| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 2.89 MB | Adobe PDF |
Advisor(s)
Abstract(s)
A presente investigação tem como objetivo compreender que estratégias de cálculo
mental os alunos do 3.º ano de escolaridade utilizam na resolução de problemas de
multiplicação. Para isso, procurei dar resposta às seguintes questões: i) Será que o
tipo de números usados influencia as estratégias utilizadas pelos alunos, em situações
multiplicativas? ii) Será que os alunos desenvolvem estratégias de cálculo mental
depois de já terem aprendido o algoritmo da multiplicação e se sim, como o fazem? e
iii) Será que a utilização do algoritmo ajuda ou condiciona as estratégias utilizadas
pelos alunos na resolução de problemas de multiplicação?
Esta investigação desenvolveu-se, no ano letivo 2015/2016, numa turma com 20
alunos do 3.º ano de escolaridade, de uma escola pública do concelho da Amadora.
As tarefas foram desenvolvidas na turma no período de outubro a dezembro de 2015.
Tendo em conta os objetivos do estudo, a investigação seguiu uma metodologia de
natureza qualitativa. Os instrumentos de recolha de dados utlizados foram a
observação participante, apoiada pelos registos áudio e vídeo das aulas, incluindo o
trabalho a pares e as discussões e a recolha documental. Foi desenvolvida com os
alunos uma experiência de ensino que incluía três tarefas (com desafios).
Na exploração das tarefas matemáticas foi interessante perceber que o trabalho a
pares permitiu um maior confronto de ideias e uma escolha de procedimentos na
maioria das vezes mais eficazes.
Os resultados deste estudo indicam que os alunos ao longo das tarefas
desenvolveram diversas estratégias de cálculo evoluindo, quase sempre, de um
contexto aditivo para um novo contexto multiplicativo criando estratégias cada vez
mais eficazes. Os alunos associaram os procedimentos multiplicativos à disposição
retangular e foram capazes de aplicar propriedades da multiplicação nos cálculos dos
produtos que tinham de efetuar.
Quando a grandeza do número aumentou constatou-se que a maioria dos pares, que
apresentaram um resultado correto, usou a multiplicação com recurso ao algoritmo,
possivelmente por ser um procedimento mais confiável e simples para os alunos.
O facto de os alunos não conhecerem o algoritmo quando o multiplicador é um número
de dois algarismos, não condicionou a construção dos seus próprios procedimentos
nem a resolução correta do problema.
Abstract The present research aims to understand which mental calculation strategies 3rd grade students use to solve multiplicative problems. To achieve this, I intended to answer the following questions: i) Do the type of numbers used by students influence the strategies they utilize, in multiplicative situations? ii) Do students develop mental calculation strategies after they learned the multiplication algorithm, and if so, how do they do it? and, iii) Does the use of this algorithm benefit or condition the strategies used by students in solving multiplication problems? This research took place in the school year of 2015/2016, in a class with 20 students of the 3rd grade, in a public sector school in the county of Amadora. The tasks occurred in class during the period ranging from October to December 2015. Taking into account the study objects, this research followed a methodology of a qualitative nature. The data collection instruments employed were participant observation, supported by audio and video records taken in class, including pair work and discussions and document gathering. A teaching experience involving three tasks (with challenges) was developed with the students. During exploration of mathematical tasks, it was interesting to realize that pair work allowed for a better idea confrontation and a choice of procedures, which were, most often, more effective. The study’s results indicate that over the course of these tasks students developed several strategies of calculation evolving, usually, from an additive context to a new multiplicative context, creating strategies increasingly more effective. Students associated multiplicative procedures to rectangular arrangement and were able to apply multiplication properties in the calculation of the products they had to effect. As the size of the number increased, it was noticed that most of the pairs, which presented a correct result, used multiplication with the algorithm, possibly because it is a more reliable and simple procedure for the students. The fact that these students aren’t aware of the algorithm composed of two numbers in the multiplier conditions neither the construction of their own procedures nor the correct solving of the problem.
Abstract The present research aims to understand which mental calculation strategies 3rd grade students use to solve multiplicative problems. To achieve this, I intended to answer the following questions: i) Do the type of numbers used by students influence the strategies they utilize, in multiplicative situations? ii) Do students develop mental calculation strategies after they learned the multiplication algorithm, and if so, how do they do it? and, iii) Does the use of this algorithm benefit or condition the strategies used by students in solving multiplication problems? This research took place in the school year of 2015/2016, in a class with 20 students of the 3rd grade, in a public sector school in the county of Amadora. The tasks occurred in class during the period ranging from October to December 2015. Taking into account the study objects, this research followed a methodology of a qualitative nature. The data collection instruments employed were participant observation, supported by audio and video records taken in class, including pair work and discussions and document gathering. A teaching experience involving three tasks (with challenges) was developed with the students. During exploration of mathematical tasks, it was interesting to realize that pair work allowed for a better idea confrontation and a choice of procedures, which were, most often, more effective. The study’s results indicate that over the course of these tasks students developed several strategies of calculation evolving, usually, from an additive context to a new multiplicative context, creating strategies increasingly more effective. Students associated multiplicative procedures to rectangular arrangement and were able to apply multiplication properties in the calculation of the products they had to effect. As the size of the number increased, it was noticed that most of the pairs, which presented a correct result, used multiplication with the algorithm, possibly because it is a more reliable and simple procedure for the students. The fact that these students aren’t aware of the algorithm composed of two numbers in the multiplier conditions neither the construction of their own procedures nor the correct solving of the problem.
Description
Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de Mestre em Educação Matemática na Educação Pré-escolar e nos 1º e 2º Ciclos do Ensino Básico
Keywords
Aprendizagem da multiplicação Estratégias de cálculo Cálculo mental Algoritmo. Learning multiplication Calculation strategies Mental calculation Algorithm