2026-10-212026-10-212026-03-26SILVA, Vitor Vasconcelos. Área e volume de uma esfera: experimentação matemática com recursos manipuláveis e digitais. Orientador: Fábio José da Costa Alves. 2026. 131 f. Dissertação (Mestrado Profissional em Ensino de Matemática) - Centro de Ciências Sociais e Educação, Universidade do Estado do Pará, Belém, 2026.https://portaldaposgraduacao.uepa.br/handle/riuepa/372AbertoVolume da esferaSequência de atividadeSoftware geogebraSólidos geométricos de revoluçãoGeometria espacialVolume of the sphereActivity sequenceGeogebra softwareGeometric solids of revolutionSpatial geometryDissertaçãoCiências HumanasThis research investigated an approach to teaching the calculation of the area and volume of a sphere, based on Rabardel's (1995) Instrumentation Theory, which guided the construction of the activities, and Duval's (2012) Theory of Semiotic Representation Registers. To this end, a sequence of problem-solving activities was applied, integrating manipulable materials and digital resources, such as the GeoGebra software. The concepts of area and volume of a sphere, essential in the high school mathematics curriculum, were explored with the aim of promoting geometric understanding and the development of spatial and visualization skills. The experimentation was structured in four main stages: (1) reflection on the elements that compose the sphere, through the manipulation of physical objects; (2) exploration of the spatial meaning of the sphere's volume with the support of concrete materials; (3) construction of a sphere in GeoGebra, stimulating creativity and dynamic visualization; (4) construction of the formula for the volume of a sphere by the students; and (5) deduction of the formula for the surface area of the sphere by the students. The data analysis was conducted using a qualitative approach, considering the students' interactions with the learning tools. Written records, audio, and images were used as sources of evidence. Duval's (2012) Theory of Registers allowed for the identification of behavioral patterns, conversion strategies between registers, and levels of understanding of the geometric concepts addressed during the treatments. The results offered a broad and detailed view of the learning process, highlighting the role of artifacts as cognitive mediators and the importance of the multiplicity of representations in the construction of mathematical knowledge.PPGEM - Metodologia para ensino de matemática no nível médio