INTRODUCTION
Several authors have been stressing the need for a deeper understanding of the
mathematical activities in which young people engage, particularly in technologically
rich environments that can be considered extensions of the school curriculum (Barbeau
& Taylor, 2009). The University of Algarve has been promoting a web-based
mathematical problem solving competition, addressed to 7th and 8th graders (12-13
years-old), named SUB14®. In this beyond-school and web-based competition there is
a mathematical problem published every two weeks that the participants must solve
individually or in small teams. Students have to send their solutions electronically,
using attachments if they wish so, but those must include a complete and detailed
explanation of their reasoning and solving process. Previous results indicate that the
SUB14’s participants often show sophisticated technological fluency when solving the
competition’s problems (Jacinto, Carreira, & Amado, 2011), although we know that
putting such abilities into practice in the classroom is still rare for most of them.
This study extends the research on understanding mathematical problem solving in a
beyond-school technologically rich environment, by characterizing how SUB14’s
participants reveal their technological fluency and their mathematical competence.
Moreover, we aim at understanding how the use of a technological tool, like
GeoGebra, supports and shapes four different approaches to a geometry problem.