Volume I , issue 1 ( 1998 ) | back |

Selected chapters from algebra, I | 1$-$22 |

**Abstract**

The aim of this publication (this paper together with several its continuations) is to present algebra as a branch of mathematics treating the contents close to the usual teaching matter. The whole exposition presupposes not a large frame of knowledge: operations with integers and fractions, square roots, removing of parentheses and other transformations of literal terms, properties of inequalities. The exposition clusters round a number of main themes: ``Number'', ``Polynomial'', ``Set'', each of which is treated in a series of chapters listed in Preface.

**Keywords:** Irrational numbers, square roots, prime factorization.

**MSC Subject Classification:** 00A35

Explorations and discoveries in the classroom | 23$-$30 |

**Abstract**

One way of introducing youngsters to independent study is to get them involved in work on projects. The aim of this paper is to describe problems selected for five projects on topics from geometry. The first three projects are designed for 10--12 year old pupils, and the remaining projects for youngsters aged 13--14.

**Keywords:** Polyhedra with congruent euqilateral faces, nets of tetrahedra
(cubes), geomatrical patterns, centre of gravity

**MSC Subject Classification:** 00A35

Schematic learning of the addition and multiplication tables---sticks as concrete manipulatives | 31$-$51 |

**Abstract**

The numbers 1, 2, \dots, 20 are represented in the form of arrangements of horizontal and vertical lines and, when materialized, these lines are replaced by flat, longitudinal, rectangular sticks each having two sides dyed in two different colors. Sharp individuality of these arrangements is excellent for quick recognition of the numbers they represent. The way of arranging emphasizes the relation of the numbers 1, 2, \dots, 10 to five and ten and this ``ten fingers'' model is basic, both conceptually and operationally, for our approach to schematic learning of the arithmetic tables. In case of addition and subtraction, the chosen structures of the arrangements reflect clearly ``crossings the five and ten lines'', serving efficently as illustrations (and explanations) of these methods. The suggested designs of pictured products $m\times n$ are easily seen as $m$ groups of $n$ sticks and, in the same time, as groups of tens and ones. Wall maps of these designs might be used in the class, letting the pupil have them to fall back on and so helping him/her form gradually a store of mental images related to the multiplication table. The use of space holders is also suggested to help the child compose the symbolic codes which immediately follow manipulative activities. Thus, a one-to-one correspondence between manipulative, reflective and symbolic operations is established, what also makes them connected in a child's mind.

**Keywords:** Addition and multiplication tables

**MSC Subject Classification:** 00A35

Improper integral | 53$-$58 |

**Abstract**

In the following we shall show how to extend the class of Riemann integrable functions with the class of functions integrable in the improper sense. The extension is made in such a way that the same procedure can be applied to the class of Lebesgue integrable functions.

**Keywords:** Riemann integral, improper integral, Lebesgue integral

**MSC Subject Classification:** 00A35

The 8th International Congress on Mathematical Education | 59$-$68 |

**Abstract**

This article is an experts' report on the 8th International Congress on Mathematical Education (ICME-8)---Sevilla (Spain), July 14--21, 1996. A short historical survey is followed by a detailed review of this Congress. The final part of the article is dedicated to some selected topics, concerning the mathematics teaching and learning, which are, according to the authors' view, the most important for further development: scientific research; increased interest in the teaching of mathematics in general education; computerization of the educational process; internationalisation of the didactic of teaching of mathematics; education of teachers of mathematics; curriculum and its improvement; studies in humanistic sciences and the necessity of nonformal presentation of mathematics.

**MSC Subject Classification:** 00A35