Grupo de estudo: uma proposta à (re)significação de alguns saberes da experiência pré-profissional, em relação à Matemática, na formação inicial do pedagogo
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Data
2019-02-04
Autores
Caetano, Richael Silva
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Universidade Estadual Paulista (Unesp)
Resumo
A presente pesquisa investigou os limites e as possibilidades de um Grupo de Estudo – alicerçado em elementos teóricos advindos da Epistemologia Genética e dos resultados de estudos acerca da Formação (Inicial) de professores – à (re)significação de alguns saberes da experiência pré-profissional, em relação à Matemática e ao seu processo de ensino aprendizagem, de duas licenciandas em Pedagogia. O referido Grupo de Estudo – pensado enquanto um espaço formativo – visou propiciar: a) a construção de alguns conteúdos matemáticos ainda não aprendidos pelas licenciandas durante a Educação Básica; b) o estudo de alguns tópicos da Epistemologia Genética – desenvolvida por Jean Piaget e colaboradores – visando à compreensão, pelas licenciandas, da gênese e do processo de construção do conhecimento; c) a discussão de conhecimentos e saberes didático-metodológicos e curriculares acerca dos referidos conteúdos matemáticos quando estes se tornam objeto de ensino nos anos iniciais do Ensino Fundamental; d) a reflexão/reeducação em torno de alguns saberes da experiência em relação à Matemática (e ao seu processo de ensino e aprendizagem) construídos pelas licenciandas enquanto alunas da Educação Básica. Para a identificação dos referidos limites e possibilidades, foram elaborados dois estudos de caso considerando-se duas, dentre as sete licenciandas que participaram do Grupo de Estudo. Para a obtenção dos dados, e considerando o fenômeno investigado, fez-se necessária a utilização de diversos instrumentos, a saber: a) questionários; b) escala de atitude; c) discussão de grupo (entrevista informal); d) tarefas matemáticas (do tipo lápis e papel); e) observação participante. Após a análise dos referidos dados, concluiu-se o seguinte a respeito das possibilidades do Grupo de Estudo às (re)significações: a) a Matemática passou a ser concebida/(re)significada enquanto uma ciência possível de ser construída, além de possuir sentido; b) a construção das licenciandas acerca de alguns conhecimentos (do tipo esquemas matemáticos) – referentes ao conteúdos de média aritmética, permutação, arranjo e combinação – colaborou na/para a (re)significação anterior, inclusive para a própria (re)significação acerca do bloco ‘Tratamento da Informação’; c) não há mais, para as licenciandas, um único caminho à resolução dos problemas matemáticos; as ‘fórmulas’ deixaram de representar o ‘tudo ou nada’ para tal resolução, ou seja, sem as mesmas faz-se possível ‘fazer Matemática’; d) o aprender Matemática – antes pautado na aplicação obrigatória das ‘fórmulas’ – agora decorre da ação das licenciandas sobre as situações problema, ação essa significada mediante a elaboração de diversos esquemas. Em relação aos limites do Grupo de Estudo à referida (re)significação, identificaram-se: a) a ainda presença da concepção epistemológica empirista no que se refere à explicação, pelas licenciandas, de como se dá o processo de ensino e aprendizagem da Matemática; b) a não conceituação dos conteúdos matemáticos (média aritmética, permutação, arranjo e combinação) em sua forma final (abstração refletida) representada em linguagem formal.
The present study investigated the limitations and possibilities of the learning characteristics of a Study Group based on both, the theoretical elements coming from Genetic Epistemology and the results of studies regarding the Teachers’ Formation in their very initial stages of their education. The research addressed the meaning of mathematics’ knowledge acquired previous to the professionalization in relation to the teaching/learning process of two Teachers of Pedagogy. The Study Group was created to work as a formative space to allow the promotion of the following: a) the construction of a few mathematical contents still not learned by the teachers during their Basic Education Formation; b) the study of a few topics based on the Genetic Epistemology developed by Jean Piaget and his collaborators seeking the measurement of the comprehension absorbed by the licensed Teachers of the genesis and the process of knowledge building; c) the discussion of the didactics, methodologies and academic histories’ understanding and knowledge about the mathematic contents at the moment that they started to teach at the initial years of Fundamental School; d) the reflection and reeducation linked to the knowledge about the experience in relation to Mathematics’ Contents (and its teaching/learning process) built by the licensed teachers while they still were students of the Basic Education. In order to identify the limitations and possibilities of the learning process, it was elaborated two case studies utilizing two out of seven licensed teachers who participated of the Study Group. The data gathering considered the investigated phenomenon and utilized a diversity of instruments, such as: a) questionnaires; b) attitude scale; c) group discussion (informal interview); d) mathematic tasks (such as paper and pencil); e) participants’ observation. Following the analysis of the data, it was possible to conclude a few results about the possibilities of the Study Group and their (re)significations: a) the Mathematics became to be understood/(re)understood as a science that is possible to be constructed and to make sense to the student; b) the licensed teachers building processes about some knowledge (like mathematics’ schemes) linked to the arithmetic mean contents, permutation, arrangement and combination – collaborated to the previous (re)signification, as well as to the (re)signification about the subject “Information Processing” itself; c) it become clear to the licensed teachers that there is not a single way to solve the mathematics’ problems; the formulae stopped representing the ‘everything or nothing’ to the problem solving task, meaning that, without them is still possible to ‘do math’; d) the learning of Mathematics – previously pointed at the necessary application of the formulae – now is understood as the result of the action taken by the licensed teachers on the problem solving situation, meaning which is based on the elaboration of diverse schemes. Lastly, in relation to the limitations of the Study Group about the referred (re)signification, were identified the following: a) the presence of the empirical epistemological conception concerning the meaning of how the process of learning and teaching mathematical skills is built; b) the no- conceptualization of the mathematical contents (arithmetic average, permutation, arrangements and combinations) in its final form (reflected abstraction) represented in the formal language.
The present study investigated the limitations and possibilities of the learning characteristics of a Study Group based on both, the theoretical elements coming from Genetic Epistemology and the results of studies regarding the Teachers’ Formation in their very initial stages of their education. The research addressed the meaning of mathematics’ knowledge acquired previous to the professionalization in relation to the teaching/learning process of two Teachers of Pedagogy. The Study Group was created to work as a formative space to allow the promotion of the following: a) the construction of a few mathematical contents still not learned by the teachers during their Basic Education Formation; b) the study of a few topics based on the Genetic Epistemology developed by Jean Piaget and his collaborators seeking the measurement of the comprehension absorbed by the licensed Teachers of the genesis and the process of knowledge building; c) the discussion of the didactics, methodologies and academic histories’ understanding and knowledge about the mathematic contents at the moment that they started to teach at the initial years of Fundamental School; d) the reflection and reeducation linked to the knowledge about the experience in relation to Mathematics’ Contents (and its teaching/learning process) built by the licensed teachers while they still were students of the Basic Education. In order to identify the limitations and possibilities of the learning process, it was elaborated two case studies utilizing two out of seven licensed teachers who participated of the Study Group. The data gathering considered the investigated phenomenon and utilized a diversity of instruments, such as: a) questionnaires; b) attitude scale; c) group discussion (informal interview); d) mathematic tasks (such as paper and pencil); e) participants’ observation. Following the analysis of the data, it was possible to conclude a few results about the possibilities of the Study Group and their (re)significations: a) the Mathematics became to be understood/(re)understood as a science that is possible to be constructed and to make sense to the student; b) the licensed teachers building processes about some knowledge (like mathematics’ schemes) linked to the arithmetic mean contents, permutation, arrangement and combination – collaborated to the previous (re)signification, as well as to the (re)signification about the subject “Information Processing” itself; c) it become clear to the licensed teachers that there is not a single way to solve the mathematics’ problems; the formulae stopped representing the ‘everything or nothing’ to the problem solving task, meaning that, without them is still possible to ‘do math’; d) the learning of Mathematics – previously pointed at the necessary application of the formulae – now is understood as the result of the action taken by the licensed teachers on the problem solving situation, meaning which is based on the elaboration of diverse schemes. Lastly, in relation to the limitations of the Study Group about the referred (re)signification, were identified the following: a) the presence of the empirical epistemological conception concerning the meaning of how the process of learning and teaching mathematical skills is built; b) the no- conceptualization of the mathematical contents (arithmetic average, permutation, arrangements and combinations) in its final form (reflected abstraction) represented in the formal language.
Descrição
Palavras-chave
Grupo de estudo, Saber da experiência pré-profissional, Formação Inicial do pedagogo em relação à Matemática, Epistemologia genética, Ensino de Matemática, Study group, Knowledge of the pre-professional experience, Initial formation of the pedagogue in relation to Mathematics, Genetic epistemology, Mathematics’ teaching