Introdução à álgebra nos anos iniciais do Ensino Fundamental: uma análise a partir da Teoria da Objetivação
The purpose of this investigation occurs in the Brazilian cultural context where the systematic teaching-learning of algebra in the early years of elementary school was specifically oriented after the approval of the Common National Curricular Base, at the end of 2017. Thus, as it is a recent dem...
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Formato: | doctoralThesis |
Idioma: | pt_BR |
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Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/29327 |
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Resumo: | The purpose of this investigation occurs in the Brazilian cultural context where the
systematic teaching-learning of algebra in the early years of elementary school was
specifically oriented after the approval of the Common National Curricular Base, at the
end of 2017. Thus, as it is a recent demand, we verified, by means of a survey carried
out on didactic materials, on portals of journals and on official documents, incipient
orientations, especially with regard to the approach of algebra with a focus on the
function of the equality symbol in sentences mathematics with an unknown term. In the
investigative path, to know, learn and investigate the systematic teaching-learning of
algebra in the early years, we chose to follow the socio-cultural perspective of the
Theory of Objectivation, which considers thought as a way of acting and reflecting on
the world. For that theory, algebraic thinking is based on three vectors: indeterminacy,
that is, the presence of the unknown term and the treatment given to it in mathematical
situations; the semiotic expression, constituted in the recognition and reference to the
indeterminate and the analyticity, which consists of the deductive operation with the
unknown. So, the general objective of the research is to characterize, based on the
Theory of Objectification, thinking strategies demonstrated by 4th and 5th grade
children of Elementary Education at the Center for Childhood Education - Application
College of the Federal University of Rio Grande do Norte, in process of introducing
algebra, in tasks that address mathematical sentences in which one of the terms is
unknown. In this sense, as a specific objective we propose to analyze evidence of the
three characteristic vectors of algebraic thinking (analyticity, semiotic expression and
indeterminacy) in the thinking strategies raised by children. The research is outlined
as qualitative of the descriptive and interpretive type with the method of multisemiotic
or multimodal analysis, the Theory of Objectification characteristic. Our analyses
indicate that, in the process of introducing algebra, the strategies demonstrated by
children show the latent presence of proto-analyticity as a characteristic that makes up
this process. We also conclude, from the analysis of the thinking strategies
demonstrated by the children that: algebraic thinking presents a break with arithmetic
thinking, this differentiation can be demonstrated by the difficulty of children in
operating with the unknown; the use of refined arithmetic strategies and the use of
mathematical operations properties collaborate in the development and structuring of
algebraic thinking; algebraic and / or arithmetic thinking can be expressed in multiple
ways, so it is necessary to provide freedom for children to solve problems in their own
way, as well as to value their strategies. |
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