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A aprendizagem comparticipada dos números racionais através da percentagem
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Este estudo procura compreender os contributos que a percentagem pode dar na construção de uma aprendizagem comparticipada dos números racionais numa etapa inicial do seu estudo – 3.º e 4.º ano de escolaridade do 1.º ciclo do ensino básico – alicerçada numa perspetiva de sentido de número e de continuidade no desenvolvimento numérico dos alunos. Especificamente, pretende perceber de que modo a percentagem contribui para o alargamento do conhecimento de número ao conjunto dos números racionais, bem como para uma compreensão inter-relacionada de percentagem, numeral decimal e fração. Pretende perceber também de que modo as normas sociais e sociomatemáticas contribuem para a construção de uma aprendizagem comparticipada dos números racionais através da percentagem. O quadro conceptual remete para uma abordagem sociocultural da aprendizagem da Matemática, como atividade humana, inerentemente social e cultural. As ideias que o alicerçam envolvem a aprendizagem dos números racionais como construção comparticipada e realista, interpretada como uma extensão do conhecimento dos números inteiros, que privilegia a percentagem numa compreensão entrelaçada de representações, numa perspetiva de sentido de número. Do ponto de vista metodológico, trata-se de uma investigação baseada em design, com base numa experiência de ensino na sala de aula. A situação de aprendizagem envolve uma turma, no 3.º e no 4.º ano de escolaridade, numa escola pública em Lisboa, em que a professora da turma é também a investigadora. Os dados foram recolhidos através de observação participante, apoiada num diário de bordo, e de gravações áudio e vídeo de momentos de discussão matemática coletiva e da recolha documental, nomeadamente das produções escritas dos alunos. A análise procurou evidências de construção de um conhecimento conceptual de percentagem e de número racional, bem como a interpretação das ações dialógicas na turma, com vista à identificação das normas sociais e sociomatemáticas. Os resultados evidenciam que as normas sociais e sociomatemáticas da cultura da sala de aula, como comunidade de aprendizagem de matemática, permitiram suportar a compreensão dos conceitos e relações envolvidos na noção de percentagem, tendo conduzido à construção de práticas matemáticas partilhadas relativas à natureza multiplicativa dos números racionais. Para além disso, através da percentagem, foi possível integrar os conhecimentos numéricos prévios e conhecimentos intuitivos dos alunos e apoiar a construção de uma aprendizagem das diferentes representações simbólicas, de forma inter-relacionada, numa perspetiva de desenvolvimento de sentido de número. Deste estudo emerge ainda um conjunto de princípios que suportam uma conjetura sobre a aprendizagem comparticipada dos números racionais que privilegia a percentagem, nesta etapa da escolaridade, no sentido promover o envolvimento dos alunos e produzir efeitos na sua aprendizagem.
This study seeks to understand the contributions of percentage in fostering co-participated initial learning of rational numbers, at grades 3 and 4, in primary school, rooted in a number sense perspective and seen as process of progressively broadening of students’ numerical development. In particular, it aims to understand how percentage allows the extension of number understanding to rational numbers and fosters an entwined understanding of percentages, decimals and fractions. It also aims to understand how social and sociomathematical norms contribute to a co-participated learning of rational numbers enhanced by percentage. The conceptual framework involves a sociocultural perspective of mathematical learning, as a human activity, inherently social and cultural. The theoretical elements considered concern rational number learning as realistic and co-participated, entailed as an extension of the understanding of whole numbers, which addresses percentage, as an entwined understanding of rational number representations, in a number sense perspective. This study is developed as design based research methodology through a classroom experiment. It takes place in grades 3 and 4 within a classroom, in a public primary school in Lisboa, where the researcher is also the teacher. Data collection took place through participant observation, supported by the teacher’s research journal, video and audio recorded moments of whole-class discussions and students’ written work. The analysis sought for evidences of students’ percentage and rational number conceptual understanding, as well for social and sociomathematical norms, as students participated in classroom social interaction. The results highlight that social and sociomathematical norms of the classroom culture, as a mathematical learning community, supported conceptual understanding of percentage for learning rational numbers as it enabled an approach to its multiplicative nature and the establishment of mathematical practices taken as shared. Additionally, through percentage, it was possible to connect students’ prior whole numbers knowledge with intuitive understandings and relations to support the understanding of different symbolic representations, in an entwined manner, attending to a number sense perspective. From this study it emerges a set of principles, that supports a conjecture to improve co-participated learning through percentage, in these grades of primary school, in order to promote student engagement and improve learning.
This study seeks to understand the contributions of percentage in fostering co-participated initial learning of rational numbers, at grades 3 and 4, in primary school, rooted in a number sense perspective and seen as process of progressively broadening of students’ numerical development. In particular, it aims to understand how percentage allows the extension of number understanding to rational numbers and fosters an entwined understanding of percentages, decimals and fractions. It also aims to understand how social and sociomathematical norms contribute to a co-participated learning of rational numbers enhanced by percentage. The conceptual framework involves a sociocultural perspective of mathematical learning, as a human activity, inherently social and cultural. The theoretical elements considered concern rational number learning as realistic and co-participated, entailed as an extension of the understanding of whole numbers, which addresses percentage, as an entwined understanding of rational number representations, in a number sense perspective. This study is developed as design based research methodology through a classroom experiment. It takes place in grades 3 and 4 within a classroom, in a public primary school in Lisboa, where the researcher is also the teacher. Data collection took place through participant observation, supported by the teacher’s research journal, video and audio recorded moments of whole-class discussions and students’ written work. The analysis sought for evidences of students’ percentage and rational number conceptual understanding, as well for social and sociomathematical norms, as students participated in classroom social interaction. The results highlight that social and sociomathematical norms of the classroom culture, as a mathematical learning community, supported conceptual understanding of percentage for learning rational numbers as it enabled an approach to its multiplicative nature and the establishment of mathematical practices taken as shared. Additionally, through percentage, it was possible to connect students’ prior whole numbers knowledge with intuitive understandings and relations to support the understanding of different symbolic representations, in an entwined manner, attending to a number sense perspective. From this study it emerges a set of principles, that supports a conjecture to improve co-participated learning through percentage, in these grades of primary school, in order to promote student engagement and improve learning.
Descrição
Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2018
Palavras-chave
Teses de doutoramento - 2018