Area as a geometric magnitude: A study in 6th grade Elementary Education using the geometry software Apprenti Géomètre 2 (Research, Society and Development, 2024)
Understanding the concept of area enables citizens to develop essential skills for practical applications, facilitating planning and informed decision-making in everyday situations, such as calculating the amount of tile needed to cover a bathroom floor or the amount of paint to cover a wall. However, research in mathematics education and learning performance assessments indicate that elementary and high school students face difficulties in grasping this concept. In light of this, the objective of this study is to analyze the procedures and strategies used by 6th-grade elementary students when solving a task that involves comparing the area of flat shapes. This activity was conducted with the support of the geometry software Apprenti Géomètre 2 (AG2). Based on the findings, the study aims to diagnose the main difficulties students encounter with the concept of area and evaluate the impact of this tool on problem-solving related to the topic. To achieve these objectives, a qualitative study was conducted with eight 6th-grade students from a public school in the state of Pernambuco. The results indicated that, although AG2 facilitated the use of strategies such as decomposition, recomposition, superposition, rotation, translation, and reflection to compare areas—allowing students, in some cases, to arrive at correct answers—difficulties in understanding the concept of area persist. It was observed that students struggle to understand that two shapes can have the same area regardless of whether one can be decomposed and recomposed to be compared by superposition.