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Promover o raciocínio matemático de alunos do 4ºano de escolaridade
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Abstract(s)
O presente relatório surge no âmbito do Mestrado em Educação Pré-Escolar e Ensino do 1.o Ciclo do Ensino Básico (1.o CEB) e tem como temática a promoção do raciocínio matemático em alunos do 4.o ano de escolaridade, recorrendo a práticas de ensino exploratório. Neste sentido, o objetivo da investigação é compreender quais os processos de raciocínio utilizados pelos alunos ao resolverem tarefas geométricas com grau de desafio elevado. Para que este objetivo fosse cumprido, foram desenvolvidas duas questões: (i) Que processos de raciocínio matemático usam os alunos quando resolvem tarefas de geometria com grau de desafio elevado?; (ii) Que dificuldades manifestam os alunos no uso de processos de raciocínio matemático na resolução de tarefas geométricas com grau de desafio elevado?
A fundamentação teórica realça o aprofundamento teórico da temática em estudo, incluindo tópicos tais como: a aprendizagem da geometria e, em particular, no 4.o ano do 1.o CEB; o raciocínio matemático no que respeita à sua caracterização, tipos e processos; o desenvolvimento do raciocínio matemático em sala de aula e, por fim, um tópico referente ao ensino exploratório enquanto promotor do raciocínio matemático dos alunos.
No que respeita à metodologia adotada, o presente estudo enquadra-se no paradigma interpretativo, seguindo uma abordagem qualitativa de investigação-ação. O estudo decorreu numa turma de 4.o ano, sendo os seus participantes dois grupos compostos por quatro alunos cada. Estes foram selecionados considerando o facto de serem bons informantes. Foi construída uma proposta pedagógica constituída por quatro tarefas, com nível de desafio elevado e que incidiram sobre conceitos geométricos, que foram realizadas por toda a turma. Os dados relativos aos participantes do estudo foram recolhidos através da observação participante e da recolha documental, complementada através da gravação áudio, vídeo e de notas de campo. A análise dos dados foi realizada através da análise de conteúdo, nomeadamente, das produções escritas dos alunos, isto é, as respostas de cada grupo ao enunciado das quatro tarefas e das transcrições das discussões coletivas relacionadas com a resolução das tarefas propostas.
A análise dos dados recolhidos permitiu dar contributos de resposta às questões do estudo. No que respeita à mobilização de processos de raciocínio matemático, constatou- se que os alunos nem sempre recorreram a processos de raciocínio matemático para responder às questões enunciadas. Contudo, foi sendo evidente a mobilização de alguns dos processos de raciocínio matemático, nomeadamente dos processos de justificação e generalização o ao longo das tarefas, sobretudo, nas T3 e T4.
Relativamente à segunda questão do estudo, as dificuldades apresentadas pelos alunos foram, numa primeira fase, relativas à exploração de tarefas que se caracterizaram por ter um elevado grau de desafio. No entanto, este aspeto foi mais evidente nas primeiras duas tarefas, o que fez sobressair as dificuldades dos alunos ao nível do registo e exposição oral dos seus raciocínios como forma de justificação das suas respostas.
This report is part of the Master's Degree in Pre-school Education and Primary School Teaching (1.o CEB) and its theme is the promotion of mathematical reasoning in 4th grade students, using exploratory teaching practices. In this sense, the aim of the research is to understand which reasoning processes are used by students when solving geometric tasks with a high level of challenge. In order to fulfill this goal, two questions were developed and are intended to be answered: (i) What mathematical reasoning processes do students use when solving high-challenge geometry tasks? (ii) What difficulties do students manifest in the use of mathematical reasoning processes in solving geometry tasks with a high degree of challenge? The theoretical background highlights the theoretical deepening of the theme under study, including topics such as: the learning of geometry and, in particular, in the 4th grade of Primary School; mathematical reasoning with regard to its characterization, type, and processes; the development of mathematical reasoning in the classroom and, finally, a topic concerning exploratory teaching as a promoter of mathematical reasoning. With regard to the methodology adopted, this study is framed within the interpretative paradigm following a qualitative action-research approach. The study took place in a 4th grade class, and its participants were two groups composed of four students each. These were selected considering the fact that they were good informants and comfortable in the subject of mathematics. A pedagogical proposal consisting of four tasks that focused on geometric concepts was constructed and carried out by the whole class. Data regarding the participants of the study was collected through participant observation and document collection, supplemented, through audio and video recording and field notes. The data analysis was performed through content analysis, namely, the students' written productions, i.e., each group's answers to the statement of the four tasks. The analysis of the data collected allowed answering the study questions. With regard to the mobilization of reasoning processes, it was found that they did not always use mathematical reasoning processes to answer the questions posed. However, a development of their use was evident throughout the tasks, especially in T3 and T4, as a result of a greater habituation to this type of task and to the way of answering. iv In relation to the second question of the study, the difficulties presented by students were, in a first approach, related to the exploration of tasks that are characterized by having a high degree of challenge. However, this aspect was only more evident in the first two tasks, which highlighted the students' difficulties in recording and orally exposing their reasoning as a way to justify their answers.
This report is part of the Master's Degree in Pre-school Education and Primary School Teaching (1.o CEB) and its theme is the promotion of mathematical reasoning in 4th grade students, using exploratory teaching practices. In this sense, the aim of the research is to understand which reasoning processes are used by students when solving geometric tasks with a high level of challenge. In order to fulfill this goal, two questions were developed and are intended to be answered: (i) What mathematical reasoning processes do students use when solving high-challenge geometry tasks? (ii) What difficulties do students manifest in the use of mathematical reasoning processes in solving geometry tasks with a high degree of challenge? The theoretical background highlights the theoretical deepening of the theme under study, including topics such as: the learning of geometry and, in particular, in the 4th grade of Primary School; mathematical reasoning with regard to its characterization, type, and processes; the development of mathematical reasoning in the classroom and, finally, a topic concerning exploratory teaching as a promoter of mathematical reasoning. With regard to the methodology adopted, this study is framed within the interpretative paradigm following a qualitative action-research approach. The study took place in a 4th grade class, and its participants were two groups composed of four students each. These were selected considering the fact that they were good informants and comfortable in the subject of mathematics. A pedagogical proposal consisting of four tasks that focused on geometric concepts was constructed and carried out by the whole class. Data regarding the participants of the study was collected through participant observation and document collection, supplemented, through audio and video recording and field notes. The data analysis was performed through content analysis, namely, the students' written productions, i.e., each group's answers to the statement of the four tasks. The analysis of the data collected allowed answering the study questions. With regard to the mobilization of reasoning processes, it was found that they did not always use mathematical reasoning processes to answer the questions posed. However, a development of their use was evident throughout the tasks, especially in T3 and T4, as a result of a greater habituation to this type of task and to the way of answering. iv In relation to the second question of the study, the difficulties presented by students were, in a first approach, related to the exploration of tasks that are characterized by having a high degree of challenge. However, this aspect was only more evident in the first two tasks, which highlighted the students' difficulties in recording and orally exposing their reasoning as a way to justify their answers.
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Keywords
1.o Ciclo do Ensino Básico Raciocínio matemático Processos de raciocínio matemático Ensino exploratório Mathematical reasoning Mathematical reasoning processes Exploratory teaching