HOW 8TH-GRADE STUDENTS CONSTRUCT THE CONCEPT OF AREA: FIGURAL APPREHENSIONS THROUGH THE USE OF MANIPULATIVE MATERIALS

Abstract

This research aimed to investigate the possibilities of figural apprehensions mobilized in the manipulation of figures during the resolution of a geometric problem by 23 eighth-grade students. Grounded in Duval’s theory on apprehensions and studies on problem-solving with manipulable materials, the research employed a qualitative and interventional methodology, over three sessions, participants’ strategies and comments were observed, using task protocols, observations, and video and audio recordings for data collection. The results highlighted the development of heuristic potential in the exploration of figures and the emergence of perceptual, discursive, sequential, and operative apprehensions. The integration of manipulable materials facilitated the comprehension and development of apprehensions, promoting engagement and creativity. However, the study identified challenges related to the development of figural apprehensions, such as some students’ difficulty in interpreting the problem and correctly applying mathematical concepts.