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O papel do professor na condução da discussão matemática
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Este estudo pretende compreender como se carateriza e desenvolve a condução de
discussões coletivas em torno da exploração matemática de tarefas de investigação
sobre o estudo de Funções no 12.º ano do ensino secundário, com recurso à utilização
da calculadora gráfica. O trabalho incide no tema II – Introdução ao Cálculo
Diferencial II na unidade de ensino sobre o tópico Funções exponenciais e logarítmicas.
Pretende-se dar resposta às seguintes questões: (1) Que tipo de ações e com que
frequências são utilizadas pela professora na condução da discussão matemática
coletiva? (2) Que tipos de discussão são utilizados pela professora no desenvolvimento
da aula? E (3) Que problemas e constrangimentos se colocam à professora no decurso
das discussões em sala de aula? Foi analisado o trabalho em aula de uma professora
experiente que leciona no 12.º ano do ensino secundário. O quadro conceptual apoia-se
no modelo desenvolvido por Ponte, Mata-Pereira & Quaresma (2013) para as ações do
professor na condução de discussões matemáticas, distinguindo entre convidar,
sugerir/informar, apoiar/guiar ou desafiar os alunos para a realização da tarefa. A
análise usa também o modelo desenvolvido por Henning, McKeny, Foley & Balong
(2012) que referem três tipos distintos de discussão matemática: enquadramento,
conceptual e aplicação. O estudo segue uma abordagem qualitativa interpretativa, na
modalidade de observação participante. A recolha de dados inclui a gravação em vídeo
das aulas onde decorreu este estudo.
Os resultados mostram que as discussões matemáticas coletivas usam sobretudo
discussões do tipo aplicação, apesar de também se identificarem discussões de tipo
enquadramento e conceptual. Os resultados mostram também que a discussão é
fortemente marcada por ações de apoiar/guiar, que tanto surgem de ações convidar e
sugerir/informar, como de ações desafiar; que as ações apoiar/guiar tanto se seguem
umas às outras como alternam com ações desafiar e sugerir/informar, e têm uma grande
importância na condução das discussões; que um segmento começa com uma ação
convidar e usualmente termina com uma ação de sugerir/informar; e que são as ações
desafiar que promovem um maior aprofundamento e compreensão dos conceitos e
ideias matemáticas novas por parte dos alunos. Nas discussões surgem problemas que a
professora procura enfrentar utilizando sobretudo ações que promovam a reflexão sobre
ideias e estratégias, introduzam e aprofundem novos conceitos e ideias matemáticas ou
avaliem conjeturas e ideias através da reformulação de questões já colocadas e
solicitando a participação de outros alunos para avaliar as ideias em discussão.
This study aims to understand the characteristics and development of whole class discussions regarding the mathematical exploration of investigation tasks for the study of the unit about Functions in grade 12, the final year of high school in Portugal, with the use of a graphic calculator. The study focuses on Unit II - Introduction to Calculus II for the teaching of the topic about Exponential and Logarithmic Functions. This study seeks to answer the following questions: (a) What kind of actions and with which frequency are used by the teacher in the conduction of whole class mathematical discussions? (b) Which types of discussion are used by the teacher to promote the lesson? And (c) Which problems and constrains does the teacher face during the discussions in the classroom? The work in class of an experienced teacher who teaches in grade 12 of high school was analyzed. The conceptual framework is based on a model developed by Ponte, Mata-Pereira & Quaresma (2013) that distinguishes among inviting, suggesting/informing, supporting/guiding and challenging actions to lead the students in performing the task. The framework is also based on the model developed by Henning, McKeny, Foley & Balong (2012), that distinguish three distinct types of mathematical discussion: framework, conceptual and application. The study follows a qualitative and interpretative approach with participant observation. The data collection includes video recording of the lessons where the study took place. This study suggests that whole class mathematical discussions use mainly application discussions, despite also identifying framework and conceptual discussions. The results also show that whole class discussions are strongly marked by supporting/guiding actions, which both arise from inviting actions or suggesting/informing as well as challenging actions. Actions of support/guidance, which both follow each other as alternate with challenging and suggesting/informing actions, have a great importance in the discussions. A segment starts initially with an invitation action and usually ends with an action of suggesting/informing. The results also suggest that challenging actions promote a greater deepening and understanding of the mathematical concepts and ideas that are the objective of the lesson. In the discussions many problems arise to the teacher that seeks to face them using especially actions that promote the reflection on ideas and strategies used, introduce and deepens into new concepts and mathematical ideas or evaluate conjectures and ideas through the reformulation of questions already asked and requesting the participation of other students to evaluate the ideas under discussion.
This study aims to understand the characteristics and development of whole class discussions regarding the mathematical exploration of investigation tasks for the study of the unit about Functions in grade 12, the final year of high school in Portugal, with the use of a graphic calculator. The study focuses on Unit II - Introduction to Calculus II for the teaching of the topic about Exponential and Logarithmic Functions. This study seeks to answer the following questions: (a) What kind of actions and with which frequency are used by the teacher in the conduction of whole class mathematical discussions? (b) Which types of discussion are used by the teacher to promote the lesson? And (c) Which problems and constrains does the teacher face during the discussions in the classroom? The work in class of an experienced teacher who teaches in grade 12 of high school was analyzed. The conceptual framework is based on a model developed by Ponte, Mata-Pereira & Quaresma (2013) that distinguishes among inviting, suggesting/informing, supporting/guiding and challenging actions to lead the students in performing the task. The framework is also based on the model developed by Henning, McKeny, Foley & Balong (2012), that distinguish three distinct types of mathematical discussion: framework, conceptual and application. The study follows a qualitative and interpretative approach with participant observation. The data collection includes video recording of the lessons where the study took place. This study suggests that whole class mathematical discussions use mainly application discussions, despite also identifying framework and conceptual discussions. The results also show that whole class discussions are strongly marked by supporting/guiding actions, which both arise from inviting actions or suggesting/informing as well as challenging actions. Actions of support/guidance, which both follow each other as alternate with challenging and suggesting/informing actions, have a great importance in the discussions. A segment starts initially with an invitation action and usually ends with an action of suggesting/informing. The results also suggest that challenging actions promote a greater deepening and understanding of the mathematical concepts and ideas that are the objective of the lesson. In the discussions many problems arise to the teacher that seeks to face them using especially actions that promote the reflection on ideas and strategies used, introduce and deepens into new concepts and mathematical ideas or evaluate conjectures and ideas through the reformulation of questions already asked and requesting the participation of other students to evaluate the ideas under discussion.
Descrição
Tese de mestrado, Educação (Área de especialidade em Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2017
Palavras-chave
Professores Investigação matemática Funções (Matemática) Calculadora gráfica Ensino secundário Teses de mestrado - 2017