CHECKING THE EQUIVALENCE OF EXPRESSIONS IN COMPUTER ALGEBRA SYSTEMS – APPLICATION POSSIBILITIES IN MATHEMATICS EDUCATION

In connection with the spread of computer algebra systems (and algebraic calculators), the natural question arises: how to change the requirements and emphases of mathematics syllabuses? One possible domain that might be given more consideration in the future is checking the equivalence of expressions. It plays an important role in solving equations, manipulating expressions, and other domains (be it performed on a computer or by hand). In this paper, we examine some possibilities of integrating checking the equivalence expression in computer algebra systems more fully into the educational process. We present different schemes that describe the teacher's and student's activities in different situations, considering the particular goal, problem setup, student's preparedness, the specifics of the computer algebra system, access to computer algebra systems, etc. The schemes are based on problems of manipulating expressions selected from various areas of college algebra. They include step-by-step (line-by-line) solutions as well as solutions in which computers are used for solving larger blocks in one step. The described variants are titled:-The student writes on paper,-Computer algebra system as a text editor,-Computer algebra system as an assistant in discovering errors,-Computer algebra system as the maker of the next step,-Computer algebra system as a solver,-Computer algebra system as a component of an intelligent tutoring system,-The student as the evaluator of computer algebra system. Such a description of schemes may be beneficial not only to teachers, syllabus developers, textbook authors and the like but also to developers of computer algebra systems. The features expected from computer algebra systems for the realization of these schemes are described. The schemes are primarily designed fo