TECHNOLOGY OF CONSTRUCTING OF GUADRATIC EQUATIONS AND SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH PARAMETERS IN A MAPLE-MEDIUM

Abstract

The problem of constructing quadratic equations and systems of equations with parameters using Maple-technology is studied. Today, the "learning tasks of reverse thinking" (V.A. Krutetsky) or simply "inverse problems" (P.M.Erdniev) are increasingly being introduced into the educational process. The tasks of constructing mathematical tasks in advance of a certain type and certain properties are inverse problems that unfold another aspect of the learning situation and thereby create a "surplus of its vision" (M.M. Bakhtin). The solution of inverse problems develops students’ thinking, imagination and other higher mental functions. However, their introduction into the educational process is still insufficient. One of the reasons for this situation is the insufficient number of benefits with a sufficient number of variants of the same type of tasks. Especially it concerns the construction of problems with parameters. Designing in "manual mode" requires significant temporary cognitive, physical and other efforts, carries the risks of allowing technical and computational errors. In the days of the information society and the digital economy, there are all the possibilities to perform the chain of design actions in a certain ICT environment (we have a Maple-environment). It solves the resulted difficulties of construction, creates a new educational and information environment, allows to produce automatically a sufficient number of different versions of the same type of tasks.
Tasks with parameters require creativity from the students, non-standard approaches to the solution. Each task with parameters requires the creation of its own method and algorithm for solving and productive learning. The article is devoted to solving of the above problems.