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Advisor(s)
Abstract(s)
Os objetivos do estudo são perceber o que os alunos já aprenderam sobre a divisão e como desenvolver o ensino/aprendizagem da divisão com compreensão e incentivar a utilização de estratégias mais sofisticadas em problemas de divisão.
Para tal, colocaram-se as questões: (1) Quais as estratégias utilizadas pelos alunos na resolução de problemas de divisão? (2) Que compreensão evidenciam de ideias fundamentais relacionadas com a operação da divisão? Que dificuldades revelam? (3) Que papel pode ter o desenvolvimento do cálculo mental? (4) Será que as interações entre professor e alunos e entre alunos contribuem para a compreensão dos aspetos fundamentais sobre a divisão e para o desenvolvimento de estratégias de resolução de problemas mais sofisticadas?
A investigação enquadra-se no paradigma interpretativo, desenvolvida através de uma metodologia do tipo qualitativo, no formato de estudo de caso.
Para a recolha de dados foi organizada uma sequência de 7 tarefas de divisão, desenvolvidas numa sala de aula de 4º ano em 2015/2016.
Recolheram-se dados de dois pares de alunos através diversas técnicas.
Em conclusão verificou-se que inicialmente a estratégia de divisão mais utilizada foram os procedimentos de construção, mas a estratégia preferida acabou por ser os algoritmos alternativos. A única ideia fundamental da divisão de que ambos os pares revelaram algum domínio foi na identificação desta operação em situações de partilha e de medida. Mostraram dificuldade na identificação da relação possível entre situações de medida e partilha, na utilização do modelo retangular, na utilização da relação inversa entre a multiplicação e divisão e na compreensão da influência do resto. Sobre o papel do cálculo mental verificou-se que este esteve presente em quase todas as estratégias desenvolvidas e quase sempre associado à estimativa e tentativa e erro. Relativamente à contribuição das interações, apurou-se que fizeram surgir oportunidades adicionais de aprendizagem sobre aspetos fundamentais da divisão e para o desenvolvimento de estratégias mais sofisticadas.
ABSTRACT The goals for the present study are the understanding of students’ proficiency on the division operation, and how division teaching and learning process can be developed with comprehension and incentivizing the use of more sophisticated resolution strategies. For this purpose, the following questions were put forth: (1) What are the strategies used by students in division problem resolution? (2) What knowledge and what difficulties they have regarding the big ideas for division? (3) What role can the mental computation strategies development play? (4) Will teacher-student and inter-student interaction contribute to the understanding of the big ideas for division, as well as to the development of more sophisticated problem solving strategies? This research is framed within the interpretative paradigm and developed under a qualitative methodology in the form of case study. For data collection purposes, a sequence of 7 division tasks was developed in a 4th grade class throughout 2015-2016. The data were collected over two student pairs, relying on diverse techniques. The study results show that, at an early stage, the most common division strategy consisted on building procedures, although the overall preferred approaches were alternative algorithms. The only big idea for division that both subject pairs have shown some proficiency was in the identification of the division operation in partitive and quotative situations. Subjects showed difficulties in identifying relationships between partitive and quotative situations, in the use of arrays, in the use of the reverse relationship between multiplication and division, and in the understanding of the influence of the remainder. Mental computation was present in nearly all the developed strategies and generally used in connection with estimation and trial and error. As for the interactions’ contribution, the results show they allowed additional learning opportunities regarding the big ideas for division as for the development of more sophisticated division strategies.
ABSTRACT The goals for the present study are the understanding of students’ proficiency on the division operation, and how division teaching and learning process can be developed with comprehension and incentivizing the use of more sophisticated resolution strategies. For this purpose, the following questions were put forth: (1) What are the strategies used by students in division problem resolution? (2) What knowledge and what difficulties they have regarding the big ideas for division? (3) What role can the mental computation strategies development play? (4) Will teacher-student and inter-student interaction contribute to the understanding of the big ideas for division, as well as to the development of more sophisticated problem solving strategies? This research is framed within the interpretative paradigm and developed under a qualitative methodology in the form of case study. For data collection purposes, a sequence of 7 division tasks was developed in a 4th grade class throughout 2015-2016. The data were collected over two student pairs, relying on diverse techniques. The study results show that, at an early stage, the most common division strategy consisted on building procedures, although the overall preferred approaches were alternative algorithms. The only big idea for division that both subject pairs have shown some proficiency was in the identification of the division operation in partitive and quotative situations. Subjects showed difficulties in identifying relationships between partitive and quotative situations, in the use of arrays, in the use of the reverse relationship between multiplication and division, and in the understanding of the influence of the remainder. Mental computation was present in nearly all the developed strategies and generally used in connection with estimation and trial and error. As for the interactions’ contribution, the results show they allowed additional learning opportunities regarding the big ideas for division as for the development of more sophisticated division strategies.
Description
Dissertação apresentada à Escola Superior de Educação de Lisboa para a obtenção de grau de mestre em Educação Matemática na Educação Pré-Escolar e nos 1º e 2º Ciclos do Ensino Básico
Keywords
Conceito de divisão Sentido do número Ideias fundamentais da divisão Estratégias de cálculo Interações Compreensão. Division concept Number sense Big ideas for division Calculation strategies Interaction Understanding
Citation
Publisher
Instituto Politécnico de Lisboa, Escola Superior de Educação de Lisboa