Main presenter			Co-presenter(s)
Name :	Eno Tonisson		Name:
E-mail:	eno@ut.ee		E-mail:
Institution or Company:	University of Tartu		Name:
Department:	Institute of Computer Science		E-mail:
City:	Tartu		Name:
State/Province:			E-mail:
Country:	Estonia		Name:
Type of presentation:	Lecture :  50 minutes.		E-mail:
Conference strand and number:	ACDCA ,    Number: A42		Schedule:   Room:	Friday, 10h30   1302
Related website:
Title of presentation:	The Correctness, Completeness and Compactness Standards of Computer Algebra Systems and of School Ma
Abstract:
In many cases when solving a school algebra problem (e.g. an equation) using a computer algebra system (e.g. Derive, Maple, Mathematica, MuPAD) we get the answer that is perfectly suitable for both the teacher and the student as well as others. Nevertheless, one may encounter answers having some qualities that are disturbing when used at school, such as the answer being valid on certain conditions only, solving is not brought to an end, the answer containing elements unknown at the specific school level, etc. The qualities can be represented as deficiencies in relation to correctness, completeness and compactness. Based on the smoothing of disturbing qualities, the answers offered by computer algebra systems may conditionally be divided as follows: applicable with the help of extra explanations provided to students; adaptable using the resources of the same computer algebra system; unsuitable. The paper also provides examples of smoothing possibilities. The problems (or rather answers) treated in this paper concern division by zero – from calculating 1/0 to literal equations and inequalities. An analysis of textbooks reveals that the standards vary. There are various conventions, e.g. assume that variables are restricted, check solutions in the end of solving process only, and such like. In this paper the different standards of computer algebra systems and of school mathematics have been compared.