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  • A prática de umaprofessora de Matemática ao conduzir uma discussão coletiva sobre sequências
    Publication . Rodrigues, Cátia; Menezes, Luís; Da Ponte, João Pedro
    Mathematics learning with understanding can be improved by engaging students in whole-class discussions as they are called upon to present, justify and argue their strategies and the strategies of their colleagues and, later, to systematize the main ideas emerging from this discussion. This qualitative and interpretive study, is a case study of a grade 7 mathematics teacher, and aims to understand this practice in conducting the whole-class discussions, in connection with her didactic knowledge, when exploring a task involving sequences. The results show that the teacher, based on her didactic knowledge and preparation of the lesson, organizes the whole-class discussion in three moments (presentation; comparison, evaluation and filtering; and conclusion) in which she undertakes various teaching actions.
  • A prática de uma professora de Matemática ao conduzir uma discussão coletiva sobre sequências
    Publication . Rodrigues, Cátia; Menezes, Luís; Da Ponte, João Pedro
    Mathematics learning with understanding can be improved by engaging students in whole-class discussions as they are called upon to present, justify and argue their strategies and the strategies of their colleagues and, later, to systematize the main ideas emerging from this discussion. This qualitative and interpretive study, is a case study of a grade 7 mathematics teacher, and aims to understand this practice in conducting the whole-class discussions, in connection with her didactic knowledge, when exploring a task involving sequences. The results show that the teacher, based on her didactic knowledge and preparation of the lesson, organizes the whole-class discussion in three moments (presentation; comparison, evaluation and filtering; and conclusion) in which she undertakes various teaching actions.
  • Práticas de discussão matemática no ensino da Álgebra
    Publication . Rodrigues, Cátia; Menezes, Luís; Da Ponte, João Pedro
    Mathematical discussions contribute strongly to pupils’ learning, as they put into play a set of social interactions and processes of negotiation of mathematical meanings. This communication analyzes the discussion practices of a mathematics teacher of the 3rd cycle of basic education, in the context of collaborative work. The study is interpretive, qualitative and draws on interviews and participant observation of collaborative work sessions and of the teacher’s lessons, supported in field notes. The results show that the teacher focuses on supporting and extending actions in collective discussions.
  • Tarefas matemáticas no ensino da álgebra
    Publication . Rodrigues, Cátia; Menezes, Luís; Da Ponte, João Pedro
    As tarefas matemáticas desempenham um papel importante na aprendizagem dos alunos, ao contribuírem para o desenvolvimento do seu pensamento matemático. Nesta comunicação procuramos compreender de que forma o conhecimento mobilizado por uma professora na seleção e exploração de tarefas contribui para essa aprendizagem dos alunos, nomeadamente ao nível da justificação e generalização de raciocínios algébricos. A metodologia envolve a observação de aulas e de sessões de trabalho colaborativo com a professora, que são complementadas pela elaboração de notas de campo. Os resultados mostram que a professora mobiliza diversos aspetos do seu conhecimento didático na seleção das tarefas e na forma de as explorar em sala de aula, tanto no momento de planificação como na ação em aula. Em particular, na aula, acompanha os alunos e favorece os momentos de apresentação e discussão de ideias matemáticas, desafiando-os a justificarem e generalizarem ideias, aspetos importante do conhecimento da prática letiva.
  • Práticas discursivas de professores de Matemática na condução de discussões coletivas
    Publication . Rodrigues, Cátia; Da Ponte, João Pedro; Menezes, Luís
    Mathematical discussions are a tool within the reach of the teacher to promote communication in the mathematics class, as students are asked to present their resolution strategies, to compare them with those of their peers, to justify and argue about the mobilized reasoning in these solutions of a task proposed by the teacher. When class discourse focuses on algebraic ideas, symbolization and generalization are enhanced, as students are encouraged to use increasingly formal language and broaden their thinking beyond the considered cases. This qualitative and interpretative study seeks to understand how three teachers of mathematics in the 3rd cycle of basic education manage and promote discourse during a collective discussion with mathematical tasks with a view to teaching Algebra. The results show that teachers, supported by the teaching actions of eliciting, supporting, informing, and challenging, direct the discourse through a cyclical process of requesting and discussing many ideas and of filtering, seeking to lead students to relate, generalize and justify algebraic ideas.
  • Desafios e tensões de professores de matemática na dinamização de discussões em temas da Álgebra
    Publication . Rodrigues, Cátia; Menezes, Luís; Da Ponte, João Pedro
    Whole class discussions have come to be seen in mathematics teaching as a tool available to teachers to promote their students’ learning, insofar as they can involve them in the presentation and justification of previously selected strategies for solving mathematical tasks. In these discussions, the teacher relies on his/her didactic knowledge of mathematics to carry out a set of teaching actions to involve the students in the classroom discourse. The orchestration of these actions generates tensions in teachers, especially when they try to reconcile the discussion of important mathematical ideas with students’ participation. In this research, part of a larger study, we try to understand the tensions that three mathematics teachers face in leading whole class discussions based on algebraic tasks and how they try to overcome them. This qualitative and interpretative study is based on case studies of three teachers who are part of a collaborative group. Data were collected by interview, participant observation of teachers’ classes and collaborative work sessions and documentary analysis. Data analysis is based on a recursive process that led to the construction of formal categories, supported by the theoretical framework. The results show that teachers face diverse tensions when they try to involve the students in sharing and justifying algebraic ideas, recognizing that collaboration and planning the discussions are important mechanisms to help them cope with these tensions.
  • Práticas profissionais dos professores de matemática: o projeto P3M
    Publication . Da Ponte, João Pedro; Oliveira, Hélia; Canavarro, Ana Paula; Moreira, Darlinda; Martinho, Maria Helena; Menezes, Luís; Tomás Ferreira, Rosa
    O projeto P3M tem como objetivo estudar as práticas profissionais na sala de aula de professores de Matemática. Pretende igualmente produzir recursos multimédia para formação inicial e contínua de professores do ensino básico e do ensino secundário. Neste poster apresentamos o projeto, indicando os seus objetivos, quadro conceptual, metodologia de trabalho e resultados preliminares, tanto no que se refere às práticas dos professores como aos materiais produzidos.
  • Prática de discussão coletiva de uma professora em Álgebra
    Publication . Rodrigues, Cátia; Da Ponte, João Pedro; Menezes, Luís
    This article presents a study that aims to describe and to understand the mathematical discussion practice of a teacher during the preparation and promotion of a collective discussion in Algebra with 7th grade students. The study follows a qualitative and interpretative approach and follows a case study design of a mathematics teacher. The results show that the teacher begins by carefully selects the task she intends to present to the students, anticipating possible strategies for resolving the problem, using algebraic language. In class, in the promotion of the discussion, he/she concretizes the preparation made leading the students to present their strategies of resolution, to compare and evaluate the colleagues, filtering the various contributions, so that the most relevant aspects of their work are synthesized. The teacher leads students to generalize and justify algebraic ideas, by combining intentional actions of eliciting, supporting, informing and challenging.