Investigation and Visual Explanation in Dynamic Geometry Environment

摘要

Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra software, can be used to offer insight and support understanding of geometry problem solving and proofs through investigation and experimentation. Our case studies show in particular how prospective teachers of mathematics deal with difficult geometry problems, designated initially to mathematically gifted students for competition, using investigation in GeoGebra. We attempt to reveal the prospective teachers' consideration systematically when they are solving a geometric problem. The prepared visual explanation and visual proof steps serve as clues or scaffolding to facilitate geometric problem solving, and they can be useful also for mathematics teachers in preparing their students for mathematics competitions.