Volume VII , issue 1 ( 2004 ) | back |

The problem of arrangement of new notions and objects in the school course of mathematics | 1$-$9 |

**Abstract**

The purpose of this article is to invite all those who are interested in the subject, experts and the general public at large, to answer the question: ``is a modernization of the school mathematics curriculum necessary, and if it is, what kind of modernization is to be implemented". We shall deal with subjects like the problems of curriculum's content, the bifurcation of the process during the change of its parameter, fractals and chaos, the position of computational mathematics in the curriculum, and particularly the possibility of laboratory work in mathematics. We think that the most important science, which investigates and establishes principles and methods of teaching mathematics, needs a serious conceptual reconstruction. Particular attention will be paid to a new ``area" of mathematics, the so-called ``mathematics of entrance exams".

**Keywords:** Bifurcation, fractals, chaos, computational mathematics,
laboratory work, entrance exams.

On the psycho-linguistic basis of teaching mathematics in English as a foreign language | 11$-$33 |

**Abstract**

This paper is an attempt of the author to answer the question ``What is the psycho-linguistic basis of teaching Mathematics in English to non-native speakers?" The idea presented is based on Piaget's Theory of Cognitive Development and Chomsky's Extended Standard Theory (Transformational Syntax). The core of the author's idea is the proposal that there exists a connection between Piagetian operations and operational schemes, on one hand, and Chomsky's Deep Structures from which the sentences describing these operations have been derived, on the other. Two SAT coaching courses have been explored and much literary evidence found in support of this idea. As many as possible examples taken from these books have been included to help teacher's practice. At the end, the author expresses his conviction that this approach can be most generally applied to the formation of a psycho-linguistic basis of using English for specific purposes.

**Keywords:** English for Specific Purposes, Teaching Mathematics in English,
Piagetian Operations, Deep Structures, Surface Structures.

A broader way through themas of elementary school mathematics, VI | 35$-$52 |

**Abstract**

Multiplicative structure of the block of numbers 1–-100 is designed here as an activity of comprehension of multiplicative (and divisional) schemes, followed by their symbolic coding. At this stage, arithmetic operations and their properties gain their meaning as pull-outs from intuition. To help grasp that meaning and recognition of outer space appearances, we are elaborating here a system of iconic signs upon which such a learning process is founded. In particular, based on this system of signs, a method (that we call Pythagorean) for establishing properties of multiplication and division has been developed and discussed in depth here. A step-by-step building of the multiplication table, iconic representation and explanation of its entries are elaborated as to facilitate learning and retention in memory. At the end, two-box place holders have also been designed and digits in colour used for developing calculation skills in the case of addition and subtraction of two-digit numbers.

**Keywords:** Multiplicative structure of the block 1--100, Pythagorean
method, multiplicative schemes.

How successful is mathematics education in Serbia according to the TIMSS 2003 primary results and what should be done to improve it? | 53$-$60 |

**Abstract**

The main Serbian TIMSS 2003 results showed that (a) mathematics achievement of the Serbian students, expressed by average percent correct on all test items, was 41, being equal to the international average; (b) the best achievement of the Serbian students was found for tasks on algebra, whereas the poorest achievement was obtained for tasks on data; and (c) while 21\% of the Serbian students had reached the high TIMSS 2003 international benchmark, 20\% of themhad not attained basic mathematical knowledge and skills. These results were examined the light of the TIMSS 2003 results of other economically and educationally similar entities as well as the results of relevant educational studies realized in Serbia in last twenty years. The article also gives a direction for improvements of the Serbian mathematics education supported by the Serbian TIMSS 2003 results.

**Keywords:** TIMSS 2003.