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Advisor(s)
Abstract(s)
Este estudo tem como objetivo compreender como tarefas de resolução de problemas com sequĂȘncias contribuem para o desenvolvimento do raciocĂnio dos alunos. A investigação baseia-se numa metodologia qualitativa de carĂĄter interpretativo com a realização de uma experiĂȘncia de ensino, a partir da qual se elaboram quatro casos. Esta foi realizada numa turma do 2.Âș ano de escolaridade de uma escola pĂșblica, no ano letivo 2015/2016, onde a investigadora assume, simultaneamente, o papel de professora. O estudo incidiu em quatro pares de alunos da turma. Os mĂ©todos de recolha de dados foram a observação participante com gravação ĂĄudio e vĂdeo e a recolha documental.
Foram apresentadas oito tarefas Ă turma. Cada par do estudo realizou-as com empenho e dedicação. Naturalmente, uns manifestaram mais confiança na realização das atividades propostas do que outros. Foi percetĂvel a utilização de diferentes estratĂ©gias, tendo-se verificado que a representação numĂ©rica Ă© mais frequentemente adotada pelos alunos que revelam menor dificuldade. Os outros alunos recorrem preferencialmente Ă representação pictĂłrica.
As tarefas que se baseiam na exploração de padrĂ”es permitem aos alunos um maior envolvimento nas atividades de matemĂĄtica e fomentam um raciocĂnio organizado, assente na generalização e na argumentação, facilitando a melhoraria da sua capacidade para resolver situaçÔes problemĂĄticas, o desenvolvimento do seu pensamento algĂ©brico e contribuem para a progressĂŁo de competĂȘncias noutras ĂĄreas. A partilha que se verifica na realização deste tipo de tarefas Ă© crucial para o desenvolvimento do raciocĂnio flexĂvel, promovendo a explicitação e consequente compreensĂŁo do seu pensamento.
ABSTRACT The objective of this study is to understand how problem solving tasks with sequences contribute to studentsâ reasoning development. The research is based on a qualitative methodology of interpretative nature. A teaching experiment was carried in a 2nd grade classroom, on a public school, in the school year of 2015/2016, and the researcher assumed, simultaneously, the role of the teacher. The study focused on four pairs of students of the class. The data collection methods were the participant observation with audio and video recording and the writing documents with studentsâ work. Eight tasks were presented to the class. Eachpair made these tasks with commitment and dedication. Naturally, when made proposed activities, some students were more confidents than others. The use of different strategies was observed and it was verified that the numerical representation was the most frequent strategy adopted by students that present more performance difficulties, while, the other students used preferably the pictorial representation. The tasks that are based on the pattern exploration allow students to experiment a greater involvement in the mathematical activities and promote the organized reasoning, grounded on the generalization and on the argumentation, facilitating the improvement in their problem solving skills, the development of the algebraic thinking and contribute to the progression of skills in other areas. The sharing observed in carrying out this type of tasks is crucial to the development of flexible reasoning, endorsing the explicitation and consequent understanding of their thinking.
ABSTRACT The objective of this study is to understand how problem solving tasks with sequences contribute to studentsâ reasoning development. The research is based on a qualitative methodology of interpretative nature. A teaching experiment was carried in a 2nd grade classroom, on a public school, in the school year of 2015/2016, and the researcher assumed, simultaneously, the role of the teacher. The study focused on four pairs of students of the class. The data collection methods were the participant observation with audio and video recording and the writing documents with studentsâ work. Eight tasks were presented to the class. Eachpair made these tasks with commitment and dedication. Naturally, when made proposed activities, some students were more confidents than others. The use of different strategies was observed and it was verified that the numerical representation was the most frequent strategy adopted by students that present more performance difficulties, while, the other students used preferably the pictorial representation. The tasks that are based on the pattern exploration allow students to experiment a greater involvement in the mathematical activities and promote the organized reasoning, grounded on the generalization and on the argumentation, facilitating the improvement in their problem solving skills, the development of the algebraic thinking and contribute to the progression of skills in other areas. The sharing observed in carrying out this type of tasks is crucial to the development of flexible reasoning, endorsing the explicitation and consequent understanding of their thinking.
Description
Dissertação apresentada Ă Escola Superior de Educação de Lisboa para obtenção do grau de Mestre em Educação MatemĂĄtica na Educação PrĂ©-escolar e nos 1Âș e 2Âș Ciclos do Ensino BĂĄsico
Keywords
Pensamento algĂ©brico PadrĂ”es Regularidades SequĂȘncias RaciocĂnio. Algebraic thinking Patterns Regularities Sequences Reasoning