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 geometría a pesar de ser considerada un tema de gran importancia sigue siendo, sin embargo, un tópico en el cual los estudiantes muestran, todavía, muchas dificultades. En este trabajo, hemos analizado la forma en cómo visualizan y presenta la idea de cuadrado un grupo de estudiantes del sexto grado. Esta investigación ha permitido caracterizar la posición del razonamiento geométrico de cada estudiante teniendo como base los niveles de van Hiele. Los resultados obtenidos permiten concluir que el nivel de razonamiento geométrico de los alumnos es menor de lo deseable y necesario a esta fase de aprendizaje en Geometría. Además, la definición del cuadrado presentada por la mayoría de los estudiantes está basada solamente en la congruencia de los lados. Así ambos resultados muestran que los alumnos tienen dificultades en la jerarquía de las propiedades geométricas, hecho que los autores consideran pertinente para seguir investigando, sea en el campo de las posibles causas, sea en cómo intervenir en el aula, así como la formación inicial y continua de los profesores.
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