Mathematical connections involved in area measurement processes

摘要

The present study seeks to explore the mathematical connections that 13-14-year-old secondary school students establish when solving area tasks. Emphasis is placed on different mathematical objects, and the connections between them, that allow students to successfully solve the tasks. The study follows a mixed methodology using qualitative and quantitative method of analysis. The results show that representations play a key role in solving area tasks, as they condition the use of alternative procedures to the use of formulas. Likewise, the properties involved in area measurement processes may condition the use of geometric procedures, such as surface decomposition and reorganisation. Finally, results show that to accurately carry out area measurement processes, it is necessary to bring different mathematical objects into play simultaneously. If these connections between mathematical objects do not occur, there is a risk of using the formulas in a mechanical way.