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As aulas ditas tradicionais, essencialmente expositivas, caracterizam-se pela centralidade do papel do professor no processo de ensino-aprendizagem. Deste modo, em geral, os alunos têm uma atitude passiva e o professor, essencialmente, pratica a transferência de conhecimento. Estudos, de várias áreas que não só da Educação Matemática e da Didática da Matemática, apontam para as vantagens na mudança do paradigma do referido tipo de aulas. Concretamente, apela-se à centralidade do aluno no processo de ensino-aprendizagem e à sua aprendizagem ativa.
A Aprendizagem pelos Pares, designada originalmente por Peer Instruction nos trabalhos do Físico Eric Mazur, surge no contexto dessa mudança e ainda pela observação de falhas na aprendizagem conceptual dos alunos. O referido método de ensino-aprendizagem é centrado no aluno e pretende, por um lado, a substituição da transferência do conhecimento pela assimilação do mesmo e, por outro lado, a aprendizagem conceptual. Nas palavras de Mazur, "Ensinar é apenas ajudar a aprender" e o desafio é o de encontrar novas maneiras de chegar aos alunos.
Do referido método de ensino-aprendizagem fazem parte: o estudo prévio dos conteúdos pelos alunos; a proposta de questões conceptuais pelo professor; as votações dos alunos nestas; a discussão entre pares, neste caso, alunos. No mesmo foram adotados os princípios da Aprendizagem Cooperativa, com base na Teoria Socioconstrutivista de Vygotsky, a qual realça a importância das atividades sociais, nomeadamente da discussão entre alunos sobre o que se está a realizar, para a promoção da aprendizagem.
No âmbito deste trabalho, foi efetuado um estudo norteado pelas seguintes questões de investigação: 1 - Quais os erros decorrentes das principais dificuldades dos alunos no Tema II - Introdução ao Cálculo Diferencial II do 12.º ano?; 2 - Com base nos mesmos, que questões conceptuais podem ser construídas para aplicação da Aprendizagem pelos Pares nesse tema?; 3 – Que adaptações podem e/ou devem ser feitas à Aprendizagem pelos Pares na sua aplicação ao nível do Ensino Secundário?. No estudo utilizámos uma metodologia de natureza qualitativa e interpretativa, com recurso a um questionário dirigido a professores de Matemática e a testes de avaliação de alunos como instrumentos de recolha de dados.
Procurámos, em primeiro lugar, conhecer o método Aprendizagem pelos Pares e eventuais adaptações que podem ser feitas no Ensino Secundário. Em segundo lugar, procurámos identificar e compreender as dificuldades e os erros que experimentam os alunos do 12.º ano no Tema II - Introdução ao Cálculo Diferencial II. Em terceiro lugar, também com o apoio da revisão de literatura feita, construímos questões conceptuais, criando recursos didáticos, para o tópico Regras Operatórias de Logaritmos selecionado do tema mencionado.
Por último, apresentamos uma planificação, para o tópico referido mas não implementada, de uma aula com o método de Aprendizagem pelos Pares. Para sustentar a mesma, para além das fundamentais questões conceptuais, apresentámos, descrevemos e analisámos um manual de 12.º ano. Elaborámos ainda um trabalho de casa associado ao estudo prévio do tópico pelos alunos. No futuro, com a reflexão após a implementação, haverá certamente aspetos (tarefas propostas, materiais utilizados, comunicação) da prática letiva do professor a melhorar.
The so-called traditional lectures, mainly expository, are characterized by the centrality of the teacher’s role in the teaching-learning process. Thus, in general, students have a passive attitude and the teacher, essentially, transfers knowledge to the students. Studies, in many fields other than Mathematics Education and Didactics of Mathematics, point to the benefits of shifting the paradigm of this type of classes. In particular, they call for the centrality of students in the teaching-learning process and for their active learning. Peer Learning, originally named Peer Instruction in the works of the physicist Eric Mazur, arises in the context of that shift as well as from observing gaps in students’ conceptual learning. This student-centred teaching-learning method aims, on the one hand, to replace knowledge transfer by its assimilation and, on the other hand, conceptual learning. In Mazur’s own words, "Teaching is just helping students to learn" and the challenge is to find new ways to reach students. This teaching-learning method comprises: pre-class study of contents by the students; the conceptual questions proposed by the teacher; the votings of the students on these; the discussion among peers, in this case, students. Moreover, it incorporates the principles of Cooperative Learning, based on Vygotsky’s Social Constructivist Theory, that emphasizes the importance of social activities, namely the discussion among students of what is taking place, to promote learning. In the context of this work, a study based on the following research questions was conducted: 1 – What mistakes arise from the main difficulties of students in Theme II – Introduction to Differential Calculus II of the 12th grade?; 2 – Based on these, what conceptual questions can be formulated to apply Peer Instruction to this theme?; 3 – What adjustments can and/or should be made to Peer Instruction in its implementation in High School?. In this study, a qualitative and interpretive methodology was used, involving a questionnaire aimed at teachers of Mathematics and student assessment tests as data collection tools. In the first place, we sought to know the Peer Instruction method and possible adaptations that can be made in High School. Secondly, we sought to identify and to understand the difficulties and the mistakes experienced by the students of the 12th grade in Theme II - Introduction to Differential Calculus II. Thirdly, also based on the review of the literature, we formulated conceptual questions, creating teaching resources for the topic Logarithm Rules selected from the above theme. Finally, we present an unimplemented lesson plan, for the mentioned topic, using the Peer Instruction method. In order to support it, beyond the fundamental conceptual questions, we presented, described and analysed a handbook of the 12th grade. Furthermore, we produced a homework assignment associated with students’ pre-class study on the topic. In the future, by reflecting on its implementation, there will surely be aspects (proposed tasks, materials used, communication) of the teacher’s classroom practice to be improved.
The so-called traditional lectures, mainly expository, are characterized by the centrality of the teacher’s role in the teaching-learning process. Thus, in general, students have a passive attitude and the teacher, essentially, transfers knowledge to the students. Studies, in many fields other than Mathematics Education and Didactics of Mathematics, point to the benefits of shifting the paradigm of this type of classes. In particular, they call for the centrality of students in the teaching-learning process and for their active learning. Peer Learning, originally named Peer Instruction in the works of the physicist Eric Mazur, arises in the context of that shift as well as from observing gaps in students’ conceptual learning. This student-centred teaching-learning method aims, on the one hand, to replace knowledge transfer by its assimilation and, on the other hand, conceptual learning. In Mazur’s own words, "Teaching is just helping students to learn" and the challenge is to find new ways to reach students. This teaching-learning method comprises: pre-class study of contents by the students; the conceptual questions proposed by the teacher; the votings of the students on these; the discussion among peers, in this case, students. Moreover, it incorporates the principles of Cooperative Learning, based on Vygotsky’s Social Constructivist Theory, that emphasizes the importance of social activities, namely the discussion among students of what is taking place, to promote learning. In the context of this work, a study based on the following research questions was conducted: 1 – What mistakes arise from the main difficulties of students in Theme II – Introduction to Differential Calculus II of the 12th grade?; 2 – Based on these, what conceptual questions can be formulated to apply Peer Instruction to this theme?; 3 – What adjustments can and/or should be made to Peer Instruction in its implementation in High School?. In this study, a qualitative and interpretive methodology was used, involving a questionnaire aimed at teachers of Mathematics and student assessment tests as data collection tools. In the first place, we sought to know the Peer Instruction method and possible adaptations that can be made in High School. Secondly, we sought to identify and to understand the difficulties and the mistakes experienced by the students of the 12th grade in Theme II - Introduction to Differential Calculus II. Thirdly, also based on the review of the literature, we formulated conceptual questions, creating teaching resources for the topic Logarithm Rules selected from the above theme. Finally, we present an unimplemented lesson plan, for the mentioned topic, using the Peer Instruction method. In order to support it, beyond the fundamental conceptual questions, we presented, described and analysed a handbook of the 12th grade. Furthermore, we produced a homework assignment associated with students’ pre-class study on the topic. In the future, by reflecting on its implementation, there will surely be aspects (proposed tasks, materials used, communication) of the teacher’s classroom practice to be improved.
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Aprendizagem pelos pares Didáctica da matemática
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Universidade da Beira Interior