O conhecimento declarativo do professor alfabetizador no ensino de geometria
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2018-02-28
Autores
Silva, Gilmara Aparecida da
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Universidade Estadual Paulista (Unesp)
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Esta tese, vinculada ao Programa Educação para a Ciência, da Faculdade de Ciências, Unesp Bauru/SP, foi concretizada por meio de estudos sobre a formação conceitual em Geometria com professores alfabetizadores. A pergunta norteadora da pesquisa foi: Qual o conhecimento declarativo apresentado por professores alfabetizadores participantes do Programa de Formação Continuada Pacto Nacional de Alfabetização na Idade Certa – PNAIC de Matemática em relação aos conceitos geométricos? Para tanto, teve como objetivo investigar quais conceitos geométricos, especialmente no que diz respeito ao conhecimento declarativo, os professores participantes do PNAIC mobilizam ao ensinar Matemática, no ciclo de alfabetização (1º ao 3º ano do ensino fundamental). Para isso, apoiamo-nos nos estudos sobre os atributos definidores e os níveis cognitivos do desenvolvimento conceitual, de Klausmeier e Goodwin (1977); sobre as habilidades básicas de Geometria, de Hoffer (1981), e sobre o conhecimento declarativo proposto por Sternberg (2000). A pesquisa tem abordagem de interpretação quanti-qualitativa, cujo percurso metodológico está delineado nas etapas da pesquisa de campo, a qual foi realizada em duas etapas: uma anterior ao estudo do Caderno de Geometria e outra posterior a esse estudo, feito no curso de formação continuada do PNAIC com ênfase em Matemática. Os instrumentos utilizados para a produção dos dados foram dois questionários, sendo que um foi aplicado na primeira etapa da pesquisa e o outro, na segunda etapa. Da tabulação dos dados da primeira etapa, foram construídas as categorias de análise, de acordo com os atributos definidores para, a partir dessas, verificar qual o conhecimento declarativo (atributos definidores) e quais habilidades geométricas o professor alfabetizador apresentava depois da formação. De maneira geral, a análise dos questionários mostrou pouco conhecimento declarativo sobre as figuras geométricas, utilização de atributos equivocados para conceituá-las e processos de subgeneralização por parte dos professores que atuam no ciclo de alfabetização. Os resultados de análise também mostraram que o conhecimento declarativo evidenciado pelas repostas dos professores aproxima-se do conhecimento declarativo de alunos da Educação Básica, de acordo com os estudos desenvolvidos no âmbito da Educação Matemática. Em termos de habilidades, foi verificado que a habilidade verbal apresentou-se como elemento dificultador no processo de identificação e nomeação de atributos definidores.
This thesis, linked to the Science Education Program, from College of Science at Unesp, Bauru/SP, was accomplished through studies related to the conceptual formation in Geometry with literacy teachers. The guiding question of this research was: What was the declarative knowledge presented by literacy teachers who were participants of the Program of continual formation literacy national pact in the right age – PNAIC of Math in relation to the geometrical concepts. Therefore, the purpose was to investigate which geometrical concepts, especially the ones related to the declarative knowledge, the participant teachers of PNAIC impel when teaching Math in the literacy cycle (1st to 3rd year of elementary school). To do it, we have supported on the studies of the defining features and the cognitive levels of the conceptual development, from Klausmeier and Goodwin (1977); on the basic abilities of Geometry from Hoffer (1981) and on the declarative knowledge proposed by Sternberg (2000). The research has the quantity-qualitative approach of interpretation, and its methodological course is traced on the field research stages, which was developed in two stages: one that was prior to the study of Geometry Notebook and another one after this study, which was done in the continued formation course from PNAIC with emphasis in Math. The used instruments to the data production were two questionnaires - one was applied in the first stage of the research and the other, in the second one. Analysis categories were built from the data tabulation of the first stage according to the defining features to, as from them, verify which declarative knowledge (defining features), and which geometric abilities the literacy teacher presented after the formation. In general, the questionnaire analysis, showed little declarative knowledge on geometric figures, use of mistaken features to conceptualize them, and sub generalization processes from the teachers who work in the literacy cycle. The analysis results also show that the declarative knowledge verified by the teachers‘ answers is close to the declarative knowledge of students on Basic Education, according to the studies that were developed in the Math Education scope. In terms of abilities, the verbal ability was the difficult element in the process of identification and nomination of defining features.
This thesis, linked to the Science Education Program, from College of Science at Unesp, Bauru/SP, was accomplished through studies related to the conceptual formation in Geometry with literacy teachers. The guiding question of this research was: What was the declarative knowledge presented by literacy teachers who were participants of the Program of continual formation literacy national pact in the right age – PNAIC of Math in relation to the geometrical concepts. Therefore, the purpose was to investigate which geometrical concepts, especially the ones related to the declarative knowledge, the participant teachers of PNAIC impel when teaching Math in the literacy cycle (1st to 3rd year of elementary school). To do it, we have supported on the studies of the defining features and the cognitive levels of the conceptual development, from Klausmeier and Goodwin (1977); on the basic abilities of Geometry from Hoffer (1981) and on the declarative knowledge proposed by Sternberg (2000). The research has the quantity-qualitative approach of interpretation, and its methodological course is traced on the field research stages, which was developed in two stages: one that was prior to the study of Geometry Notebook and another one after this study, which was done in the continued formation course from PNAIC with emphasis in Math. The used instruments to the data production were two questionnaires - one was applied in the first stage of the research and the other, in the second one. Analysis categories were built from the data tabulation of the first stage according to the defining features to, as from them, verify which declarative knowledge (defining features), and which geometric abilities the literacy teacher presented after the formation. In general, the questionnaire analysis, showed little declarative knowledge on geometric figures, use of mistaken features to conceptualize them, and sub generalization processes from the teachers who work in the literacy cycle. The analysis results also show that the declarative knowledge verified by the teachers‘ answers is close to the declarative knowledge of students on Basic Education, according to the studies that were developed in the Math Education scope. In terms of abilities, the verbal ability was the difficult element in the process of identification and nomination of defining features.
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Palavras-chave
Geometria, Alfabetização matemática, Formação continuada, Formação de conceitos, Math literacy, Continued formation, Geometry, Formation of concepts