ResumoEste artigo descreve um estudo de aula realizado com cinco professoras do 5.º e 6.º ano numa escola de Lisboa, analisando episódios especialmente relevantes. O nosso objetivo é compreender as potencialidades do estudo de aula como processo de desenvolvimento profissional e os desafios que se colocam à sua realização. Os resultados mostram que as professoras, depois de alguma estranheza inicial com o formato da formação, envolveram-se fortemente na resolução de tarefas matemáticas e na exploração de questões como a natureza das tarefas e os processos de raciocínio dos alunos. As professoras evidenciam diversas aprendizagens profissionais por si realizadas, valorizando em especial as discussões coletivas na sala de aula, e destacam o trabalho colaborativo e a oportunidade para se constituírem num grupo de trabalho na escola. Palavras-chave: AbstractThis paper describes a lesson study carried out with five teachers of grades 5 and 6 in a school in Lisbon, analyzing especially relevant episodes. We aim to understand the potential of the lesson study as a professional development process and the challenges posed by its undertaking. The results show that the teachers, after some initial resistance regarding the kind of professional development activity proposed, highly involved themselves in solving mathematical tasks and in exploring issues such as the nature of tasks and the students' reasoning
A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students' mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while followup guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students' mathematical reasoning processes such as generalization and justification.
Purpose-The purpose of this paper is to review the research concerning the use of lesson studies in the education of secondary school prospective mathematics teachers. It discusses the adaptations made on the designs, the aims and outcomes established, the processes used, and the needed improvements in the experiences reported so far. Design/methodology/approach-The scientific studies reviewed were identified in a Google search, using the key words "lesson study", "mathematics", and "secondary." The identified material was recorded in a database and the themes for the analysis cover the planning, execution, and reflection phases of a formative process. Findings-The paper identifies the several pending issues regarding the use of lesson studies in prospective teacher education such as defining the aims, establishing the relationships among participants, scaling, and adapting lesson studies for the particular purpose of educating future teachers. Research limitations/implications-At a practical level, this review suggests that lesson studies in pre-service teacher education must have a clear formative aim. It also shows that many formats are possible and must be chosen according to the specific conditions. In addition, it suggests the need for research regarding the definition of the aims, the working relationships established among participants, the problem of scale, and the problem of adaptation or simplification. Originality/value-The paper identifies the key issues in the design of lesson studies in initial teacher education. It argues that besides signaling the positive outcomes, more critical (or selfcritical) investigations are needed, e.g. using external researchers as "critical friends", which address their difficulties, limitations, and drawbacks in a more thorough way.
Este artigo analisa os desafios que as tecnologias de informação e comunicação (TIC) colocam à formação de professores: Primeiramente, estuda o modo como as TIC marcam a sociedade atual, com efeitos profundos não só na vida econômica mas também na cultura e na identidade humana. A Internet, pontualmente, representa uma oportunidade além do acesso à informação, de produção e divulgação de materiais próprios, como também de interação. Posteriormente analisa o papel que estas tecnologias têm tido na escola e as dificuldades que têm surgido na sua integração. Após considera as alterações que as TIC estão trazendo ao trabalho dos professores e às suas relações com outros agentes educativos. Mais adiante apresenta alguns programas inovadores de formação inicial e contínua de professores, paradigmáticos dos rumos que actualmente pode assumir a formação e do seu paralelismo com os processos educativos em geral. Finalmente, apresenta algumas sugestões sobre os desafios para uma integração profunda e, ao mesmo tempo, crítica e de emancipação das TIC na atividade educativa.
Abstract. In Portugal, since the beginning of the 1990s, problem solving became increasingly identified with mathematical explorations and investigations. A number of research studies have been conducted, focusing on students' learning, teachers' classroom practices and teacher education. Currently this line of work involves studies from primary school to university mathematics. This perspective impacted the mathematics curriculum documents that explicitly recommend teachers to propose mathematics investigations in their classrooms. On national meetings many teachers report experiences involving students' doing investigations and indicate to use regularly such tasks in their practice. However, this still appears to be a marginal activity in most mathematics classes, especially when there is pressure for preparation for external examinations (at grades 9 and 12). International assessments such as PISA and national assessments (at grades 4 and 6) emphasize tasks with realistic contexts. They reinforce the view that mathematics tasks must be varied beyond simple computational exercises or intricate abstract problems but they do not support the notion of extended explorations. Future developments will show what paths will emerge from these contradictions between promising research and classroom reports, curriculum orientations, professional experience, and assessment frameworks and instruments.Keywords. Problem-solving, Mathematical investigations, Mathematical explorations, Curriculum, Assessment, Learning.Resumo. Em Portugal, desde o princípio dos anos 90, a resolução de problemas tornou-se cada vez mais identificada com explorações e investigações matemáticas. Diversos estudos de investigação foram realizados tendo por foco as aprendizagens dos alunos, as práticas lectivas dos professores e a formação de professores. Presentemente, esta linha de trabalho envolve estudos desde o 1.º ciclo do ensino básico até ao ensino superior. Esta perspectiva teve impacto nos documentos curriculares de Matemática que recomendam explicitamente aos professores que proponham investigações matemáticas nas suas salas de aula. Nos encontros nacionais muitos professores relatam experiências envolvendo os alunos a realizar investigações e indicam usar regularmente estas tarefas na sua prática. Contudo, este tipo de trabalho parece ser ainda marginal na maioria das aulas de Matemática, especialmente quando existe pressão para preparação para exames externos (no 9.º e 12.º anos de escolaridade). Avaliações internacionais tais como PISA e avaliações nacionais (nos 4.º e e 6.º anos de escolaridade) enfatizam tarefas com contextos realísticos. Estas avaliações reforçam a perspective que as tarefas matemáticas devem ser vistas para além dos simples exercícios de cálculo ou problemas abstractos complicados mas não apoiam a noção de explorações aprofundadas. Os desenvolvimentos futuros mostrarão que caminhos poderão emergir destas contradições entre investigação e relatórios da sala de aula prometedores, orientações curriculares, experiência p...
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