*T. Nemetz, O. Vancso, G. Wintsche*

1. Talking about teaching something within a given system presupposes some information about that system itself. In the case of the Hungarian educational system, this was an easy task till recently, see e.g. Nemetz [2], [3]. Political changes have altered this situation starting from the 80's. Statements like "Schooling in Hungary starts with kindergarten" are not valid anymore: The system of kindergartens has been demolished, practically speaking.

The simple three-age-group classification of pre-university education - namely the lower primary four years for ages 6-10, upper primary for the next four years, and the secondary schools for ages 15-18 - is no longer general, as was predicted e.g. by Howson [1]. The duration of compulsory schooling has been changed (in principle) from 14 to 16 by the new Educational Law in 1992. We shall nevertheless follow the old classification, since this practice has remained typical after all. (Teachers have been trained, and are still being trained, according to the old age-classification. The budgets and the administration of schools are unchanged).

As a tradition, at pre-university level, probability and statistics are dealt with in parallel, within the mathematics curriculum, except for some special secondary schools. It schould be pointed out that statistics does not play an important role in the intended curriculum, and even less so in the implemented one. During the last 20 years, for instance, no statistical question was included in the school leaving final examinations.

2. At lower primary level, the "1978 mathematics syllabus" is still commonly practised, although it has been under revision since 1987. The subject matter is classified under five sub-titles, one of them being "combinatorics, probability and statistics". We describe the goals, specified for the four grades:

- Grade 1:
- Arranging things according to different properties.
Differentiating the notions <certain>, <probable, but not sure> and
<impossible>. Experiencing data collection while becoming more and
more familiar with numbers.
- Grade 2:
- Listing and counting all pairs of elements in a given set.
Pairing the elements of two sets. Listing possible outcomes of random
events. Recording outcomes of random experiments (counting frequencies).
Differentiating among degrees of "probable but not sure events".
- Grade 3:
- Searching for possible cases when making observations or
carrying out experiments. Classifying outcomes according to their likelihood.
Collecting and recording data. Representing such data in tables and
graphs. Preparing the introduction of the notion of the arithmetic mean.
- Grade 4:
- Finding all possible combinations by listing them in tables or by using flow-charts. Representing frequency distributions by bar-diagrams. Guessing frequencies before performing random experiments, comparing the guesses with the experimental results. Selecting the most frequent element of a given set of data. Location parameters and their meaning. Calculating the average of integers.

3. The variety of types of schools does not allow us to refer to "grades" in general. Instead we refer to the age of the students. Unfortunately, there is not much to report on: At the age of 12 and 13, no stochastics is included in any of the school types. During the beginning of age 11 curricula discuss some problems concerning producing and interpreting graphs, calculating averages, and grouping collected data. The syllabus calls for recapitulation of statistical knowledge at the age of 14. However, beyond an estimated 10%, teachers do not devote any time to such units.

4. In the general secondary schools ("gymnasiums") the mathematics curriculum is divided into compulsory and optional parts. The final school leaving examination, as well as the university entrance examinations, are related to the compulsory part only. This part does not offer stochastics. The suggested curriculum for the optional part contains a unit on stochastics during the last 2 years. This unit starts with descriptive statistics, explaining the mathematical beckground of the location and dispersion parameters. These are used to motivate the introduction of concepts in probability. Probability is restricted to the discrete case. Its means are then used to formulate and solve statistical decision problems and estimation tasks. There are now 19 highly maths-specialized classes per year in the country, where, depending on the teacher's decision, this unit may be dealt with much more in depth, reaching the level of a simpler introductory university course. Textbooks for both kinds of options are written by the first author of this article.

Statistics is receiving more direct attention in schools specialized in economics and computer technology. They follow the same philosophy as in the optional parts referred to above, but greater emphasis is placed on concrete calculations, and solution of problems. A textbook written by the second author of this article contains a number of real life problems and presupposes very active work of the students.

5. In teacher training for lower primary and secondary schools no credit course on statistics are offered. Future teachers might attend some seminars on statistics or on the didactics of stochastics, but this not typical. The program for prospective teachers for the middle age group (11-14 year olds), prepared by the third author, integrates statistics into a probability course, similar to the optional program already mentioned.

6. A new "National Basic Curriculum" has been under development for the last 4-5 years, and will proceed to legistration in the fall of 1995. This curriculum will prescribe subject matter in mathematics for about half of the time. It seems to give a more prominent role to statistical thinking. Key words from the syllabus are: elements of descriptive statistics, collecting and representing data, interpreting graphs, location parameters, performing random experiments, frequency distributions. The intended minimum goals are not very ambitious: By the age of 12 students should be able to calculate averages, and at 14 to produce and interpret graphs.

[1] G.A. Howson: National Curricula in Mathematics, The Mathematical
Association, Univ. of Southampton, 1991, pp. 115-125.

[2] T. Nemetz: "Pre--University Stochastics Teaching in Hungary". In : V.
Barnett, (ed.): Teaching Statistics Schools throughout the World, Ch. 4.
Voorburg, 1982, 85--112.

[3] T. Nemetz: "Mathematics education in Hungary." In : I. Morris, S.A.
Arora: Moving into the twenty first century, UNESCO Series: Studies in
mathematics education, No.8., 1991, pp. 105-112.

The above article is a slightly revised version of an article prepared for a booklet which is to be published by the Royal Statistical Society, UK. The editor is grateful to the RSS, and to Ms. Flavia Jolliffe, University of Greenwich, for having permitted its publication in the ICMI Bulletin.

This work was supported by Grant No. T 17427 of the National Scientific Research Foundation (OTKA).

T. Nemetz

Hungarian Academy of Sciences,

P.O.Box 127, H-1364.

E-Mail: <nemetz@math-inst.hu>

O. Vancso

ELTE, Faculty of Science,

Dept. of Didactics of Maths.,

H-1088 Budapest, Rakoczi u. 5.

E-Mail: <vancso@ludens.elte.hu>

G. Wintsche

ELTE, Faculty of Teacher Training for General Schools,

Dept. of Maths.,

H-1055 Budapest V. Marko u. 29

E-Mail: <wgerg@ludens.elte.hu>