Background: Several studies have shown that many preservice teachers (PTs) who teach in the early years have a superficial knowledge about repeating patterns (RPs), which affects their knowledge about children’s algebraic thinking. Objective: This article aims to understand PTs’ algebraic thinking and their ability to notice preschoolers algebraic thinking and how these two domains articulate within a teacher education experiment. Design: The study follows a qualitative methodology based on participant observation, complemented by document collection. Setting and participants: The study stems from a teaching experiment carried out in a school module focused on patterns and algebra of a degree in basic education, with two pairs of PTs as participants. Data collection and analysis: The data come from the written productions and discussions between the elements of each pair of PTs within the scope of the tasks proposed in the teacher education course, adopting an original analysis framework. Results: The results reveal that the PTs successfully identify the structure of the RPs and the general position of each term; however, one of the pairs still find difficulties in fully understanding that mathematical object. The pairs attend to relevant aspects of children’s algebraic thinking, although sometimes with limited interpretation. Conclusions: This study highlights the importance of creating opportunities in initial teacher education for PTs to develop their algebraic thinking from an early algebra perspective and to analyse, in this context, the preschoolers’ work.
Background: Mathematical reasoning is fundamental for mathematics learning from the first years of schooling. It is a challenge for students and teachers, so it is relevant to deepen ways to develop this ability with the prospective teachers. Objectives: Identify the challenges in supervised practice with a view to developing students’ mathematical reasoning, seeking to answer the following question: What challenges do prospective teachers face in planning and exploring tasks that promote mathematical reasoning? Design: It is based on a formative experiment and follows an interpretive methodology. Setting and participants: This experiment was conducted during 13 sessions of the curricular unit (CU) Didactics of Mathematics of the 2nd year of the master’s course in Pre-School Education and Teaching of the 1st Cycle of Basic Education, in a class of 25 students. The participants were four students - two pairs in teaching practice- whose selection followed the following criteria: not having any of the researchers as teaching practice supervisors and regularly intervening in class. Data collection and analysis: the data were collected through participant observation of the CU classes, interviews, and document collection. Results: Students face more challenges associated with mathematical reasoning during monitoring phases of the exploration of the tasks and their final discussion. Conclusions: These results point to the need for initial training programs to prioritise activities that support prospective teachers in the understanding of mathematical reasoning processes and that involve them in the planning of tasks and analysing practical exploration that will enhance their development.
ResumoEste artigo tem como propósito compreender o modo como alunos do 2.º ano resolvem problemas. Discute-se a importância da resolução de problemas na aprendizagem da Matemática, o entendimento de problema, as etapas do processo de resolução de problemas e as principais estratégias de resolução A investigação subjacente foi realizada em Portugal, numa turma do 2.º ano de uma escola dos arredores de um meio urbano. A pesquisa seguiu uma metodologia qualitativa e a recolha de dados incluiu observação de aulas da turma do 2.º ano e recolha documental a propósito da resolução de seis problemas. Neste artigo são analisadas as resoluções de um dos alunos da turma, Daniel, caracterizando as estratégias que usa, as dificuldades que manifesta e as etapas de resolução por que passa. Os resultados salientam que usa diferentes estratégias, suportadas por representações icónicas e simbólicas. Manifesta dificuldades relacionadas com a interpretação do problema, a utilização de conteúdos matemáticos e o uso da estratégia trabalhar do fim para o princípio. Nem sempre é possível compreender se Daniel percorreu todas as etapas de resolução de problemas. Palavras-chave: AbstractThis paper aims to understand how 2 nd grade students solve problems. We present an overview about the importance of problem solving in the learning of Mathematics, what is understood as a problem, the phases of problem solving and the main problem-solving strategies. The research was developed in a 2 nd grade class of a school situated in Portugal on the outskirts of a city. The research that underlies this paper follows a qualitative methodology. Data collection was carried out by participant observation in a 2 nd grade class and document collection about students' problem solving. This article analyses Daniel problem-solving that includes: the characterization of his strategies, the difficulties that he reveals and the phases of problem solving that he goes through. The results show that Daniel uses different strategies supported by iconic and symbolic representations. He has some difficulties related with the interpretation of the problem, the use of mathematical content and the use of work backward strategy. It is not always possible to understand if Daniel went through all the phases of problem solving.
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