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Abstract(s)
Documentos curriculares recentes, como por exemplo, o Perfil dos alunos à saída da
escolaridade obrigatória, referem como é essencial que os alunos, quer a nível geral, quer
a nível da Matemática, sejam criativos e flexíveis. Criatividade e flexibilidade devem ser
desenvolvidas na realização de projetos de diferentes naturezas e também no âmbito da
aprendizagem de conteúdos das várias disciplinas. Neste artigo começamos por situar a
flexibilidade na comparação multiplicativa, entendendo-a como refletida nas conexões
entre conceitos, símbolos e procedimentos, evidenciadas na resolução de tarefas
matemáticas sobre proporcionalidade. Mais concretamente, a flexibilidade na comparação
multiplicativa é um processo dinâmico de adaptação de estratégias de resolução e de
representações utilizadas pelos alunos às características das tarefas, em que as relações
numéricas e as propriedades das operações assumem um papel relevante. Em seguida,
salientamos as duas conclusões mais relevantes de um estudo que segue uma metodologia
de investigação baseada em design, realizado com alunos de duas turmas do 6.º ano de
escolaridade: (1) quando usam estratégias e representações adequadas, os alunos não
mostram grande apetência para as alterar. Perante um procedimento que funciona, não
ponderam o uso de outros, eventualmente mais adequados aos valores numéricos em jogo,
menos trabalhosos ou mais rápidos; (2) nas suas resoluções, os alunos usam relações
numéricas multiplicativas e propriedades da operação multiplicação que conseguem
articular com as estratégias e as representações a que recorrem, revelando uma flexibilidade
que se confina às suas opções de abordagem. A partir destas conclusões propomos um
conjunto de ideias que nos parecem dever ser equacionadas numa discussão sobre a
formação de professores e que deverão contribuir de modo decisivo para desenvolver o
Perfil dos alunos à saída da escolaridade obrigatória. A nível geral destacamos a
importância de a formação inicial de professores criar condições propícias a que o futuro
professor comece a interiorizar a sua responsabilidade ao nível do seu crescimento
profissional. A nível mais específico, a partir do estudo empírico realizado, concretizamos
como o futuro professor de matemática pode promover nos seus alunos a flexibilidade na
comparação multiplicativa.
Recent curriculum guidelines, such as Students’ profile after leaving compulsory schooling, refer to how it is essential that students, both at general level, and at Mathematics’ level, are creative and flexible. Creativity and flexibility must be developed when carrying out projects of different nature and in the context of learning the contents of different subjects. In this paper, we begin by situating flexibility in the multiplicative comparison, understanding it as reflected in the connections between concepts, symbols and procedures evidenced in the resolution of mathematical proportionality tasks. More specifically, flexibility in multiplicative comparison is a dynamic process of adapting resolution strategies and representations used by students to the tasks’ characteristics, in which the numerical relations and the operations’ properties assume a relevant role. Then, we highlight the two most relevant conclusions of a study that follows a design-based research methodology, carried out with students from two sixth grade classes: (1) when using appropriate strategies and representations, students are unwilling to change them. Faced with a procedure that works, they do not consider using others, even if possibly more appropriate to the real numerical values, less laborious or faster; (2) in their resolutions, students use multiplicative numerical relations and multiplication properties that they manage to articulate with strategies and representations they use, revealing a flexibility that is confined to their approach options. Based on these conclusions, we propose a set of ideas that we believe should be considered in teacher training and that have a decisive contribution to develop the Students’ profile after leaving compulsory schooling. At general level, we highlight the importance of initial teacher training creating conditions that will enable future teachers to begin to internalize their responsibility in terms of their professional development. At a more specific level, from the empirical study carried out, we grasped how future mathematics teachers can promote flexibility in multiplicative comparison to their students.
Recent curriculum guidelines, such as Students’ profile after leaving compulsory schooling, refer to how it is essential that students, both at general level, and at Mathematics’ level, are creative and flexible. Creativity and flexibility must be developed when carrying out projects of different nature and in the context of learning the contents of different subjects. In this paper, we begin by situating flexibility in the multiplicative comparison, understanding it as reflected in the connections between concepts, symbols and procedures evidenced in the resolution of mathematical proportionality tasks. More specifically, flexibility in multiplicative comparison is a dynamic process of adapting resolution strategies and representations used by students to the tasks’ characteristics, in which the numerical relations and the operations’ properties assume a relevant role. Then, we highlight the two most relevant conclusions of a study that follows a design-based research methodology, carried out with students from two sixth grade classes: (1) when using appropriate strategies and representations, students are unwilling to change them. Faced with a procedure that works, they do not consider using others, even if possibly more appropriate to the real numerical values, less laborious or faster; (2) in their resolutions, students use multiplicative numerical relations and multiplication properties that they manage to articulate with strategies and representations they use, revealing a flexibility that is confined to their approach options. Based on these conclusions, we propose a set of ideas that we believe should be considered in teacher training and that have a decisive contribution to develop the Students’ profile after leaving compulsory schooling. At general level, we highlight the importance of initial teacher training creating conditions that will enable future teachers to begin to internalize their responsibility in terms of their professional development. At a more specific level, from the empirical study carried out, we grasped how future mathematics teachers can promote flexibility in multiplicative comparison to their students.
Description
Keywords
Flexibilidade Comparação multiplicativa Formação de professores Flexibility Multiplicative comparison Teacher training
Citation
Cebola, G., & Brocardo, J. (2020). Flexibilidade na comparação multiplicativa: Desafio para a formação de professores de matemática. In R. P. Lopes, C. Mesquita, E. M. Silva, M. V. Pires (Eds.), V Encontro Internacional de Formação na Docência: Livro de Atas, (pp. 91-101). Instituto Politécnico de Bragança.