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Resolução de problemas com a função afim em diferentes contextos
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Este relatório visa compreender de que modo alunos do 8.º ano do ensino básico resolvem problemas com a função afim, em particular em dois contextos, com e sem o recurso ao software de Geometria Dinâmica GeoGebra. Com esta intenção, tentei perceber a que estratégias e representações recorrem os alunos na resolução de problemas com a função afim e que conhecimentos matemáticos mobilizam, nos dois contextos. O estudo que apresento foi desenvolvido no âmbito da prática de ensino supervisionada e baseia-se no trabalho realizado ao longo da minha intervenção letiva na unidade “Gráficos de Funções Afins”, com uma turma do 8.º ano, da Escola Secundária de Caneças. Esta lecionação decorreu no início do terceiro período escolar, ao longo de 18 tempos de 45 minutos.
A metodologia deste estudo insere-se numa abordagem qualitativa e teve como principais métodos de recolha de dados: a observação participante, com a gravação áudio/vídeo, as produções escritas dos alunos da turma e a realização de entrevistas de tipo clínico a dois pares de alunos.
A análise dos dados evidencia que i) segmentar o problema em etapas e ii) utilizar representações e esquemas são as estratégias heurísticas a que os alunos mais recorrem, na resolução de problemas com a função afim, e realça que estas estratégias tendem a ocorrer numa fase mais inicial da resolução de problemas. Além disso, os alunos revelam privilegiar a representação gráfica e algébrica de uma função afim e, em contrapartida, evidenciam maiores dificuldades com a representação tabular. Ainda como conclusão deste estudo destaco que o recurso ao GeoGebra permite descentrar a atividade dos alunos de procedimentos de cálculo, embora as noções que mobilizaram sejam, nos dois contextos, muito semelhantes. Na resolução de problemas, a utilização do software promoveu a cooperação entre alunos do mesmo par e permitiu o desenvolvimento de estratégias menos demoradas. Quanto aos conceitos mobilizados, na análise de dados foi percetível que, comparativamente, os alunos que recorreram ao GeoGebra revelaram maior destreza ao interpretar a representação gráfica de uma função afim, enquanto os alunos que optaram por não usar este recurso, em geral, mostraram dominar a notação algébrica.
The aim of this report is to address how the dynamic geometry software GeoGebra influences eighth graders while solving problems with the affine function when compared to the ones that did not use this software. With this aim in mind, I tried to understand, in the two above scenarios, which strategies and representations the students used while solving problems with the affine function and also what was the pre-acquired mathematical knowledge they resorted. This study was part of my supervised teaching practice and was based on my teaching intervention, specifically when I taught the “Graph of Affine Functions” unit to a 8th grade class at Escola Secundária de Caneças. This unit started to be taught in the beginning of the third school term and was taught throughout eighteen 45-minutes lessons. The research methodology follows a qualitative approach and has as main data collection methods audiovisual recordings of participant observation, students’ written answers to problems and clinical interviews to two pairs of students. The data analysis reveals that i) breaking down the problem into steps and ii) making representations and schemes are the heuristic strategies that the students choose more when solving problems with the affine function and also these strategies usually are used in an initial stage of problem solving. Besides, the students tend to prefer graphic and algebraic representations of the affine function, while they have more difficulties with the numeric representation. Also I can also conclude that when students used GeoGebra software they were less centered in calculus procedures, even if the mathematical notions were, in the two scenarios, very similar. Furthermore, the software promoted the cooperation between students of the same pair and allowed the students to think of less time-consuming heuristics. In terms of resorted concepts, the data analysis allows concluding that the GeoGebra users demonstrate to know how to interpret a affine function graph, whereas the non-users show to have knowledge of the algebraic notation.
The aim of this report is to address how the dynamic geometry software GeoGebra influences eighth graders while solving problems with the affine function when compared to the ones that did not use this software. With this aim in mind, I tried to understand, in the two above scenarios, which strategies and representations the students used while solving problems with the affine function and also what was the pre-acquired mathematical knowledge they resorted. This study was part of my supervised teaching practice and was based on my teaching intervention, specifically when I taught the “Graph of Affine Functions” unit to a 8th grade class at Escola Secundária de Caneças. This unit started to be taught in the beginning of the third school term and was taught throughout eighteen 45-minutes lessons. The research methodology follows a qualitative approach and has as main data collection methods audiovisual recordings of participant observation, students’ written answers to problems and clinical interviews to two pairs of students. The data analysis reveals that i) breaking down the problem into steps and ii) making representations and schemes are the heuristic strategies that the students choose more when solving problems with the affine function and also these strategies usually are used in an initial stage of problem solving. Besides, the students tend to prefer graphic and algebraic representations of the affine function, while they have more difficulties with the numeric representation. Also I can also conclude that when students used GeoGebra software they were less centered in calculus procedures, even if the mathematical notions were, in the two scenarios, very similar. Furthermore, the software promoted the cooperation between students of the same pair and allowed the students to think of less time-consuming heuristics. In terms of resorted concepts, the data analysis allows concluding that the GeoGebra users demonstrate to know how to interpret a affine function graph, whereas the non-users show to have knowledge of the algebraic notation.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática, Universidade de Lisboa, Instituto de Educação, 2016
Palavras-chave
Resolução de problemas 3º Ciclo do Ensino Básico Heurísticas Relatórios da prática de ensino supervisionada - 2016