Volume V , issue 1 ( 2002 ) back
 Selected chapters from algebra, VII. Power series. 1$-$36 I. R. Shafarevich

Abstract

This paper is the seventh (and last) part of the publication Selected chapters from algebra'', the first six having been published in previous issues of the Teaching of Mathematics, Vol\. I (1998), 1--22, Vol\. II, 1 (1999), 1--30, Vol\. II, 2 (1999), 65--80, Vol\. III, 1 (2000), 15--40, Vol\. III, 2 (2000), 63--82, Vol\. IV, 1 (2001), 1--34 and Vol\. IV, 2 (2001), 71--104.

Keywords: Generating functions, Gauss polynomials, reciprocal polynomial, power series, Catalan's numbers, partition of a number, pentagonal numbers, Euler's pentagonal theorem, Bernoulli's numbers.

MSC Subject Classification: 00A35

 Looking at function concept through interactive animations 37$-$45 Martti E. Pesonen, Lenni Haapasalo and Hanna Lehtola

Abstract

If we agree that the main goal of mathematics education is to develop both procedural and conceptual knowledge and to make links between the two, an important research domain is the analysis of appropriate pedagogical solutions achieving this goal at the university level. This paper presents CAL activities for enhancing university freshmen's understanding of the function concept, and summarizes some outcomes of these activities concerning these knowledge types.

Keywords: Procedural and conceptual knowledge, CAL activities, function concept.

MSC Subject Classification: 00A35

 A broader way through themas of elementary school mathematics, IV 47$-$55 Milosav M. Marjanović

Abstract

Continuing with the didactical analysis of main topics of school arithmetic, first we cover the technique of using place holders as an indispensable device for realization of aims and objectives present in the contemporary process of learning and teaching arithmetic. To ensure the enforcement of correct responses and clear goals of calculation, we insist on the function of these graphical signs as being holders of blank spaces (and it means that a numerical value should never be assigned to such signs). Though an ongoing idea of early algebra'' has not yet got its clear contours, it puts forward a more extensive use of numerical expressions in the elaboration of arithmetical topics. In this frame, we consider meaning-based equating of different numerical expressions and establishing of the main rules of arithmetic on that same base. The manner of expressing these rules is of three kinds: procedural (example by example), rhetoric (in words) and symbolic (using letters in the role of variables). The order in which these three manners have just been mentioned is the natural one to be followed in school practice. The procedural manner is also one which is inevitably connected with the use of place holder technique and we treat it here with scrupulous attention to detail.

Keywords: Place holders, manners of expressing arithmetical rules.

MSC Subject Classification: 00A35

 Judita Cofman (1936--2001), Obituary 57 Mileva Prvanović

MSC Subject Classification: 00A35