Construção de conceitos algébricos com alunos do 7º ano
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Data
2017-06
Autores
Orientador
Böckel, Wolmir José
Banca
Böckel, Wolmir José
Rehfeldt, Márcia Jussara Hepp
Quartieri, Marli Teresinha
Oliveira, Eniz Conceição
Hoehne, Lucélia
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Esta dissertação teve como propósito analisar as dificuldades para a construção de conceitos algébricos por alunos do 7º ano de uma escola de Ensino Fundamental, localizada no município de Santana, Estado do Amapá. O problema de pesquisa foi: Como os alunos do 7º ano desenvolvem conceitos algébricos? Como objetivos específicos, a pesquisa procurou: (i) Explorar atividades com padrões geométricos com os alunos para investigar como se dá a passagem da linguagem corrente para a algébrica e (ii) Analisar as contribuições de atividades com padrões geométricos para a compreensão de algumas operações da álgebra por letra ou símbolo. O aporte teórico utilizado teve como base os estudos de Usiskin (1999), que aponta a generalização de padrões como um caminho para o estudo do ensino e aprendizagem da álgebra, e os trabalhos de Lins e Gimenez (2006), que estudam o desenvolvimento do pensamento algébrico. Esta pesquisa, de natureza qualitativa, foi desenvolvida com oito alunos selecionados de uma turma com 34 alunos do 7º ano. Nesse contexto, a coleta de dados ocorreu em três momentos: 1º) por meio da aplicação de questionário investigativo, 2º) pela realização de oito aulas práticas e 3º) pela aplicação do questionário de percepção. A análise dos dados revelou que a maioria dos alunos consegue identificar e desenhar os elementos que completam uma sequência, empenhando-se nas atividades. No entanto, apresentam lacunas em relação à aritmética, erros no uso da elaboração das regras, problemas na leitura e na interpretação da situação problema, dificuldades para identificar generalizações e dificuldades na escrita de seu pensamento algébrico.
This dissertation aimed to analyze the difficulties for the construction of algebraic concepts by students of the 7th year of grade school (Fundamental Teaching), in Santana City, state of Amapá. The research problem was: How do the students of the 7th year build algebraic concepts? As specific objective, the research sought (i) to make the most of the activities with geometric patterns with the students in order to investigate how the change from the current language into algebraic one is carried out; (ii) to analyze the contributions of activities with geometric patterns for the comprehension about some operations in algebra with letter or symbol. The theoretical framework was based on the study by Usiskin (1999) that points the generalization of patterns as way to the study of Teaching and Learning of algebra, and the works by Lins and Gimenez (2006) that study the development of algebraic thought. This research, of qualitative basis, has been developed with eight students selected from a group of 34 in a class of the 7th year. In this context, the data collection was accomplished in three moments, 1) by applying investigative questionnaires; 2) by carrying out eight practical classes; and 3) by applying a questionnaire to analyze ones perception. The analysis of the data has revealed that most of the students are able to identify and draw the elements that complete a sequence when striving in the activities. Nevertheless, they show some learning gaps in relation to arithmetic, take mistakes in rule making, problems in reading and difficulties in: interpreting the problem situation, identifying generalizations and writing their algebraic thought.
This dissertation aimed to analyze the difficulties for the construction of algebraic concepts by students of the 7th year of grade school (Fundamental Teaching), in Santana City, state of Amapá. The research problem was: How do the students of the 7th year build algebraic concepts? As specific objective, the research sought (i) to make the most of the activities with geometric patterns with the students in order to investigate how the change from the current language into algebraic one is carried out; (ii) to analyze the contributions of activities with geometric patterns for the comprehension about some operations in algebra with letter or symbol. The theoretical framework was based on the study by Usiskin (1999) that points the generalization of patterns as way to the study of Teaching and Learning of algebra, and the works by Lins and Gimenez (2006) that study the development of algebraic thought. This research, of qualitative basis, has been developed with eight students selected from a group of 34 in a class of the 7th year. In this context, the data collection was accomplished in three moments, 1) by applying investigative questionnaires; 2) by carrying out eight practical classes; and 3) by applying a questionnaire to analyze ones perception. The analysis of the data has revealed that most of the students are able to identify and draw the elements that complete a sequence when striving in the activities. Nevertheless, they show some learning gaps in relation to arithmetic, take mistakes in rule making, problems in reading and difficulties in: interpreting the problem situation, identifying generalizations and writing their algebraic thought.
Descrição
Palavras-chave
Ensino da álgebra; Padrões; Generalização
Citação
MAGALHÃES, Ayrton Góes De. Construção de conceitos algébricos com alunos do 7º ano. 2016. Dissertação (Mestrado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 22 set. 2016. Disponível em: http://hdl.handle.net/10737/1570.