Abstract:

Geometry plays a fundamental role in the development of mathematical thinking, particularly through the study of three-dimensional objects that foster spatial visualization, logical reasoning, and an understanding of structural relationships between shapes. In basic education, the exploration of geometric solids provides valuable opportunities for students to observe, compare, and generalize mathematical properties. However, classroom practices tend to focus mainly on more common solids such as prisms and pyramids, while other polyhedra with significant didactic potential remain largely unexplored. In this context, this study proposes an alternative pedagogical approach to the study of geometric solids, based on the exploration of bipyramids and antiprisms in lower secondary education.

This proposal presents a pedagogical intervention designed for students in the 5th and 6th grades, grounded in an inquiry‑based learning approach that integrates hands‑on activities, the exploration of nets, and the use of digital tools for three‑dimensional visualisation. The learning process is structured through a narrative context in which students assume the role of explorers collaborating with archaeologists in the investigation of unfamiliar geometric solids. This scenario is intended to stimulate curiosity, encourage active participation, and promote meaningful mathematical learning.

Throughout the activities, students observe, construct, and analyse geometric models, explore two-dimensional nets, and compare different polyhedra. The tasks include constructing bipyramids and antiprisms from their corresponding nets, identifying and counting faces, vertices, and edges, and analysing structural regularities that lead to the formulation of mathematical conjectures. Investigating these relationships allows students to identify patterns and develop generalizations, fostering connections between geometric reasoning and the early development of algebraic thinking.

The intervention is organized into three sequential lessons. In the first two lessons, students investigate the properties of polyhedra and the relationships between their structural elements, while the third lesson introduces the concept of volume using unit cubes and contextualized problem-solving tasks. Throughout the process, students are encouraged to formulate hypotheses, test conjectures, and communicate their mathematical reasoning.

The proposed approach highlights the potential of combining hands-on exploration, digital visualization, and narrative contexts to promote meaningful learning in geometry. By introducing less commonly explored solids such as bipyramids and antiprisms, this approach broadens students’ understanding of geometric structures and supports the discovery of mathematical regularities. The study contributes to diversifying geometry teaching practices and provides an example of a pedagogical intervention that can support teachers in fostering mathematical reasoning, communication, and critical thinking among students.

Keywords:

Geometry Education, Polyhedra, Hands-On Activities, Spatial Reasoning.