out of the classroom, and attending meetings. This part of the report finishes with a reflection on teaching practice. The second part of the report presents a study aiming to understand how the students react to problem solving, in a real-life context, while studying Inequalities. The students’ approach to the problems was analysed based in their written reports and in their own explanations pro-vided during a set of interviews. The purpose underlying the establishment of this aim was to answer the following re-search questions: 1. How do the students explain the problems in real life and translate it in algebra? 2. Which steps do the students surpass during the problems solving? 3. How do the problems of the real life contribute to the understanding of inequalities? 4. What is the analysis that the students do between the acquired solution and the adequate answer to the problem? The study followed a qualitative methodology based in three case studies. Data collection was based in observation, the documentary data collection and semi-structured interviews. The conclusions of the study suggest that the students have skills to translate the problems algebraically. The steps to solve the problems followed are in line with the heuristic proposed by Pólya. It must be highlighted that the students analyzed and reflected on the solution ob-tained, and even in cases of successful problem solving it would be pertinent, in a future study, to consider the susceptibility of generalization. The proposal of problems with real context, involving inequalities, seems to contribute positively to the students' learning, by promoting a deeper involvement.
The present report is a result of a Master's Degree in Mathematics Teaching in Secondary Education and it aims to describe and reflect on the work done in the supervised teaching prac-tice, in the school year 2021/2022, as well as the research conducted with some students of a 9𝑡ℎ grade class that the student teacher has accompanied. The first part of the report focus on the supervised teaching practice and includes a de-scription and analysis of the pedagogical work developed during the school year. On one hand, the teaching practice, including observation, planning and classes teaching and, on the other hand, the non-teaching practice, including the dynamization of a diversified set of activities promoted out of the classroom, and attending meetings. This part of the report finishes with a reflection on teaching practice. The second part of the report presents a study aiming to understand how the students react to problem solving, in a real-life context, while studying Inequalities. The students’ approach to the problems was analysed based in their written reports and in their own explanations pro-vided during a set of interviews. The purpose underlying the establishment of this aim was to answer the following re-search questions: 1. How do the students explain the problems in real life and translate it in algebra? 2. Which steps do the students surpass during the problems solving? 3. How do the problems of the real life contribute to the understanding of inequalities? 4. What is the analysis that the students do between the acquired solution and the adequate answer to the problem? The study followed a qualitative methodology based in three case studies. Data collection was based in observation, the documentary data collection and semi-structured interviews. The conclusions of the study suggest that the students have skills to translate the problems algebraically. The steps to solve the problems followed are in line with the heuristic proposed by Pólya. It must be highlighted that the students analyzed and reflected on the solution ob-tained, and even in cases of successful problem solving it would be pertinent, in a future study, to consider the susceptibility of generalization. The proposal of problems with real context, involving inequalities, seems to contribute positively to the students' learning, by promoting a deeper involvement.
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Resolução de problemas Inequações do 1.º grau matemática