The Intuitive Way to Solve Construction Problems in the Dynamic Geometry Environment

Abstract

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci method, in which the main element of the required object forms as the intersection of two loci, each one obtained by purposely ignoring part of the conditions of the problem. With GeoGebra, the relevant locus may be visualized and detected in trace mode. Using dynamic geometry this way for problem solving replaces the single object by the infinite locus and is similar to the introduction of variables for solving equations in school algebra. This paper presents some examples of how this approach may be realized along with the results of a small-scale experiment with pre-service mathematics teachers.