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Estamos a viver num mundo complexo e com rápidas mudanças no qual será muito difícil sobreviver, sem sólidos conhecimentos e capacidades adequadas. Assim, o professor deve procurar estratégias, dentro e fora da sala de aula, que permitam ir ao encontro dos diferentes modos de pensar dos alunos, confrontando-os com tarefas, com múltiplas resoluções, que os desafiem a ver fora da caixa, os entusiasmem para aprender e os ponham a trabalhar uns com os outros. Por outro lado, há estudos que recomendam que as crianças precisam de se movimentar, pois um corpo ativo incita o cérebro, tornando os alunos mais envolvidos, o que contribui para um melhor desempenho. Neste sentido, a formação de professores, inicial e continuada, deve promover uma visão sobre a natureza da matemática e do seu ensino, que permita aos (futuros) professores ter diferentes experiências de ensino e de aprendizagem, que se espera venham a usar com os seus próprios alunos. Neste contexto, surge a gallery walk (GW) como uma estratégia a contemplar nas práticas de sala de aula, que permite que os alunos, através do trabalho colaborativo, resolvam problemas, apresentem e discutam as suas resoluções em pôsteres, localizados à volta da sala de aula. Neste artigo, discute-se um estudo de natureza qualitativa e interpretativa, numa abordagem exploratória, desenvolvido no âmbito da formação inicial de professores do 1.º e 2.º ciclos do ensino básico em Portugal (6-12 anos), no qual se pretende identificar as estratégias utilizadas pelos alunos na resolução de problemas com múltiplas resoluções, utilizando uma GW, bem como caracterizar sua reação durante o envolvimento nessa estratégia. Os resultados permitiram identificar as estratégias usadas e verificar o potencial da GW no envolvimento nas resoluções e discussões, que se mostrou mais eficaz do que nas discussões mais tradicionais, permitindo aumentar o repertório de processos de resolução de cada aluno.

The aim of this paper is to share part of an ongoing study in which we are interested in introducing a Gallery Walk (GW) as an instructional strategy to contemplate in the classroom, in the context of preservice teacher training for elementary education (6-12 years old), to promote students' mathematical knowledge and skills, through problem solving abilities. In this study we intend, in particular, to identify the strategies used by students when solving challenging tasks with multiple approaches, using a GW, as well as characterize their reaction during their engagement in the GW as a teaching and learning strategy. A qualitative and interpretive study, with an exploratory approach, was adopted and the collected data included classroom observations and written productions. The results allowed to identify the strategies used by the participants and to verify the potential of the GW in the quality of the written productions and discussions, which proved to be more effective than in more traditional discussions, allowing to increase the repertoire of solving strategies of each student and communication and collaborative skills; it had a positive effect on the participants’ achievements and it was an enjoyable and rewarding experience for all of them.

Para que os alunos sejam competentes em álgebra, devem compreender os conceitos e relações muito para além da manipulação simbólica, o que implica que o seu estudo se inicie nos primeiros anos com o desenvolvimento do pensamento algébrico. Naturalmente, a formação dos futuros professores deve acompanhar esta tendência. Assim, apresenta-se parte de um estudo de natureza qualitativa, no qual se procura caracterizar o pensamento algébrico de futuros professores do ensino básico (3-12 anos) na resolução de tarefas envolvendo padrões figurativos. Os resultados mostraram que os participantes usaram estratégias visuais e analíticas, tendo prevalecido as primeiras, e que as maiores dificuldades surgiram nas questões de generalização distante, frequentemente influenciadas pelo tipo de estratégias usadas.

Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context, known to promote positive attitudes and additional engagement for the learning of mathematics, confronting students with a sequence of real-life tasks, related to a particular mathematical theme. Recently, mobile devices and apps, i.e., MathCityMap, have been recognized as an important resource to facilitate the extension of the classroom to the outdoors. The study reported in this paper intends to identify the principles of design for mobile theme-based math trails (TBT) that result in rich learning experiences in early algebraic thinking. A designed-based research is used, through a qualitative approach, to develop and refine design principles for TBT about Sequences and Patterns. The iterative approach is described by cycles with the intervention of the researchers, pre-service and in-service teachers and students of the targeted school levels. The results are discussed taking into account previous research and data collected along the cycles, conducing to the development of general design principles for TBT tasks.

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This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent and creative, they must be able not only to solve traditional computational problems but also to use models/visual representations when solving all types of mathematical problems, including those in which the visual component is not evident. We developed a qualitative study based on a didactical experience involving 14 future teachers who were attending a Didactics of Mathematics unit course that included a module about problem solving with emphasizes in visual approaches. The main purpose of the study was to identify the strategies used by the future teachers when solving problems with multiple solutions, before and after that module. Data was collected through observation and the written productions of the participants. It was possible to conclude that they tended to privilege analytical approaches before the intervention and, after the teaching experience, they started to value visual approaches, which generated an increase of the productions involving this type of solutions.