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Tarefas de investigação novas tecnologias e conexões e a aprendizagem de conteúdos algébricos no 8º ano
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Resumo(s)
A Álgebra é um dos campos do currículo de Matemática onde se revela mais
difícil pôr em prática metodologias adequadas às características de cada aluno. O
presente estudo tem por objectivo conhecer a influência que pode ter na aprendizagem
dos alunos uma proposta curricular para o ensino da Álgebra que dá ênfase às tarefas de
exploração e investigação, às conexões dentro e fora da Matemática e ao uso da
tecnologia. O estudo foi realizado numa das minhas turmas do 8.º ano, o que me
proporcionou também a oportunidade de explorar novas perspectivas metodológicas e
reflectir sistematicamente sobre vários aspectos da minha prática. A investigação é
qualitativa e envolve estudos de caso de três alunos. Para averiguar o seu pensamento
algébrico e as suas concepções sobre o ensino e a aprendizagem dos conceitos
algébricos, utilizei três métodos de recolha de dados: observação participante com
registo em diário de bordo, entrevistas e documentos produzidos pelos alunos.
Com a concretização da experiência, as concepções dos alunos sobre o ensino e
a aprendizagem da Álgebra sofreram algumas alterações. Assim, no final do estudo, eles
valorizam as tarefas inovadoras e centradas em situações reais, o trabalho de grupo, a
avaliação sistemática e contínua, e a construção/compreensão dos conceitos
matemáticos. A experiência permitiu também modificar a forma como eles estudam a
Álgebra. Assim, no final, os alunos exploram tarefas semelhantes às da proposta
curricular, analisam as conclusões obtidas durante as aulas e tentam redigir textos de
qualidade. Para além disto, a experiência alterou também a forma com os alunos
abordam as tarefas. Para explorar tarefas envolvendo os conceitos de função e
sequência, recorrem à utilização da folha de cálculo, representam as relações e resolvem
as situações. Para resolver equações, aplicam as regras e determinam o valor da
incógnita. No entanto, referem que apenas durante a exploração das tarefas da proposta
curricular, compreenderam os conceitos algébricos. O estudo sugere que a realização de
tarefas de exploração e investigação visando promover a compreensão e a aprendizagem
de conceitos algébricos e estabelecer conexões entre várias áreas da Matemática,
utilizando a folha de cálculo, pode influenciar o pensamento algébrico e as concepções
dos alunos sobre a Álgebra e a sua aprendizagem.
Algebra is one of the mathematics curriculum topics where adequate methodologies, adjusted to the needs of each student, are more difficult to put into practice The present study aims to know the influence of a curriculum proposal in algebra, emphasising exploration and investigation tasks, connections inside and outside mathematics, and the use of technology, in students’ learning The study was carried out in one of my 8th year classes and provided me also with the opportunity to explore new methodological perspectives and to systematically reflect on some aspects of my practice. The investigation is qualitative and involved case studies of three students. To inquire their algebraic thinking and their conceptions about teaching and learning of algebraic concepts, I used three methods of data collection: participant observation using a log book, interviews, and documents produced by students. With the implementation of the experience, the conceptions of the students on teaching and learning algebra had some changes. In the end of the study, the students value innovative tasks centred in real situations, work in groups, systematic and continuous evaluation, and the construction/comprehension of mathematical concepts. The experience also allowed them to modify the way they study algebra. Thus, in the end, the students explore tasks similar to those of the curriculum proposal, analyse the conclusions they arrived during the lessons and try to write good texts. Moreover, the experience also modified the way students approach tasks. To explore tasks involving functions and sequences, they use the spreadsheet, represent the relations and decide the situations. To solve equations, they apply the rules and determine the value of the unknown. They report that only during the exploration of the tasks of this experience, they understood the algebraic concepts. The study suggests that carrying out exploration and investigation tasks that they aim at promoting the understanding and the learning of algebraic concepts and establishing connections between different areas of mathematics, using the spreadsheet, can influence the algebraic thinking and the conceptions of the students on algebra and its learning.
Algebra is one of the mathematics curriculum topics where adequate methodologies, adjusted to the needs of each student, are more difficult to put into practice The present study aims to know the influence of a curriculum proposal in algebra, emphasising exploration and investigation tasks, connections inside and outside mathematics, and the use of technology, in students’ learning The study was carried out in one of my 8th year classes and provided me also with the opportunity to explore new methodological perspectives and to systematically reflect on some aspects of my practice. The investigation is qualitative and involved case studies of three students. To inquire their algebraic thinking and their conceptions about teaching and learning of algebraic concepts, I used three methods of data collection: participant observation using a log book, interviews, and documents produced by students. With the implementation of the experience, the conceptions of the students on teaching and learning algebra had some changes. In the end of the study, the students value innovative tasks centred in real situations, work in groups, systematic and continuous evaluation, and the construction/comprehension of mathematical concepts. The experience also allowed them to modify the way they study algebra. Thus, in the end, the students explore tasks similar to those of the curriculum proposal, analyse the conclusions they arrived during the lessons and try to write good texts. Moreover, the experience also modified the way students approach tasks. To explore tasks involving functions and sequences, they use the spreadsheet, represent the relations and decide the situations. To solve equations, they apply the rules and determine the value of the unknown. They report that only during the exploration of the tasks of this experience, they understood the algebraic concepts. The study suggests that carrying out exploration and investigation tasks that they aim at promoting the understanding and the learning of algebraic concepts and establishing connections between different areas of mathematics, using the spreadsheet, can influence the algebraic thinking and the conceptions of the students on algebra and its learning.
Descrição
Tese de mestrado em Educação (Didáctica da Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2006
Palavras-chave
Álgebra Investigação matemática Tarefas Teses de mestrado - 2006