Da aritmética a álgebra: um passo importante nos anos finais do ensino fundamental
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Data
2018-02-19
Autores
Furquim, Augusto Sergio
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho, promovemos um estudo acerca da introdução `a Álgebra nos Anos Finais do Ensino Fundamental. Para tanto, perpassamos pela construção lógica e a Aritmética do conjunto dos números Naturais, Inteiros e Racionais. Além disso, abordamos a Álgebra em seus aspectos históricos, concepções, resultados em avaliações de larga escala, disposição no Currículo do Estado de São Paulo - onde constatamos um salto entre Aritmética e Álgebra - e sua introdução através de situações de aprendizagem as quais denominamos atividades de “Pré-Álgebra”. Ao longo do desenvolvimento de nosso trabalho discutimos, em revisão de literatura e, também, experimentalmente, as implicações de um adiantamento, com relação ao currículo supracitado, no tratamento da Álgebra em atividades introdutórias. Como resultado, verificamos que há, sim, espaço para que a Álgebra seja previamente introduzida, em consonância com a Aritmética, através de atividades de Pré-Álgebra. No entanto, não podemos garantir que esta introdução seja mais fácil para os alunos, embora conjecturemos que a suavidade da forma como tratamos a Álgebra durante as atividades da Pré-Álgebra pode contribuir para uma melhoria no cenário de ensino da Álgebra em nosso país.
In this work, we promote a study on the introduction to Algebra in the final years of Elementary School. For this, we went through the logical construction and the arithmetic of the set of Natural, Integer and Rational numbers. Moreover, we analyzed Algebra based on its historical aspects, conceptions, the outcome on the large-scale evaluations, on how it appears on the State of S˜ao Paulo Curriculum - which showed us a jump between Arithmetic and Algebra - and its introduction by using some learning activities that we call ”pre-algebra”. Throughout the development of our work we discussed - by reviewing some literature and also experimentally - the implications of an advance in the treatment of Algebra in introductory activities, in comparison with the above mentioned curriculum. As a result, we find out that in fact there is space to introduce Algebra in advance, in line with Arithmetic, using the Pre-Algebra activities. However, we cannot guarantee that this introduction is going to be easier for the students, although we conjecture that the smoothness of the way we treat Algebra during the PreAlgebra activities can contribute for an improvement in the scenario of teaching Algebra in our country.
In this work, we promote a study on the introduction to Algebra in the final years of Elementary School. For this, we went through the logical construction and the arithmetic of the set of Natural, Integer and Rational numbers. Moreover, we analyzed Algebra based on its historical aspects, conceptions, the outcome on the large-scale evaluations, on how it appears on the State of S˜ao Paulo Curriculum - which showed us a jump between Arithmetic and Algebra - and its introduction by using some learning activities that we call ”pre-algebra”. Throughout the development of our work we discussed - by reviewing some literature and also experimentally - the implications of an advance in the treatment of Algebra in introductory activities, in comparison with the above mentioned curriculum. As a result, we find out that in fact there is space to introduce Algebra in advance, in line with Arithmetic, using the Pre-Algebra activities. However, we cannot guarantee that this introduction is going to be easier for the students, although we conjecture that the smoothness of the way we treat Algebra during the PreAlgebra activities can contribute for an improvement in the scenario of teaching Algebra in our country.
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Palavras-chave
Pré-álgebra, Ensino de matemática, Aritmética, Pre-algebra, Mathematics teaching, Arithmetic