Strategies for determining the area of an irregular surface in the 2nd Cycle of Basic Education

Abstract

Learning to measure areas is strongly characterised in primary education by the approach to plane and regular geometric figures and by the introduction of formulae for calculating them. With this problem in mind, the aim was to analyse the strategies students use to measure the area of an irregular surface, such as the leaf of a tree. The study was carried out in a 6th grade class in a school in the municipality of Loulé. In accordance with the defined objective, a qualitative methodology was used to conduct the study, encompassing methodological procedures close to those of action research. The data collection instruments were: (i) direct observations, with audio and photographic records, and (ii) documentary analysis of the students' productions. By analysing the results obtained, it was possible to identify five strategies used by the students to measure the area of an irregular surface: (i) subdivide; (ii) quantify; (iii) structure spatially; (iv) frame regular geometric figures; and (v) apply formulas. The results of each group showed that the more strategies used to measure the area of an irregular surface, the greater the complexity of the reasoning used to make this measurement.