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Authors
Abstract(s)
O presente estudo tem como foco central os resultados da implementação de uma sequência didática para o ensino-aprendizagem de Sucessões Numéricas, numa disciplina de Análise Matemática do 1º ano de uma licenciatura em Engenharia do Ambiente.
As questões de investigação incluem: a aquisição de diretrizes para a elaboração e implementação de uma sequência didática baseada na resolução de problemas contextualizados e no recurso à folha de cálculo; a compreensão sobre o modo como os alunos fazem uso de diferentes registos de representação semiótica; e a caraterização dos processos de construção de modelos conceptuais pelos alunos. Para tal, são analisados os tipos de registos de representação semiótica que os alunos produzem, a natureza dos modelos que os alunos criam quando se envolvem em atividades propulsoras de modelos, inerentes ao tópico de Sucessões Numéricas, e a utilidade que a folha de cálculo revela ter nestas circunstâncias.
Para o enquadramento teórico do estudo foram consideradas as contribuições de diversas linhas de investigação, designadamente em torno da resolução de problemas e da didática das situações de aprendizagem que sublinham o papel do aluno e do contexto educacional na sua aprendizagem. Assim, o estudo apoia-se em princípios essenciais propostos pela Teoria das Situações Didáticas para sustentar as opções didáticas e metodológicas assumidas. A natureza das questões de investigação, por seu turno, justificou a procura de articulações entre duas teorias chave, designadamente a Teoria de Registos de Representação Semiótica (TRSS) e a Perspetiva de Modelos e Modelação (M&M)
O estudo seguiu uma metodologia interpretativa, baseada em estudos de caso, e foi delineado segundo os pressupostos da Engenharia Didática enquanto modalidade de investigação de índole qualitativa, integrando uma vertente de experiência de ensino. Os participantes são os alunos do 1.º ano do curso de licenciatura em Engenharia do Ambiente ministrado na Escola Superior Politécnica do Namibe (ESPtN). Entre estes, foram selecionados três alunos que permitiram a realização de três estudos de caso. O autor do presente estudo assumiu o papel de professor-investigador, sendo assim o docente que lecionou as aulas da sequência didática implementada.
A recolha de dados incluiu a observação participante, em sala de aula, dos alunos no decurso da realização das tarefas propostas, os seus relatórios escritos, o registo vídeo e áudio das falas, argumentações e comentários proferidos pelos três alunos-casos durante a resolução de problemas e ainda os resultados de inquéritos aplicados a todos os alunos do primeiro ano do referido curso e aos professores de matemática da escola supracitada. Com este estudo, foi possível concluir que a realização de atividades propulsoras de modelos inerentes ao tópico de Sucessões Numéricas, com recurso à folha de cálculo, fornece oportunidades para os alunos alcançarem aprendizagens específicas, inerentes a conceitos matemáticos, mas também aprendizagens de caráter mais abrangente, como seja, a sua capacidade de interpretar uma situação e de a matematizar, mobilizando os seus conhecimentos anteriores ou prosseguindo para novos conhecimentos.
Os resultados evidenciaram a possibilidade de um paralelismo entre os ciclos de modelação efetuados pelos alunos e as sucessivas conversões de registos semióticos, o que confirma que a experiência do ensino proporcionou a aprendizagem dos alunos, na ótica das duas perspetivas teóricas. Por fim, importa referir que o estudo revelou que a folha de cálculo subsidiou, de forma relevante, a concretização de tratamentos de registos numéricos, bem como múltiplas conversões de registos.
The present study has as its central focus on the results of the implementation of a didactical sequence for the teaching and learning of Numerical Sequences, in a Real Analysis course, as part of the 1st year of a degree in Environmental Engineering. The research questions include: the acquisition of guidelines for the elaboration and implementation of a didactical sequence based on solving contextualized problems and the use of the spreadsheet; the understanding of how students make use of different registers of semiotic representation; and the characterization of the processes of construction of conceptual models by the students. To do so, we analyse the types of registers of semiotic representation that students produce, the nature of the models that students create when engaging in modelling activities in the topic of Numerical Sequences, and the usefulness that the spreadsheet reveals under these circumstances. For the theoretical framework of the study, the contributions of several lines of research were considered, namely around problem solving and the didactics of learning situations that emphasize the student’s role and the educational context in learning. Thus, the study is based on essential principles proposed by the Theory of Didactical Situations to support the didactical and methodological options assumed. The nature of the research questions, in turn, justified the search for articulations between two key theories, namely the Theory of Registers of Semiotic Representation (TRSS) and the Models and Modelling Perspective (M&M). The study followed an interpretative methodology, based on case studies, and was delineated according to the assumptions of Didactical Engineering as a research approach of a qualitative nature, integrating a teaching experience. The participants are the 1st year students of a degree in Environmental Engineering taught at the Namibe Polytechnic School (ESPtN). Among those, three students were selected, allowing three case studies to be carried out. The author of the present study assumed the role of teacher-researcher, being thus the teacher who taught the classes of the didactical sequence implemented. The data collection included participant observation of the students in the course of carrying out the proposed tasks, their written reports, the video and audio recording of the statements, arguments and comments made by the three student-cases during the resolution of the problems, as well as the results of surveys applied to all students in the first year of the mentioned course and to the mathematics teachers of the aforementioned School. With this study, it was possible to conclude that the model eliciting activities related to the topic of Numerical Sequences, using the spreadsheet, provided opportunities for students to achieve specific learning, regarding mathematical concepts, but also learning of a more comprehensive nature, such as the ability to interpret a situation and to mathematise it, by activating previous knowledge or pursuing new knowledge. The results evidenced the possibility of a parallelism between the modelling cycles carried out by the students and the successive conversions of semiotic registers, confirming that the teaching experience generated relevant learning, from the perspective of the two theoretical perspectives. Finally, it should be noted that the spreadsheet significantly subsidized the processing of numerical registers as well as multiple conversions between semiotic registers.
The present study has as its central focus on the results of the implementation of a didactical sequence for the teaching and learning of Numerical Sequences, in a Real Analysis course, as part of the 1st year of a degree in Environmental Engineering. The research questions include: the acquisition of guidelines for the elaboration and implementation of a didactical sequence based on solving contextualized problems and the use of the spreadsheet; the understanding of how students make use of different registers of semiotic representation; and the characterization of the processes of construction of conceptual models by the students. To do so, we analyse the types of registers of semiotic representation that students produce, the nature of the models that students create when engaging in modelling activities in the topic of Numerical Sequences, and the usefulness that the spreadsheet reveals under these circumstances. For the theoretical framework of the study, the contributions of several lines of research were considered, namely around problem solving and the didactics of learning situations that emphasize the student’s role and the educational context in learning. Thus, the study is based on essential principles proposed by the Theory of Didactical Situations to support the didactical and methodological options assumed. The nature of the research questions, in turn, justified the search for articulations between two key theories, namely the Theory of Registers of Semiotic Representation (TRSS) and the Models and Modelling Perspective (M&M). The study followed an interpretative methodology, based on case studies, and was delineated according to the assumptions of Didactical Engineering as a research approach of a qualitative nature, integrating a teaching experience. The participants are the 1st year students of a degree in Environmental Engineering taught at the Namibe Polytechnic School (ESPtN). Among those, three students were selected, allowing three case studies to be carried out. The author of the present study assumed the role of teacher-researcher, being thus the teacher who taught the classes of the didactical sequence implemented. The data collection included participant observation of the students in the course of carrying out the proposed tasks, their written reports, the video and audio recording of the statements, arguments and comments made by the three student-cases during the resolution of the problems, as well as the results of surveys applied to all students in the first year of the mentioned course and to the mathematics teachers of the aforementioned School. With this study, it was possible to conclude that the model eliciting activities related to the topic of Numerical Sequences, using the spreadsheet, provided opportunities for students to achieve specific learning, regarding mathematical concepts, but also learning of a more comprehensive nature, such as the ability to interpret a situation and to mathematise it, by activating previous knowledge or pursuing new knowledge. The results evidenced the possibility of a parallelism between the modelling cycles carried out by the students and the successive conversions of semiotic registers, confirming that the teaching experience generated relevant learning, from the perspective of the two theoretical perspectives. Finally, it should be noted that the spreadsheet significantly subsidized the processing of numerical registers as well as multiple conversions between semiotic registers.
Description
Keywords
Sucessões numéricas - Ensino Aprendizagem Didáctica da Matemática