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Ensinar a argumentar em matemática no 6º ano de escolaridade
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Abstract(s)
Este estudo visa analisar a minha prática profissional e tem como objetivo compreender de que modo posso promover e apoiar o envolvimento dos alunos em atividades de argumentação matemática e quais os principais desafios que este trabalho acarreta. Formulei, neste âmbito, as seguintes questões de investigação: (1) Que aspetos relativos à preparação das aulas favorecem a emergência de atividades de argumentação matemática? (2) Durante a lecionação das aulas, como procurarei fomentar e apoiar o envolvimento dos alunos neste tipo de atividade? (3) Que desafios enfrentarei?
No enquadramento teórico foco o significado de argumentação em matemática, os caminhos a serem percorridos para que esta atividade seja possível e, finalmente, os desafios a ela associados.
Do ponto de vista metodológico, o estudo insere-se numa abordagem qualitativa e constitui uma investigação sobre a prática. Neste sentido, foi realizada uma intervenção pedagógica nas aulas de matemática de uma turma do 6.º ano de escolaridade, em que foram propostas tarefas que do ponto de vista teórico favorecem a emergência e desenvolvimento de atividades de argumentação.
A recolha de dados foi feita através da observação participante, recolha documental e conversas informais. Neste âmbito, foram elaboradas notas de campo de caráter descritivo e reflexivo e foram registadas em áudio todas as aulas da intervenção pedagógica.
Os resultados permitiram perceber não só os aspetos que favorecem a emergência de episódios de argumentação matemática, mas também desafios associados a esta atividade. Destacam-se a seleção de tarefas desafiantes e a planificação das aulas em que estas tarefas serão propostas, principalmente a antecipação dos raciocínios dos alunos. No que respeita aos desafios, estes prendem-se com a negociação contextualizada de normas sociais e sociomatemáticas, entre as quais está a promoção da expressão audível e o comprometimento dos alunos na análise crítica dos raciocínios dos colegas; com a gestão do tempo; com a validação precipitada dos raciocínios dos alunos; e com a gestão dos contributos dos alunos durante a discussão de modo a que esta discussão seja poderosa tanto para a aprendizagem dos alunos como do ponto de vista matemático.
This study aims to analyse my professional practice. The main goal is to understand how I can promote and support student engagement in mathematical argumentation activities and what are the main challenges that this work entails. So were formulated the following investigation questions: (1) What aspects concerning lesson preparation favour the emergence of mathematical argumentation activities? (2) During instruction, how I tried to encourage and support students’ involvement in these activities? (3) What challenges I faced? The theoretical framework addresses the meaning of argumentation in mathematics, pathways to be followed for this activity be possible and, finally, in the challenges related to these pathways. Methodologically, this study is framed on a qualitative approach and is an investigation into my own practice. In this sense, an educational intervention in a mathematics class of 6th grade was held, in which I proposed tasks that, from a theoretical point of view, favor the emergence and development of mathematical argumentation activities. Data collection was carried out through participant observation, document collection and informal conversational interviews. In this context, I drew up descriptive and reflexive field notes and I recorded, into audio, all classes of the pedagogical intervention. The results allowed to see not only the aspects that favour the emergence of episodes of mathematical argumentation, but also challenges associated with this activity. Stands out the selection of challenging tasks and the preparation of lessons in which these task will be proposed, particularly the anticipation of student reasoning. The main challenges are related to: the contextualized negotiation of social norms and sociomathematical norms, among which is the promotion of audible expression and the students commitment in the critical analysis of the reasoning of colleagues; to time management; to hasty validation of students reasoning; and to the management of contributions from students during the collective discussions, so that these discussion are powerful for student learning and, simultaneously, from a mathematical point of view.
This study aims to analyse my professional practice. The main goal is to understand how I can promote and support student engagement in mathematical argumentation activities and what are the main challenges that this work entails. So were formulated the following investigation questions: (1) What aspects concerning lesson preparation favour the emergence of mathematical argumentation activities? (2) During instruction, how I tried to encourage and support students’ involvement in these activities? (3) What challenges I faced? The theoretical framework addresses the meaning of argumentation in mathematics, pathways to be followed for this activity be possible and, finally, in the challenges related to these pathways. Methodologically, this study is framed on a qualitative approach and is an investigation into my own practice. In this sense, an educational intervention in a mathematics class of 6th grade was held, in which I proposed tasks that, from a theoretical point of view, favor the emergence and development of mathematical argumentation activities. Data collection was carried out through participant observation, document collection and informal conversational interviews. In this context, I drew up descriptive and reflexive field notes and I recorded, into audio, all classes of the pedagogical intervention. The results allowed to see not only the aspects that favour the emergence of episodes of mathematical argumentation, but also challenges associated with this activity. Stands out the selection of challenging tasks and the preparation of lessons in which these task will be proposed, particularly the anticipation of student reasoning. The main challenges are related to: the contextualized negotiation of social norms and sociomathematical norms, among which is the promotion of audible expression and the students commitment in the critical analysis of the reasoning of colleagues; to time management; to hasty validation of students reasoning; and to the management of contributions from students during the collective discussions, so that these discussion are powerful for student learning and, simultaneously, from a mathematical point of view.
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Keywords
Argumentação em matemática Orquestração de discussões coletivas Papel do professor Mathematical argumentation Orchestrating collective discussions Teacher's role Relatório de projeto de investigação Relatório de estágio