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Abstract(s)
Muitos anos dedicados à prática letiva foram determinantes para a decisão de levar a cabo esta investigação. Porque os conteúdos relativos à Geometria são de forma generalizada um problema para os alunos e um entrave ao seu sucesso escolar, tem todo o sentido centralizar a investigação na área da Didática da Matemática no tema Geometria.
O objetivo desta investigação é o de averiguar como o conhecimento de outras geometrias (além da euclidiana) e a sua aplicação conduzem o pensamento geométrico dos alunos. Com o propósito bem definido de obter conclusões que possam contribuir de forma construtiva no domínio da didática da Matemática, e dar resposta a: (i) será importante, ou não, a apresentação e aplicação de outras geometrias (além da euclidiana) no ensino secundário com o objetivo de desenvolver capacidades geométricas? e (ii) de que modo o conhecimento e aplicação de outras geometrias influencia o pensamento geométrico nos alunos? Foram elaboradas propostas didáticas com um objetivo de estudo: “fazer emergir sinais” indiciadores de uma atividade intelectual, conducente à apropriação de significados geométricos, expressa através da linguagem.
A um grupo de nove alunos do ensino secundário (alunos com idades compreendidas entre 15 e 18 anos), elementos do Clube de Matemática da escola que frequentam, foi proposto a realização de algumas tarefas investigativas. Estas tarefas foram selecionadas para potenciar o desenvolvimento do processo semiótico. A professora/investigadora conduziu as sessões fomentando a discussão e a comunicação segundo uma perspetiva dialética em que promoveu a evolução de sinais (analisados na linguagem) e orientou de forma a que estes fossem consistentes com os significados matemáticos definidos na intervenção didática. De todas as sessões foi feita a gravação áudio e todas essas gravações foram transcritas permitindo uma análise ao modo como os alunos se envolveram na realização das tarefas, à interação entre si e com o professor, aos sinais emergentes de quaisquer reações no grupo de trabalho, em particular aos emergentes das discussões coletivas e à linguagem utilizada.
A análise dos dados recolhidos durante a realização das atividades pelos alunos teve em conta a mediação semiótica alicerçada na Teoria da Atividade.
Cada verbalização ocorrida dentro da discussão coletiva foi classificada por um sinal. A partir dessa classificação analisou-se o estado evolutivo dos significados pessoais dos alunos em relação ao significado matemático, de acordo com os conceitos matemáticos que associámos a cada tarefa. Essa análise levou-nos a identificação de cadeias evolutivas dentro da discussão coletiva. Essas cadeias evolutivas foram sujeitas a uma análise mais detalhada e verificou-se que a apresentação e aplicação das GNE em tarefas com os alunos não teve um efeito inócuo e pode desenvolver capacidades geométricas e influenciar o pensamento geométrico dos alunos.
Several years devoted to teaching were influencial for deciding to take upon this investigation. Because Geometry related contents are generally difficult for the students and a barrier versus their scholar sucess, it makes all sense to centralize the investigation from the field of Mathemathic Didactics in the theme Geometry. The purpose of this investigation is to check how knowledge of other geometries (besides euclidean) and its application may conduct student’s geometric thought. With the well defined end of obtaining conclusions that can contribute constructively on Math didactic’s domain, and to give answer to: (i) is it important, or not, to present and to apply other geometries (besides euclidean) on secondary school with the goal of developing geometrical capabilities?; and (ii) in what way does the knowledge and application of other geometries influences geometric thought in students? Didactic proposals have been produced with an objective for the study: “to make signs to emerge” which will indicate an intellectual activity, leading to the appropriation of geometrical meanings, express through language. To a group of nine students from secondarý school (students with ages between 15 and 18 years old), pertaining to the Maths Club of the school where they study, some investigative tasks were proposed. These tasks were projected to potentiate the development of the semiotic process. The teacher/investigator has lead the sessions encouraging discussion and comunication according to a dialectic perspective in which sign’s evolution (analised in language) are promoted and oriented in a way that these signs may be consistent with mathematical meanings defined by the didactical intervention. Of all the sessions an audio recording has been made and all those recordings were transcripted allowing for an analysis to the way the students got into the task’s accomplishment, to the interaction between them and the teacher, to the emergent signs from any reaction within the work group, particularly to the ones which emerged from colective discussions and used language. The analysis from the data gathered during student’s task accomplishment had in account the semiotic mediation based on Activity Theory. Each verbalization ocurred within the colective discussion was classified with a sign. Then starting with this classification it was annalised the evolutive status of student's personal significances regarding mathematical significance, in accordance with the mathematical concepts that were associated with each task. This analysis led us to identify evolutive chains within collective discussion. These evolutive chains were the subject of further detailed analysis and it was verified that presentation and application of Non-Euclidian Geometries in tasks with students did not have innocuous effect and may develop geometrical skills and inluenciate student's geometrical thought.
Several years devoted to teaching were influencial for deciding to take upon this investigation. Because Geometry related contents are generally difficult for the students and a barrier versus their scholar sucess, it makes all sense to centralize the investigation from the field of Mathemathic Didactics in the theme Geometry. The purpose of this investigation is to check how knowledge of other geometries (besides euclidean) and its application may conduct student’s geometric thought. With the well defined end of obtaining conclusions that can contribute constructively on Math didactic’s domain, and to give answer to: (i) is it important, or not, to present and to apply other geometries (besides euclidean) on secondary school with the goal of developing geometrical capabilities?; and (ii) in what way does the knowledge and application of other geometries influences geometric thought in students? Didactic proposals have been produced with an objective for the study: “to make signs to emerge” which will indicate an intellectual activity, leading to the appropriation of geometrical meanings, express through language. To a group of nine students from secondarý school (students with ages between 15 and 18 years old), pertaining to the Maths Club of the school where they study, some investigative tasks were proposed. These tasks were projected to potentiate the development of the semiotic process. The teacher/investigator has lead the sessions encouraging discussion and comunication according to a dialectic perspective in which sign’s evolution (analised in language) are promoted and oriented in a way that these signs may be consistent with mathematical meanings defined by the didactical intervention. Of all the sessions an audio recording has been made and all those recordings were transcripted allowing for an analysis to the way the students got into the task’s accomplishment, to the interaction between them and the teacher, to the emergent signs from any reaction within the work group, particularly to the ones which emerged from colective discussions and used language. The analysis from the data gathered during student’s task accomplishment had in account the semiotic mediation based on Activity Theory. Each verbalization ocurred within the colective discussion was classified with a sign. Then starting with this classification it was annalised the evolutive status of student's personal significances regarding mathematical significance, in accordance with the mathematical concepts that were associated with each task. This analysis led us to identify evolutive chains within collective discussion. These evolutive chains were the subject of further detailed analysis and it was verified that presentation and application of Non-Euclidian Geometries in tasks with students did not have innocuous effect and may develop geometrical skills and inluenciate student's geometrical thought.
Description
Keywords
Ensino da matemática - Aprendizagem da geometria - Alunos do Ensino Secundário Ensino da matemática - Atividades de ensino-aprendizagem - Alunos do ensino secundário Ensino da matemática - Estratégias de aprendizagem - Alunos do ensino secundário Ensino da matemática - Desenvolvimento de pensamento geométrico - Alunos do ensino secindário