The authors focus on the problem of visualization of three-dimensional constructions and the problem of formation of skills of high school students to visualize mathematical material by means of information technology. This visualization is especially helpful in the operation with locus. The concept of locus is one of the basic in mathematics education, since it introduces some common geometric objects. The locus problem in space in most cases begins with the formulation of a hypothesis about the form of the figure. This hypothesis needs to be tested on the set of test (and limit) cases. At this stage such means of visualization as dynamic mathematics software (DMS) become useful. The use of them helps to represent and then determine the form of the locus. Among the variety of dynamic mathematics software just Cabri3D and GeoGebra 5.0 have the opportunity to visualize the locus through the use of tools Trajectory and Trace. Examples of solving locus problems in three-dimensional space, algorithms of construction with the use of these software in classes of different profiles in academic, specialized and in-depth levels are made. Methodological comments are provided regarding the establishment and analysis of dynamic structures. It is noted that the solution of locus problems in space lies beyond the curriculum of the standard level, but the use of such visualization in the study of the basic concepts of the course is appropriate and effective. In addition the work with software with the foreign-language interface is helpful to students of classes of philological profile. It is a means of expanding vocabulary. For students who study mathematics at higher level, the ability to see an analogy (in some cases to solve a similar problem), "coming out" from the plane into space is useful. It indicates a high level of mathematical intuition. The described solution not only facilitate the perception of complex stereometrical material, but also enrich the arsenal of students with empirical method of solving locus problems. Authors believe that it is important in the view of the computerization of society and its requests regarding professionals who possess the skills to model problems, visualize the solutions and the skills to analyze tasks, including those that are reduced to stereometric locus problems.

Авторами акцентується увага на проблемі візуалізації тривимірних побудов і проблемі формування умінь у учнів старшої школи візуалізувати математичний матеріал засобами інформаційних технологій. Зазначено програми динамічної математики Cabri3D і GeoGebra 5.0, де сьогодні є можливою така візуалізація через використання інструментів Траекторія і Слід. Наводяться приклади розв’язування задач на побудову геометричних місць точок у тривимірному просторі, алгоритми побудов із використанням цих програм в класах різних профілів на академічному, профільному і поглибленому рівнях. Надаються методичні коментарі щодо створення і аналізу динамічних конструкцій.