\input zb-basic \input zb-matheduc \iteman{ZMATH 2013e.00340} \itemau{Mason, John; Oliveira, H\'elia; Boavida, Ana Maria} \itemti{Reasoning reasonably in mathematics.} \itemso{Quadrante 21, No. 2, 165-195 (2012).} \itemab Summary: Two tasks designed to encourage mathematical reasoning without any need for calculations were presented to students with the aim of seeking evidence of different forms of attention [{\it J. Mason}, Structure of attention in the learning of mathematics", in: J. Novotn\a (ed.), Proceedings of the international symposium on elementary mathematics teaching. Prague: Charles University. 9--16 (2003)], and using these to learn about the tasks and about students' power to reason reasonably' in mathematics. The first task that involves locating a secret place using an applet was solved by two pairs of grade 4 Portuguese students. The second task, involving the structure of magic squares, was proposed to two classes of Portuguese students, aged 12--13. The interactions between pairs of students and teacher probes were taped and transcribed, and, in the second one, students' written responses were collected as well. In both cases, the data were analysed using the fivefold framework of microstructure of attention. The first case gives evidence that young students can reason reasonably' but that there are delicate shifts which may require sensitivity on the part of the teacher to help students progress. In the second case, the data analysis shows that these students displayed the power to reason reasonably' in mathematics, and that difficulties can be accounted for in terms of not only what was being attended to, but the form of that attention. \itemrv{~} \itemab Resumo: Foram propostas duas tarefas a alunos portugueses do ensino b\'asico para os encorajar a raciocinar matematicamente sem o recurso a c\'alculos, com o objetivo de procurar evid\^encias sobre diferentes formas de aten\c c\~ao [{\it J. Mason}, Structure of attention in the learning of mathematics", in: J. Novotn\a (ed.), Proceedings of the international symposium on elementary mathematics teaching. Prague: Charles University. 9--16 (2003)] e de usar essas evid\^encias para refletir sobre as tarefas e sobre a capacidade dos alunos raciocinarem com razoabilidade" em matem\'atica. A primeira tarefa, centrada na localiza\c c\~ao de um lugar secreto usando uma applet, foi resolvida por dois pares de alunos do $4.^{\text{o}}$ ano de escolaridade. A segunda, envolvendo a estrutura de quadrados m\'agicos, foi proposta a duas turmas do $7.^{\text{o}}$ ano de escolaridade. Em qualquer dos casos, procedeu-se \a grava\c c\~ao e transcri\c c\~ao das intera\c c\~oes entre alunos e professor e na segunda tarefa recolheram-se, ainda, as resolu\c c\~oes escritas dos alunos. Os dados obtidos foram analisados usando um modelo composto por cinco formas ou microestruturas de aten\c c\~ao. No caso da primeira tarefa, evidencia-se que as crian\c cas s\~ao capazes de raciocinar com razoabilidade" mas que o seu progresso depende de mudan\c cas subtis que requerem sensibilidade por parte do professor. A an\'alise de dados relativos \a segunda tarefa, revela, igualmente, que os alunos mostram poder para raciocinar `com razoabilidade". Revela, ainda, que as suas dificuldades podem ser explicadas n\~ao s\'o em termos daquilo que \'e o objeto da aten\c c\~ao mas tamb\'em da forma desta aten\c c\~ao. \itemrv{~} \itemcc{E53 D53 A23} \itemut{mathematical reasoning; structures of attention; mathematical tasks; basic education} \itemli{} \end