Banca de DEFESA: IZAIAS DUARTE DA SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : IZAIAS DUARTE DA SILVA
DATE: 29/09/2026
TIME: 09:30
LOCAL: Remoto
TITLE:

The Concept of Distance in Different Metrics: A Proposal for an Inquiry-Based Teaching Sequence Using GeoGebra for Teaching Geometric Loci.

KEY WORDS:

Distance, Loci, Metrics, GeoGebra, Didactic sequence.

PAGES: 203
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The notion of distance is a fundamental concept in the study of different geometric objects and can be understood beyond its usual association with the Euclidean metric. This dissertation aims to develop a proposal for an investigative didactic sequence for high school that explores the notion of distance under different metrics and their influence on the representation of geometric loci. To provide the mathematical foundation for this proposal, concepts related to vector spaces, inner products, normed spaces, and metric spaces are presented, with particular emphasis on the Euclidean, sum, and maximum metrics. The representations of the circle, perpendicular bisector, ellipse, and hyperbola under these metrics are also investigated, highlighting the relationship between the way distances are measured and the resulting geometric representations. Based on this foundation, a didactic sequence consisting of eight activities is proposed, organized according to an investigative approach and aligned with the guidelines of the Brazilian National Common Core Curriculum (BNCC). The sequence begins with situations involving the movements of chess pieces in Polypad and on square grids, proceeds to the comparison of metrics in the Cartesian plane, and culminates in the investigation of geometric loci with the aid of GeoGebra. The activities are structured to foster exploration, comparison, conjecture formulation, and the systematization of the mathematical relationships involved. The didactic sequence is a proposal and was not implemented in a classroom setting. It is expected that the proposal may serve as a supporting resource for teachers interested in addressing different notions of distance and exploring geometric loci from an investigative perspective in high school.

COMMITTEE MEMBERS:
Presidente - 1690694 - PAULO ROBERTO FERREIRA DOS SANTOS SILVA
Interno - 1137010 - ESTEBAN PEREIRA DA SILVA
Externo à Instituição - MARCELO PEDRO DOS SANTOS - UFRPE