4. THE STRUCTURE OF THE ROMANIAN EDUCATION SYSTEM 1.Pre-school education (Kindergarden ) is open for children aged 3-6. The level comprises three leagues: - "Small Group" for children aged 3–4, "Middle Group", for children aged 4–5, "Big Group" for children aged 5–6. 2.Primary education (age 7- 11) comprises two periods: the first one is "School Preparation Class" for children aged 6–7 and the second is Elementary school - grades I to IV 3.Secondary School a) Lower secondary education (Gymnasium) grades V to IX b) Upper secondary education – High school – studies are three years in length(grades IX-XII) During high school, students choose a speciality: human (philology, foreign languages), science (mathematics, informatics, physics), military college, economic college....

5. There are four types of high schools in Romania allowing access to university, based on the type of education offered and their academic performance. National College — the most prestigious high schools in Romania - is a theoretical school. Some of them are over 100 years old, and have a very strong tradition in education. Military College — 3 high schools administered by the Ministry of National Defense. They are considered extremely strict and they have the same regime as army units. Economic College or Technical College - A high school with relatively good results and with an academic program based on technical education or services. Standard High school — An average high school, providing one of the available academic programs added after this designation. 4. Higher education is organized according to the principles of the Bologna process

6. Age Grades Educational levelTypes > 20 Post-University Higher and post- University education University Post-high school Post secondary education 1919XIII High school upper cycle High school-upper cycle Upper secondary education Post- compulsory 1818XII 1717XI Completing year 1616X High school lower cycle Arts and crafts school 1515IX Gymnasium Lower secondary education Compulsory 1414VIII 1313VII 1212VI 1V 10IV Elementary school Primary education 9III 8II 7I 60 School Preparation Class 3-5 Kindergarden Pre-school education

7. MATHEMATICS CURRICULUM IN ROMANIA The mathematical contents are prescribed at national level.

8. In primary school mathematics is taught as a distinct subject from the first grade onwards. Children come to school with some mathematical knowledge which they have gained in kindergarden through play and develop arithmetical operations such as addition and multiplication and their opposites: subtraction and division. Different resources may be used in maths teaching: objects, shapes, drawings, computers, but no calculators. The role of practical activities is very important. Kids use different sticks, marbles and models of geometrical shapes to help them to calculate and visualise abstract forms.

9. At the end of primary education kids: know the meaning of the position of digits in writing positive integers up to the billion; write, read, compare positive integers; use fractions for expressing subdivisions of the integer; know and use operations of positive integers; recognise 2-D and 3-D shapes, identify and describe simple properties; know the standard units for length, volume, weight, surface, time and money units and use transformations between multiples and submultiples; use symbols for replacing unknown numbers while solving problems; rules and properties of brackets, priority of operations.

10. Starting with the 5th grade children study algebra and geometry with main chapters: Sets, Numbers, Functions, Fractions, Decimals and percentages, Arithmetic and Geometric Progressions, Equations and Inequalities, Triangles, Quadrilateral, Circles, Areas and Volumes. Gymnasium

11. At the end of compulsory school students should : Write, read and compare real numbers and represent them on an axis; Perform operations with real numbers (possibly represented by letters); Use elements of logic and set theory, as well as relations, functions and sequences in solving problems; Measures consists of six strand units: Length, Area, Weight, Capacity, Time and Money; Deal with 2-D and 3-D shapes, symmetry, lines and angles; Solve equations and inequations and perform algebraic calculations using algorithms, specific formulas and methods; Solve problems using ratio and proportion;

12. High schools Starting with the 10th grade students learn about trigonometry, about functions, their properties and graph representation using differential calculus, integral calculus and its applications in determinations of areas and volumes and about differential equations. They learn to Represent various types of numbers, variables and functions using different modalities; Record, process and present data using elements of statistics and probabilities; Express properties of mathematical operations (commutativity, associativity, neutral elements, and reversibility); Make use of algorithms in a variety of problem-solving situations or for the mathematical description of a concrete situation; Use mathematical ideas, rules and models, in tasking practical problems and everyday situation; Transform word problems into exercises and vice-versa: device a variety of problems that might be processed by solving a given exercise.

15. The structure of mathematics teaching There are 3-4 classes of mathematics per week from the 1st grade to the 5th grade, 4 classes from the 6th grade to the 8th grade and 2-6 classes from the 9th grade to the 12th grade, depending on the specialised line followed by the students. Every lesson lasts about 50 minutes.

16. About textbooks There is an officially approved list of textbooks and teachers are free to choose one among the approved textbooks. In compulsory education, textbooks are paid for by the government. Teachers might get teaching guides, which are not compulsory. Assessment includes tests, traditional exercises (oral and written), project work, self-assessment. Assessment is done on the basis of the objectives for each age level prescribed by the curriculum. For the primary school grading system used is known as the calificative. These are (FB) - Excellent, (B) - Good, (S) – Satisfactory and (N) - Failed. For grade 5 to 12, a 1 to 10 grading system is used with 10 being the best and 1 being the worst and 5 is the minimum passing grade. The system of continuous assessment is used, with individual marks for each test, oral examination, project…entered in the register. Some subjects also require a partial examination at the end of the semester. The first official mathematics examination takes place at the age of 15, at the end of the 9 th grade. The role of this exam is to give access to high schools.

17. Teaching methods The teaching methods are free to be developed by each teacher. The curriculum does not impose certain methods but provides examples of learning activities for each reference objective Because the relevance of maths in everyday life, in natural sciences, in technology and social sciences there are( or it should be) some major shifts in teaching and learning mathematics What becomes less important: memorising rules and computing solving problems/exercises that have a unique answer ‘pen and pencil’ (or ‘chalk and blackboard’) maths What becomes more important: problem-solving in practical contexts, adapt learning to everyday life formulating questions, analysing the steps and motivating decisions in problem solving Using activities that stimulate students to work in teams.

18. Beside traditional chalk and talk teaching lessons there are few different lessons using resources and methods such as Powerpoint presentation, movies, cube method, gallery tour (Teams-Games- Tournaments). Most traditional lessons start with the teacher explaining the theory and problems solving methods followed by picking a list of problems connected to the theory. The teacher is supervising every solution, allowing the randomly picked student to explain his/her thoughts and displays on the blackboard. The rest of the class follow the displays, comment and writing the solutions. At the end of the lesson the students get their assignments to be completed at home. Students usually spend at least 30 minutes a day, sometimes up to one and a half hour, at home preparing or doing their assigned homework.

19. Teams-Games-Tournaments Gallery tour Teams-Games-Tournaments Power Point presentationCube method

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