SECOND FOREIGN LANGUAGE Years 9 through 12 of education
Objectives and tasks In addition to the contents of the general introduction, the objective of teaching a second foreign language is to help students acquire a second language on an elementary level during four years of study. Learning a second foreign language may be facilitated by the experience gained while learning the first foreign language, as students are already familiar with the practice of receiving instructions in the target language, the types of in-class activities and texts, the methodology of work and the requirements. The language learning strategies and self-confidence developed by students may also facilitate the learning of a new language. Compared to the previous one, this age group tend to make more spectacular progress, therefore it is a realistic expectation that students achieve a proficiency level between A1 and A1, by the end of year 10, and a level between A2 and B1 by the end of year 12. The tasks and objectives are identical with the ones described in the section about the first foreign language.
Developmental requirements Students must be able to exchange information with a few written or spoken sentences. They must be able to understand short oral and written texts in topics they are familiar with and are required to create such texts. They are required to maintain their language skills on the achieved level themselves, and develop such skills in line with their personal interests. Students should form a picture of the people and culture of other countries through the foreign language being learnt.
List of (suggested) topics:
Me and my family: personal particulars, occupations, household duties, family occasions.
At home. The immediate environment: describing the house and the living room. Personal relations: friendship, characterising people’s appearance and inner qualities.
Our wider environment: village, small town, metropolis; describing the place of living; a guided tour in the neighbourhood; plants and animals.
School life: describing the school, the ideal timetable, the ideal school, comparing a Hungarian school with a school located in an area where the target language is spoken.
Health and illness: frequent diseases and common injuries.
Food and meals: eating habits in Hungary and in other countries; dishes and recipes; restaurants and fast food restaurants.
Travelling: preparing for a journey; going on holiday in Hungary and abroad.
Leisure activities and entertainment: one’s favourite sport; collections; sport at school and outside school; video, computer and reading; cultural events; theatre and cinema; modern and classical music; the world of the Internet.
Employment: summer jobs; choice of career.
Civilisation: contact with the culture of the target country or countries; their political, economic and social conditions.
Technical and scientific culture: the role of science and technical devices in everyday life; some well-known scientific and technical achievements of the target country or countries.
Number of teaching hours per year: 111 Content The language specific requirements related to communicative intentions and concepts can be found in the Framework Curriculum broken down into seven different languages and two years.
Content The language specific requirements related to communicative intentions and concepts can be found in the Framework Curriculum broken down into six different languages and two years.
Communicative intentions Communicative intentions used in social interaction:
greetings and saying goodbye;
introducing self and others;
enquiry about how others are, and responses to similar enquiries;
asking for and giving permission;
expressing thanks and responding to expression of thanks;
Create various text types (message, greeting, informal letter).
For further reference below is a list of proficiency levels as defined by the Council of Europe:
The definition of proficiency levels on the basis of the recommendations of the Council of Europe regarding foreign language teaching* C2 The language learner can easily understand every written or heard text; can summarise information from different spoken or written sources and give a comprehensive account of arguments and reports; capable of spontaneous expression in a fully coherent and precise style; can convey finer shades of meaning even in rather complex situations.
C1 The language learner can understand extended and sophisticated texts sensing hidden meaning; capable of fluent and spontaneous expression without much obvious searching for expressions; can use the language flexibly and effectively for social and professional purposes, such as learning and work; can construct clear, well-structured, detailed text of fairly complex subjects with an assured use of templates and connective devices.
B2 The language learner can follow texts of complex concrete or abstract subjects, including conversations in his/her field of occupation; can interact with a degree of fluency and spontaneity that makes interaction with native speakers quite effortless for both parties; can present clear, detailed descriptions on a wide range of subjects and is capable of expressing personal views on an issue giving the advantages and disadvantages of various options.
B1 The language learner can understand the main points of clear standard texts on familiar matters regularly encountered in work, school, leisure, etc.; can deal with most situations likely to arise whilst travelling in areas where the language is spoken; can create simple, can create simple connected text on topics which are familiar or of personal interest; can describe experiences and events, dreams, hopes and ambitions and can briefly give reasons and explanations for opinions and plans.
A2 The language learner can understand phrases and the highest frequency vocabulary related to areas of most immediate personal relevance (e.g. very basic personal and family information, shopping, local geography, employment); can communicate in simple and routine tasks requiring a simple and direct exchange of information on family matters or everyday life; can describe in simple terms personal attitude to something in the immediate environments or in areas related to the most basic needs.
A1 The language learner can understand and use the most frequent expressions and very basic phrases used in everyday communication with the purpose of satisfying concrete immediate needs; can introduce self and other people and can answer questions concerning personal issues (e.g. place of living), people known or things possessed; can interact in a simple way provided the other person speaks slowly and clearly and prepared to help.
MATHEMATICS Years 9 through 12 of education
Objectives and tasks The objective and task of teaching mathematics is to help students develop an independent, systematic, logical way of thinking. This is ensured by the process of gradually building up the inner structure of mathematics (i.e learning concepts, axioms, theorems, methods of verification), and the acquired knowledge is applied in diverse fields. The method of raising problems should provide students with justification that it is necessary to create accurate concepts. These processes should become part of the students’ internal, exploratory learning activities.
All these are to develop students’ abstraction and synthesising skills. The creation of useful, new concepts, finding correlation, and the application of knowledge to solve problems develop students’ combinative skills and creativity, and help them approach and solve problems independently and with sufficient self-confidence.
Teaching mathematics is based on a wide range of tools which are used to develop students’ mathematising and modelling skills. It develops a need for the verification of proposed relationships and hypotheses. Also it demonstrates the use and the internal beauty of mathematics as well as the role it plays in human culture. Mathematics help developing students’ spatial orientation and sense of beauty.
The traditional and modern tools of mathematics facilitate the study of natural sciences, information technology, technology, humanities, and the profession chosen by students in vocational secondary schools. It also makes the interpretation, formulation and handling of everyday problems easier. Teachers of mathematics should promote the reasonable use of electronic devices as much as possible (e.g. pocket calculator, computer, graphical calculator, internet etc.).
It is important to note that students must become able to work with precision, endurance and discipline. They should use every opportunity to check themselves and must be able to estimate expected results. The aim is to maintain a high level of motivation among students and promote their independence. In this respect, a very important task is to demonstrate the diverse ways of applying mathematics as a tool, and to emphasise this diversity in teaching.
In contrast to elementary level mathematics, secondary school teachers should place emphasis on the deductive nature of the subject, although teaching based on a specific approach and activity remains indispensable.
Students must be equipped with the knowledge and skills necessary to pass the secondary school leaving exam successfully.
The new aspects of the Framework Curriculum for mathematics are the following:
increased significance of modelling and mathematisation;
an increased scope of application;
balance between building the inner structure of mathematics and the application of mathematical knowledge as a tool in everyday life and in other subjects;
incorporating modern teaching and learning techniques into the educational activities performed by schools on a daily basis.
Developmental requirements The application of acquired mathematical concepts
The development of a mathematical approach Secondary school studies is the level where the concepts formed earlier through demonstration and activities should be verified, certain concepts should be defined and generalisations must be made. Students’ mathematising skills are improved by applying the different types of correlation learned during the discussion of various topics for the solution of mathematical and practical problems, and by making them realise and know the possibility of application in other fields.
By the end of this period students must be familiar with the set of real numbers, and must be able to use operations discussed within the set of these numbers in practical and more abstract tasks. The calculations included in the various chapters of the textbooks may require the use of a calculator or a PC. For certain operations, the domain of interpretation includes algebraic expressions and vectors as well.
Both the study of mathematics and science and the illustration of various practical problems, makes it important to know how to represent functions in a co-ordinate system and how to identify the most important properties of functions..
The expansion of geometric skills and a more systematic review of geometrical transformations help developing a dynamic view of geometry. Trigonometric calculations have practical significance (the calculation of distance and determining angles). Concepts and theorems of plane geometry and the geometry of space are essential for a better perception of space and analogous thinking. The calculation of area, surface and volume are essential for other subjects as well. Teaching the elements of co-ordinate geometry serves the purpose of demonstrating the correlation between the various fields of mathematics as well as the complexity of the discipline. For this age group it is very important to improve deduction and verification skills. Using ‘if’ and ‘if and only if’ structures correctly is important not only in mathematics, but in a number of other fields of life.
Problem solving skills and logical thinking One of our major tasks is to develop a sensitivity to problems, and to teach students how to solve problems. An indispensable condition to this is practising how to interpret and analyse simple mathematical discourse, and to let students solve problems independently as often as possible. They should actively participate in the process of teaching and learning.
Advanced discussion skills, the ability to find and discuss alternative solutions improve logical thinking.
Studies in fields which may have practical significance (e.g. applying the components of geometrical calculations, descriptive statistics, theory of probability) are very useful for the understanding of life and the various disciplines. This will demonstrate students how useful mathematics is. We need to make sure that students get a certain level of experience in this field before the secondary school leaving examination.
The application of acquired learning methods and thinking In addition to the inductive method, in years 9 through 12 mathematics increasingly focuses on deductive conclusions. The material to be taught contains assumptions which can be proved or refuted in a few steps. Teaching should focus on developing a need for proofs. A few simple theorems are verified, and the methods used in proofs are introduced. Concepts and rules are defined accurately. In teaching mathematics, it is essential to improve abstraction skills.
During the organisation and review of knowledge prior to the secondary school leaving examination, elementary set theory and logic are used in the discussion of various topics, which shows the complexity of mathematics. Simple models (e.g. graphs) are also used.
Logical thinking is essential for problem solving as well as for algorithmic procedures and applications. Working out an algorithm with a few steps in the various fields of mathematics is important for studying information technology.
It is evident that the use of visual and other aids is essential in geometry (trigonometry), combination theory and statistics alike. Learning the various ways of describing data assemblies improves applicable knowledge in this field.
Developing the right attitude towards learning Recently acquired skills applied in practical calculations make it increasingly important to use electronic devices.
Calculations with approximate values require the application of the various methods of estimation, rounding and checking to decide whether the result is realistic or not.
Students are required to use the terminology and the sign system correctly.
Knowledgeable reading of mathematical discourse, using coursebooks and reference books, highlighting the important points of a text and learning how to take notes will make studies in higher education easier.
In mathematics, students are required to use arguments properly, whereby teaching mathematics may (and does) improve students’ communication skills.
It is important to make students able to distinguish between definition, assumption and theorem. Students have not developed mathematical skill until they are able to apply definitions and theorems.
It cannot be overlooked that mathematics is part of cultural history. Describing a few elements of the history of mathematics, explaining some of the apparently simple but unverified guesses, the life and achievements of great mathematicians may be an effective way to motivate students. Working in the library and with the internet may provide help to this.
Number of teaching hours per year: 111
Methods of thinking
PREREQUISITES OF MOVING AHEAD
Defining and establishing demonstrative concepts.
Recapitulating already known sets of numbers and points; the concept of definite and indefinite sets, interval.
Familiarity with rational numbers.
union of sets, intersection of sets, determining subsets, difference of two sets.
Subset, union, intersection difference of two sets.
Finding a method to cover all cases.
Combinatorial problems. Considering all cases.
The difference between necessary and sufficient condition.
The use of ‘if and only if’ - (continuous). Theorems and their inverse (continuous).