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Abstract(s)
Este estudo tem como principal objetivo compreender como é que os alunos se apropriam da calculadora gráfica ao longo dos dois primeiros anos do ensino secundário e qual o papel que esse instrumento desempenha na aprendizagem das funções.
O quadro teórico incide na abordagem instrumental, dando especial atenção ao processo de génese instrumental relativo à calculadora gráfica; no papel das múltiplas representações na aprendizagem das funções; e no desenvolvimento do conceito imagem de função.A metodologia do estudo insere-se no paradigma interpretativo, seguindo uma abordagem qualitativa, na modalidade de estudo de caso. A recolha de dados realizou-se em dois anos letivos consecutivos, acompanhando os alunos no décimo e décimo primeiro anos, e envolveu a observação de aulas, entrevistas clínicas aos alunos e recolha de documentos produzidos por estes e pela professora da turma. A análise de dados foi moldada pelo enquadramento teórico e pelos dados empíricos recolhidos, sendo realizados dois estudos de caso.Os resultados sugerem que o processo de génese instrumental é demorado, tal como é referido na literatura, sendo influenciado por vários fatores, nomeadamente os esquemas de utilização que são desenvolvidos e valorizados na sala de aula, o tipo de funções e as situações matemáticas em que os alunos se envolvem, os conhecimentos matemáticos que possuem e o seu próprio perfil de trabalho. No final do décimo primeiro ano, os alunos têm ainda alguma dificuldade em compreender e interpretar determinadas limitações da calculadora gráfica, em particular no que diz respeito à representação gráfica, sendo o estabelecimento de conexões entre representações essencial para evitar interpretações precipitadas.O acesso rápido à representação gráfica facilitado pela calculadora promove o desenvolvimento de uma visão estrutural do conceito de função, incentiva a exploração de situações problemáticas e contribui para uma maior flexibilidade em termos das estratégias de resolução de problemas.
The main goal of this study is to understand how students incorporate the graphic calculator in their mathematical activity, during the first two years of the secondary education, and also to understand the role of that instrument in the learning of functions.The theoretical framework focuses on the instrumental approach, paying particular attention to the process of instrumental genesis of the graphic calculator; on the role of multiple representations in the learning of functions; and in the development of the concept image of function.The methodology of the study is within the interpretive paradigm, following a qualitative approach in the form of case study. Data collection took place in two consecutive academic years, with students in the tenth and eleventh grades, and was accomplished by classroom observation, clinical interviews with the students and collection of some documents produced by these and by the classroom teacher. The data analysis was shaped by the theoretical framework and the empirical data collected, being conducted two case studies.The results suggest that the process of instrumental genesis takes time, as reported in the literature, being influenced by many factors, including the utilization schemes that are developed and valued in the classroom, the type of functions and mathematical situations in which students engage themselves, their mathematical knowledge and work profile. At the end of the eleventh grade, the students still have some difficulties in understanding and interpreting certain graphic calculator’s limitations, particularly as regards to the graphic representation, being essential that they establish connections among representations to avoid hasty interpretations. The rapid access to the graphic representation, enabled by the graphic calculator, promotes the development of a structural view of the function concept, encourages the exploration of problematic situations and contributes to a greater flexibility in terms of the strategies in problem solving.
The main goal of this study is to understand how students incorporate the graphic calculator in their mathematical activity, during the first two years of the secondary education, and also to understand the role of that instrument in the learning of functions.The theoretical framework focuses on the instrumental approach, paying particular attention to the process of instrumental genesis of the graphic calculator; on the role of multiple representations in the learning of functions; and in the development of the concept image of function.The methodology of the study is within the interpretive paradigm, following a qualitative approach in the form of case study. Data collection took place in two consecutive academic years, with students in the tenth and eleventh grades, and was accomplished by classroom observation, clinical interviews with the students and collection of some documents produced by these and by the classroom teacher. The data analysis was shaped by the theoretical framework and the empirical data collected, being conducted two case studies.The results suggest that the process of instrumental genesis takes time, as reported in the literature, being influenced by many factors, including the utilization schemes that are developed and valued in the classroom, the type of functions and mathematical situations in which students engage themselves, their mathematical knowledge and work profile. At the end of the eleventh grade, the students still have some difficulties in understanding and interpreting certain graphic calculator’s limitations, particularly as regards to the graphic representation, being essential that they establish connections among representations to avoid hasty interpretations. The rapid access to the graphic representation, enabled by the graphic calculator, promotes the development of a structural view of the function concept, encourages the exploration of problematic situations and contributes to a greater flexibility in terms of the strategies in problem solving.
Description
Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014
Keywords
Didáctica da matemática Calculadoras gráficas Funções (Matemática) Teses de doutoramento - 2014