2. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (1) European Mathematical Society ( EMS) Short unofficial summary REFERENCE LEVELS IN SCHOOL MATHEMATICS IN EUROPE Short unofficial summary: - A sense of the variety to be found in different countries - Some of the most striking similarities and differences between countries; - Some interesting examples.

3. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics In reality, the systems being described differ widely in - the age at which compulsory schooling begins and ends; - in the way the time spent in school is broken up into - "cycles"; - in the place (if any) given to vocational schools or programmes; - in the way different types of school are classified; and - in the social and political traditions which underlie their individual characteristics. EU Mathematics (2)

4. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (3) A surprising number of the educational systems surveyed are currently in a state of transition. The Hungarian model represents to some extent EU format presented in the overall summary of EMS

5. 1. General description of the mathematics teaching context 1.1. Description of the country school system 1. Pre-school institutions (Kindergarten) education (age 3-6) 2. Primary school (age 6 -14) 2. A: Lower elementary (primary) (age 6 - 10) 2. B: Upper elementary (age 10 - 14) 3. Institutions for secondary education (age 14 -18) 4. Institutions for higher education (age 18 - 25). THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics HUNGARY EU Mathematics (4)

6. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (5) Until 1990, Hungarian secondary educational system consisted of 3 well-distinguished types. From 1945, the curricula have been restructured several times. The 1995 new educational system NAT became effective since 2003/ 2004. ( Some History)

7. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (6) The National Curriculum The curriculum determines guidelines for teaching mathematics. According to the Act on Public Education, schools of all levels are entitled to modify number of classes pro subjects 1.2. Place and importance of mathematics in the curriculum

8. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (7) 2.The main objectives of mathematics The aim of mathematics teaching is to develop a flexible, disciplined way of thinking, to discover things and to search for creative solutions. Thus the objectives described herein must contain elements performing to the development of mathematical thinking as well as list of the essential concepts and most frequently used methods

9. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (8) 3. Basic contents Before 1965 the key words for mathematics education were: problem solving, developing mathematical concepts, increased emphasis on set theory, mathematical structures, geometrical transformations, functional relationships, approximational methods.

10. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (9) The future Mathematical education is to be based on the following main principles: Way of thinking (heuristic, deductive, inductive, constructive, analog, abstract, concrete, etc). Arithmetic & algebra, Relations, functions, sequences, Geometry, Measurement, Probability, Statistics.

11. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (10) 4. Exemplary topics 4.1 Quadratic equations 4.2 Pythagorean Theorem 4.3 Similarity 4.4 Word problem 4.5 Percentages 4.6 Additional topic: series

12. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (11) 5. Other subjects of interest for mathematics education around 16 year old 5.1. Regional characteristics 5.2. Teacher training 5.3. Examples of incentives for activities 5.4. Computer and other technology 5.5. Didactic of mathematics as a scientific discipline

13. THE NEW MILLENNIUM OR CURRENT TREND The 20th Century Mathematics EU Mathematics (12) 6.Research in didactics of mathematics in Hungary Some places of mathematics research with key words of interest and names of researchers. 1 Eötvös Loránd University, Group of Didactics of Mathematics H-1088 Budapest, Rákóczi - út 5. 2 József Attila University Szeged, Department of Education H-6700 Szeged, Aradi vértanuk tere 1. 7. References

14. END OF PART TWO 2.5 EU Mathematics