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Aplicações da função quadrática : um estudo sobre a aprendizagem dos alunos de 10º ano e as perceções da sua utilidade no dia-a-dia
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O presente trabalho teve como principal objetivo estudar a influência de uma experiência ancorada em tarefas de aplicações e modelação matemática nas perceções dos alunos perante a utilidade da Matemática e das suas aplicações e conexões no dia-a-dia. Analisou-se, também, o impacto da experiência de ensino na aprendizagem do tema da função quadrática e no desenvolvimento de várias capacidades matemáticas.
A experiência de ensino envolveu a lecionação de 14 aulas de 50 minutos, onde predominou o trabalho em grupo, assente numa combinação entre tarefas de natureza exploratória e de consolidação, envolvendo conexões extramatemáticas. A tarefa final, de natureza experimental, envolveu a modelação de um fenómeno STEM (estudo do espessamento de artérias por acumulação de gordura), que resultou na elaboração de um relatório. Os dados foram recolhidos através das produções dos alunos ao longo das aulas, de gravações de áudio e vídeo do trabalho dos alunos em sala de aula quando pertinente, e de dois questionários (um antes e outro após a intervenção) que incidiram sobre as perceções dos alunos perante vários tópicos relacionados com a Matemática e as suas aplicações.
Relativamente às duas dimensões em que me apoiei (aprendizagem e perceções dos alunos), os resultados sugerem que os alunos atingiram os objetivos visados em termos de aprendizagens dos conceitos e procedimentos inerentes ao tema desta intervenção letiva, tendo tido oportunidade de desenvolver a capacidades de raciocínio matemático, conexões matemáticas e modelação. Ao longo da experiência de ensino os alunos também desenvolveram perceções mais positivas: têm mais gosto em aprender Matemática quando compreendem a sua utilidade, passaram a identificar melhor a sua utilidade no dia-a-dia e a reconhecer que a Matemática é uma ajuda na sua vida diária e que aprender mais sobre funções matemáticas os ajuda a compreender melhor as aplicações e conexões da Matemática.
Assim, a par das aprendizagens desenvolvidas, este estudo indicia alterações ao nível das perceções dos alunos que podem ter impacto na sua atitude e desempenho na Matemática, o que justifica a importância de proporcionar intencionalmente oportunidades de aprendizagem sobre as aplicações e a utilidade da Matemática.
The main objective of this study was to investigate the influence of an experiment centred on tasks related to mathematical applications and modelling on students’ perceptions of the usefulness of Mathematics and its applications and connections in everyday life. Additionally, the study examined the impact of the teaching experiment on the learning of the topic quadratic functions and the development of various mathematical skills. The teaching experiment involved 14 lessons of 50 minutes each, predominantly emphasizing group work, based on a combination between exploratory and consolidation tasks, involving extramathematical connections. The final task, of an experimental nature, involved modelling a STEM phenomenon (study of artery thickening due to fat accumulation), which resulted in the preparation of a report. Data were collected through student productions throughout the lessons, audio and video recordings of students’ work in the classroom when relevant, and two questionnaires (one administered before and one after the intervention) that focused on students’ perceptions regarding various topics related to Mathematics and its applications. Regarding the two dimensions I relied on (learning and students’ perceptions), the results suggest that students achieved the intended objectives in terms of learning the concepts and procedures related to the theme of the teaching experiment, had the opportunity to develop several mathematical processes, namely mathematical reasoning, mathematical connections and mathematical modelling. Throughout the teaching experiment, students also developed more positive perceptions: they enjoy learning Mathematics more when they understand its utility, they became better at recognizing its usefulness in the daily basis, and they acknowledge that Mathematics is a helpful tool in their own daily lives. Additionally, learning more about mathematical functions helped them better understand the applications and connections of Mathematics in life. Therefore, in addition to the acquired learning outcomes, this study suggests changes in students’ perceptions that may impact their attitude and performance in Mathematics, justifying the importance of deliberately providing opportunities for learning about the applications and usefulness of Mathematics.
The main objective of this study was to investigate the influence of an experiment centred on tasks related to mathematical applications and modelling on students’ perceptions of the usefulness of Mathematics and its applications and connections in everyday life. Additionally, the study examined the impact of the teaching experiment on the learning of the topic quadratic functions and the development of various mathematical skills. The teaching experiment involved 14 lessons of 50 minutes each, predominantly emphasizing group work, based on a combination between exploratory and consolidation tasks, involving extramathematical connections. The final task, of an experimental nature, involved modelling a STEM phenomenon (study of artery thickening due to fat accumulation), which resulted in the preparation of a report. Data were collected through student productions throughout the lessons, audio and video recordings of students’ work in the classroom when relevant, and two questionnaires (one administered before and one after the intervention) that focused on students’ perceptions regarding various topics related to Mathematics and its applications. Regarding the two dimensions I relied on (learning and students’ perceptions), the results suggest that students achieved the intended objectives in terms of learning the concepts and procedures related to the theme of the teaching experiment, had the opportunity to develop several mathematical processes, namely mathematical reasoning, mathematical connections and mathematical modelling. Throughout the teaching experiment, students also developed more positive perceptions: they enjoy learning Mathematics more when they understand its utility, they became better at recognizing its usefulness in the daily basis, and they acknowledge that Mathematics is a helpful tool in their own daily lives. Additionally, learning more about mathematical functions helped them better understand the applications and connections of Mathematics in life. Therefore, in addition to the acquired learning outcomes, this study suggests changes in students’ perceptions that may impact their attitude and performance in Mathematics, justifying the importance of deliberately providing opportunities for learning about the applications and usefulness of Mathematics.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática no 3º Ciclo do Ensino Básico e no Ensino Secundário, 2023, Universidade de Lisboa, Instituto de Educação
Palavras-chave
Funções (Matemática) Modelação matemática Ensino-aprendizagem Ensino secundário Concepções dos alunos Relatórios da prática de ensino supervisionada - 2023