Ana Paula Aires holds a degree in Maths Education at University of Coimbra in 1990, having been a maths teacher of Basic and Secondary Education for one year. Since 1991, joined the University of Trás-os-Montes e Alto Douro (UTAD) and obtained her Master’s degree in Mathematics, University of Coimbra, in 1996. Her PhD in Mathematic Education (specialization in Mathematics Didactics) was obtained from University of Salamanca, in 2006. She was Research member of Research Centre of Mathematics - CM-UTAD - (UTAD), since July 2007 at October 2013, where she was Director of the Mathematics History and Methodology research group from July 2010 to October 2011. She is Research member of Research Centre Didactics and Technology in the Education of Trainers - CIDTFF- (University of Aveiro), since December 2013. She is presently Assistant Professor in the UTAD’s Mathematics Department, where she is responsible for curricular units in the initial and advanced teacher training courses. Her research interests include the lines: Didactics of Mathematics; History of Mathematics teaching; History of Mathematics; Teachers' Professional Practices; ICT in teaching Mathematics and Teacher Training; Theory of numbers.
Universidade de Tras - os - Montes e Alto Douro, UTAD
Helena Campos holds a degree in Pure Mathematics and another one in Mathematical Education, both from Coimbra University. After being a mathematics teacher of Basic and Secondary Education for a few years, in 1995 she joined the Trás-os-Montes e Alto Douro University (UTAD). She obtained a master’s degree in Mathematics Education from Minho University (Braga) in the year 2000. Her PhD in Mathematics, with a Specialisation in Topology and Geometry, was obtained from UNED in Madrid (Spain) in 2008. She was a Research member of The Research Centre of Mathematics - CM-UTAD - (UTAD) from July 2007 to October 2015. Since December 2015 she has been a Research member of the Research Centre of Didactics and Technology in the Education of Trainers at CIDTFF (Aveiro University). She is also an Assistant Professor in the Mathematics Department at UTAD. Her research interests include the fields: Didactics of Mathematics, mainly in the Didactics of Geometry, Dynamic Geometry Environments in Basic and Secondary Education and Mathematical Creativity in Geometric Reasoning Processes; Teaching and learning Mathematics in the first years of school (Pre-School and Basic Education); Teacher Training; and Geometric connections with Theory of numbers.
La géométrie malgré d'être considéré comme un problème majeur reste, cependant, un sujet dans lequel les élèves révèlent encore beaucoup de difficultés. Dans cet article, nous avons analysé un groupe d'étudiants de la 6eme année, sur la façon dont ils voyaient et présentaient la définition de carré. Cette recherche a permis de caractériser la position de chacun des élèves face à son raisonnement géométrique, basé sur les niveaux de van Hiele. Les résultats obtenus permettent de conclure que le niveau de raisonnement géométrique présenté par les étudiants est moins que souhaitable et nécessaire pour les étudiants à ce stade de l'apprentissage de la géométrie. En outre, la définition d'un carré présenté par la plupart des étudiants est basée uniquement sur les compatibilités des côtés correspondants. Ainsi, les deux résultats montrent que les élèves ont des difficultés dans la hiérarchie des propriétés géométriques, fait que les auteurs considèrent pertinent d'étudier plus avant, dans le domaine des causes possibles, à la fois en termes de formes d'intervention dans la salle de classe et dans la formation initiale et continue des enseignants.
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