Uma interface entre história e ensino de matemática: contribuições na formação de conceitos de estudantes na construção e utilização de um instrumento de medida do século XVI – O Quadrante Geométrico
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Data
2019-02-21
Autores
Silva, Ana Paula Minhano Aleixo
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Universidade Estadual Paulista (Unesp)
Resumo
O objetivo desta pesquisa é investigar o movimento de conceitos na aprendizagem da matemática, a partir de uma atividade didática elaborada com base no contexto histórico do instrumento de medida Quadrante Geométrico e no tratado Del modo di misurare, de Cosimo Bartoli. Os fundamentos teórico-metodológicos pautam-se em um delineamento possível de interface entre a história da matemática e o ensino da matemática, de modo a dar significado aos objetos matemáticos. Para aproximar a história da matemática do ensino, optamos por explorar as potencialidades didáticas do instrumento de medida, o quadrante geométrico e de seu respectivo tratado, a partir da análise do contexto histórico e do movimento do pensamento para a formação dos conceitos matemáticos sintetizados no instrumento, por meio de uma intervenção com estudantes do 9º ano do Ensino Fundamental. A atividade didática foi organizada sob pressupostos da atividade orientadora de ensino, fundamentada na Teoria da Atividade, sob a perspectiva da Teoria Histórico-Cultural. A coleta dos dados ocorreu por intermédio de gravações audiovisuais e das produções escritas dos estudantes. Os dados foram organizados em episódios e receberam uma análise qualitativa, pautada na perspectiva histórico-cultural com enfoque no pensamento empírico e teórico. Os resultados indicam articulações dos conceitos matemáticos de medida, números racionais, reta oblíqua, razão, proporção e semelhança de triângulos, no decorrer das ações da atividade didática, apontando o movimento desses conceitos no pensamento dos estudantes, de modo a propiciar a mobilização do conceito empírico e do conceito teórico desses objetos matemáticos. O salto desta pesquisa está na produção de uma interface entre a história e o ensino da matemática, por meio de uma organização intencional da atividade didática, que articulou e mobilizou conhecimentos dos estudantes para o desenvolvimento do conceito teórico dos objetos matemáticos sintetizados no processo de construção e uso do instrumento de medida, o quadrante geométrico.
The purpose of this research is to investigate the motion of concepts in the learning of mathematics, as from a didactic activity drafted on the historical context of the geometric quadrant measuring instrument and Del modo di misurare by Cosimo Bartoli. The theoretical-methodological foundations are grounded in a possible delineation of the interface between history and teaching of mathematics, in order to imply meaning for mathematical objects. To bring mathematics history and teaching closer, we opted to explore the didactic potentialities of a measuring instrument, the geometric quadrant and its respective treatise, by analyzing the historical context and the thought movement for the formation of mathematical concepts synthesized in the instrument, by means of an intervention with students attending the 9th grade of school. Such didactic activity was organized under the assumptions of the orienting teaching activity, reasoned in Theory of Activity, from the perspective of Historical-Cultural Theory. The data collection occurred through audiovisual recordings and productions written by the students. These data were arranged into episodes for review and received a qualitative analysis, based on a historical-cultural perspective, focusing on the empirical and theoretical thinking. Results indicate articulations of the mathematical concepts of measurement, rational numbers, oblique line, ratio, proportion, and similarity of triangles during the didactic activity, showing the movement of these concepts in the students' thinking and providing the mobilization of the empirical and theoretical concept of these mathematical objects. The increase of this research is in elaboration of an interface between history and teaching of mathematics, through an intentional organization of didactic activity that articulated and mobilized students’ knowledge about development of the theoretical concept of mathematical objects synthesized in the construction process and use of the measuring instrument, the geometric quadrant.
The purpose of this research is to investigate the motion of concepts in the learning of mathematics, as from a didactic activity drafted on the historical context of the geometric quadrant measuring instrument and Del modo di misurare by Cosimo Bartoli. The theoretical-methodological foundations are grounded in a possible delineation of the interface between history and teaching of mathematics, in order to imply meaning for mathematical objects. To bring mathematics history and teaching closer, we opted to explore the didactic potentialities of a measuring instrument, the geometric quadrant and its respective treatise, by analyzing the historical context and the thought movement for the formation of mathematical concepts synthesized in the instrument, by means of an intervention with students attending the 9th grade of school. Such didactic activity was organized under the assumptions of the orienting teaching activity, reasoned in Theory of Activity, from the perspective of Historical-Cultural Theory. The data collection occurred through audiovisual recordings and productions written by the students. These data were arranged into episodes for review and received a qualitative analysis, based on a historical-cultural perspective, focusing on the empirical and theoretical thinking. Results indicate articulations of the mathematical concepts of measurement, rational numbers, oblique line, ratio, proportion, and similarity of triangles during the didactic activity, showing the movement of these concepts in the students' thinking and providing the mobilization of the empirical and theoretical concept of these mathematical objects. The increase of this research is in elaboration of an interface between history and teaching of mathematics, through an intentional organization of didactic activity that articulated and mobilized students’ knowledge about development of the theoretical concept of mathematical objects synthesized in the construction process and use of the measuring instrument, the geometric quadrant.
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Ensino de matemática, História da matemática, Instrumentos de medida, Formação de conceito, Mathematics teaching, History of Mathematics, Measuring instruments, Concept formation