La résolution des problèmes écrits : l’étude auprès d’une élève présentant une dyslexie

In our previous studies, we developed an approach to teaching problem-solving we termed Equilibrated Development that allows students to better understand the quantitative relationships that arise in a mathematical problem and to better choose a solution strategy. We used the method of a teaching experiment to evaluate the applicability of the developed approach to cases of students with dyslexia and to modify it, if necessary, to meet these students’ needs. Our data suggest that: a) the understanding of the mathematical structure of a problem is independent of the student's basic numerical knowledge, and b) there are conditions that allow a dyslexic student to develop mathematical reasoning to solve written problems despite difficulties in reading and writing of numbers and text.

Uma trajetória na aprendizagem dos números racionais através da percentagemA trajectory in the learning of rational numbers enhanced by percentage

Este artigo tem como objetivo indicar os contributos que uma trajetória com um foco inicial na percentagem, que faz emergir de seguida o numeral decimal e posteriormente a fração, traz para a compreensão da natureza relacional dos números racionais. Trata-se de uma investigação baseada em design na modalidade de experiência de ensino na sala de aula. A recolha de dados resultou da observação participante, apoiada num diário de bordo, de gravações áudio e vídeo e da recolha das produções escritas dos alunos. Os resultados revelam que esta abordagem, partindo da percentagem, permite integrar os conhecimentos numéricos prévios intuitivos dos alunos na compreensão dos números racionais e apoia a construção de uma aprendizagem das diferentes representações, de forma interrelacionada, numa perspetiva de desenvolvimento de sentido de número.This article aims to figure out the contributions that a trajectory with an initial focus on percentage which leads to the emergence of decimals and later of fractions brings to the understanding of the relational nature of rational numbers. A classroom teaching experiment was developed as a design based research. Data were collected through participant observation, supported by a logbook, audio- and video-recorded lessons and collecting students’ written productions. The results show that this approach, based on percentage, allows integrating students' previous intuitive numerical knowledge into the understanding of rational numbers and supports the construction of learning of the different representations, in an interrelated way, in a perspective of the development of number sense.