Abstract:

Determining the locus of points satisfying some nontrivial conditions is usually a demanding problem in geometry. Solving the problem in the paper and pencil environment requires many discrete solutions point by point. Dynamic geometry environment (DGE) allows us to see the path of the moving point by dragging points in the plane according to the given conditions.

In our research, we followed the solution process of a demanding locus problem by different grade university students from two different universities preparing mathematics teachers. The aim of our contribution is to provide some indications of how a DGE (especially using GeoGebra software), can be utilised to give a clue and offer insight to the solution of that type of geometric problem and how it supports investigation and experimentation leading to the final result. Conducted and analysed case studies give an answer to how prospective mathematics teachers deal with a difficult geometric problem on locus of points and which steps of the solution process are most effectively supported by using GeoGebra. To reveal all of the complex picture of the solution process, we used questionnaire, interview, and Hejný's method of atomic analysis, not only for written expressions but also for GeoGebra sheet expressions of the students involved.

From the case studies, we can conclude that DGE is especially preferred and useful in some steps of solving the problem on locus of points, namely, in the exploration and generalisation phase of the process.

Keywords:

Problem solving, dynamic geometry environment, case study, locus of points.