Developing the meaning of volume and deriving the volume of hemispheres with dynamic geometry

ABSTRACT

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students’ sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving the volume of a hemisphere with minimal algebra but simple trigonometry. This method aims to support students’ geometrical reasoning through comparing the volume of different three-dimensional shapes and analysing their cross sections two-dimensionally, thus drawing on the concept of area. We highlight the affordances of the designed DGE sketches for fostering a dynamic conception of volume.

KEYWORD:

• Technology-enhanced learning
• dynamic geometry
• geometric reasoning
• classroom orchestration
• area and volume

Disclosure statement

No potential conflict of interest was reported by the authors.