Volume II , issue 1 ( 1999 ) back
 Selected chapters from algebra, II 1$-$30 I. R. Shafarevich

Abstract

This paper is the second part of the publication Selected chapters of algebra'', the first part being published in the previous volume of the Teaching of Mathematics, Vol\. I (1998), 1--22.

Keywords: Polynomial, multiple roots and derivatives, binomial formula, Bernoulli's numbers.

MSC Subject Classification: 00A35

 Dante and the Humanities 31$-$40 Jordan Tabov, John Muirhead and Albena Vassileva

Abstract

A course for interdisciplinary and integrated education dealing with Dante and his world is described and in particular the calculation of the birth and death dates of one of his ancestors using computer technology. Astronomy, mathematics, history, and literature (including the difficulties of translating Dante) were highlighted in teaching. The participants were students of the 119th High School in Sofia, Bulgaria. A brief review is made of the problems and questions relevant to this sort of education and especially those involved when teaching mathematics and the humanitites together. A detailed explanation is given of the problems, aims, and focus of the course. Also included is a description of the organization of the work, the content of the course, and the personal impressions of the authors. Finally, it is suggested that the dates normally presented by editors of Dante's {ıt Divine Comedy} may be incorrect.

Keywords: Calculations of historical dates, Dante and his Cacciaguida.

MSC Subject Classification: 00A35

 A broader way through themas of elementary school mathematics, I 41$-$58 Milosav M. Marjanović

Abstract

As a basis for treatment of elementary school mathematical themas, a phenomenological scheme representing concepts as three component entities is given. Three related components: class of examples, mental image and name, serve very well as a piece of general language used in subject analysis. With regard to iconic representation of concepts, leaf'' used in that representation is considered as being a premodel of geometric plane. To underline that idea and hence, to avoid some often encountered discrepancies, the following rule which governs such representation is formulated: two icons occupying different places are different. At the end, the first topic Sets and Counting'' is sketched, setting forth the way how the meaning of words set'' and element'' can be assimilated at the initial stage.

Keywords: Schematic representation of concepts, iconic and syntactic environments, sets and counting.

MSC Subject Classification: 00A35

 Conceptual tasks in mathematics education 59$-$64 Djordje Kadijević Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11001 Belgrade, p.p. 367, Yugoslavia,

Abstract

The article examines conceptual tasks in both mathematics teaching and research in mathematics education. It presents a number of conceptual task types and suggests several research directions that may be pursued in years to come.

Keywords: Problem selecting, conceptual tasks in teaching.

MSC Subject Classification: 00A35