ON THE ESSENCE, THE PLACE, THE PART AND CHARACTER OF THE TASKS WITH PARAMETERS IN THE GEOMETRY COURSES OF THE INSTITUTIONS OF GENERAL SECONDARY EDUCATION

Abstract

The so-called tasks with parameters for a long time now have become an integral part as of the every to some extent profound course of algebra or of algebra and the beginnings of cultures at the institutions of general secondary education, as of the corresponding tasks of the State Final Attestation in Mathematics and the External independent assessment in mathematics. And it isn’t accidental because in the most often cases the solution of the task with a parameter turns for the student into a small investigation by his own. The realization of such investigation favors the formation of the creative practical-oriented personality. Simultaneously we must state that, despite of the existence of a lot of the high scientific and methodical level created corresponding training books, it is difficult just now to find in the methodical literature the clear answers to the natural questions of what is meant on the whole by the task with parameter (or with parameters) and its solution. At the same time, in the courses of geometry of the institutions of general secondary education to the tasks with parameters it is given next to nothing consideration. But in fact such tasks in the courses are present, their importance for the proper construction of the courses can be exaggerated. In the paper the problems of what must be understand by the task with the parameter or with the parameters and by its solution are analyzed. The essence, the part and the place of the tasks with parameters in the geometry courses of institutions of general secondary education are elucidated. Euclidean geometry as an axiomatic theory investigates the sets that in their overwhelming majority represent by themselves the mathematical abstructions of the spatial forms of the surrounding, some relations between such set and quantities that characterize such sets and relations. In the contrast to the courses of algebra, in the geometrical courses the part of parameters may be played by all of the three mentioned components. Geometrical figures can change by the size and by the form. Changing by the size bring us to the concept of the scalar quantity. Changing by the form are considered in the tasks of paving and, for example, in the tasks of finding the amount and the types of symmetries of geometrical figure in dependence of its form. The part of the parameter-relation can be played by different variants of mutual displacement of the given figures in Euclidean plane or in Euclidean space. According to their content, different geometrical tasks with parameters are considered in the work. The task of the existence of geometrical figures, the tasks, conserning the character of some geometrical places of points, the tasks of tracing with the help of a compass and a ruler are among them.