Changes in mathematics education through the reunification of Germany

• Changes in the educational system
• Mathematics teaching in the GDR
• Changes in mathematics education in the new states
• Changes of teacher education

1. Changes in the educational system

The political changes since 1989 in the German Democratic Republic (GDR) culminated in the reunification of the two German states in 1991. The Federal Republic of Germany was extended by five new states:

• Brandenburg
• Mecklenburg
• Sachsen-Anhalt (Saxonia-Anhalt)
• Sachsen (Saxony)
• Thüringen (Thuringia)

The new states had to develop their own constitutions and administrative structures. Therefore the new states had also to develop their school systems. The school systems of the GDR and F.R.G. were very different from each other. Whereas education in the F.R.G. was oriented towards the ideals of a pluralistic society, the GDR had the ideal of a socialistic education. These differences in the underlying philosophy of education had consequences for the objectives, the education system and the teaching:

• The education system in the GDR was completely centralized.
• Mathematics education was based on a uniform compact syllabus for the grades 1-10 and 11-12.
• Teaching was strongly teacher-centered, which was politically required and strongly controlled.

Under the conditions of this highly standardized school, accompanied by teaching aids and control mechanisms (supervision by qualified subject teacher, school authority, headteacher and so on) the variety of teaching methods was rather restricted.

After 1989 there was very strong political pressure for the new states to take the structures of the F.R.G. as standards for the necessary changes. On the other hand, people in the new states wanted to retain the advantages of the former GDR school-system. Due to the different political majorities in the parliaments of the new states many differences can be found in their educational systems. This is above all true for the secondary school systems.
Examples:

• Grades 5 and 6 are part of the elementary school (Grundschule) in Berlin and Brandenburg. The Gymnasium starts at grade 7, but finishes at the end of the 13th year of schooling with the Abitur.
  
• In Saxony-Anhalt the Gymnasium also starts with grade 7, but ends after the 12th year of schooling with the Abitur.
• Mecklenburg-Vorpommern is the only new state that introduced the traditional system of the old states with Hauptschule, Realschule and Gymnasium after grade 4. Additionally the comprehensive school (Gesamtschule) was introduced.
• In Thuringia and Saxony only two types of secondary school were introduced: the Gymnasium and a secondary school on a lower level (Regelschule) after grade 6.
  

The main difference between the old and the new states is the possibility of placing the final examination after 12 years of school, which was acknowledged as a valid Abitur by the Conference of the Ministers of Education on June 25/26,1993. And this raised again a discussion in the old states about placing the Abitur after 12 years of school.

2. Mathematics teaching in the GDR

School in the former GDR was a part of the political system. The task of the whole of education consisted in forming young people to become convinced socialist citizens according to the programme of the former socialist party (SED).This meant that the teachers in the "socialistic comprehensive school" ("Sozialistische Einheitsschule") should see their job as a political task for the working class. From this political point of view they had to devote all their energies of teaching to the ideological upbringing of their pupils. But experience shows that the majority of teachers first of all had regard to the needs of their students and tried to help them to develop their abilities through mathematics education.

The specific function of mathematics teaching was:

• to provide pupils with knowledge of fundamental mathematical concepts, theorems, rules, methods, procedures and their relationships, and with the ability to solve internal and external mathematical problems. This should guarantee a powerful basis for an autonomous extension of their mathematical education later on;
• to use experiences of the acquisition and application of mathematical knowledge for the development of the students' personality with respect to their ways of thinking;
  
• the development of a positive attitude and a readiness for intellectual work. As a result: the students should be interested in mathematics and should take pleasure in working on problems, in overcoming difficulties, in working alone and in a team; they should be honest in their attitude, proud but also modest in their success.
• In general, they should understand the role of mathematics as "part of the recognition process in the social practice".

These goals directed the further development of mathematics education until the end of the 80's for the 10-year Oberschule. Decisions about the selection of the subject areas and goals were made in accordance with the following principles:
Mathematics education

• should be pedagogically oriented to mathematics as a scientific discipline,
• should put emphasis on the ability to use mathematics for internal and external applications on the basis of sound acquired knowledge,
• should develop mathematical and general abilities such as the ability to describe, to justify, to prove, to use mathematical symbols and to use the mother tongue correctly in mathematical contexts from the first day of school onwards.

The contents of mathematics education in grade 1 - 10 were:

• natural numbers, fractions, rational numbers,
• elementary geometrical structures such as points, straight lines, segments, triangles, four-sided figures, circles and their main characteristics,
• simple solids, their surface area, their volume, and their representation in the plane,
• linear, quadratic, exponential and trigonometric functions; linear and quadratic equations, linear inequalities, linear systems of equations, studied in a systematic way,
• the formulation of rules and the development of methods, with definitions of concepts, proofs of theorems and a consequent use of mathematical language.

A particular feature of the educational system of the GDR was that there was always just one series of textbooks for mathematics education including teaching aids for every school year. All these materials were oriented towards the syllabus as the central document, which was divided into separate learning sequences for the planning of teaching. It also included relatively detailed comments for motivation and reinforcement.

There were also uniform orientations for teaching. These were based on the realization of specific functions of mathematics teaching such as:

• motivating all students to active and intellectual discussion of the subject in all phases of teaching,
• working on problems/tasks as main objects (these tasks should be a complex process, combining the activity of teacher and pupil, and not just focused on their solution),
• enabling the students to use mathematics,
• the opinion that reinforcement (such as practice, revision and systematization) is the fundamental basis of all mathematics education.

3. Changes in mathematics education in the new states

From today's point of view most of the goals and the contents of mathematics education of the GDR seem still to be acceptable. They therefore have some influence on the curricula developed in the new states since 1990.
Example: According to the guidelines for the elementary schools in Saxony-Anhalt, the concern of mathematics teaching is:

• to give the students a solid knowledge of fundamental concepts, rules, theorems, methods and procedures,
• to enable them to use this knowledge to solve internal and external mathematical problems successfully,
• to educate students to act responsibly in a pluralistic society.
  
  Pupils should become aware
• of the instrumental character of mathematics,
• of mathematics as a part of culture and humanity,
• they should gain the experience that solving mathematical tasks can be an enjoyable and an enjoyable leisure time activity.

Considering all these facts, global aims of mathematics teaching can be derived:

• development of language abilities,
• development of logical abilities including abilities to define, argue, justify and prove,
• development of three-dimensional imagination,
• competence in algorithmical working,
• competence in numerical working,
• competence in heuristic working.

These aims find their realization mainly in identical subject areas of the curriculum of the GDR except in elements of probability and statistics, which were not taught in the GDR. But they are now taught in different ways in the new states.

The main change is the substantial reduction of the proportion of mathematics as against other subjects compared with the GDR school. This is also true for other science subjects, such as physics, chemistry and biology.
Another change is the higher proportion of students who want to change to the Gymnasium (on average more than 30% in the new states of Germany). This requires new methods of inner differentiation and individualization of teaching in the early secondary schools.

4. Changes of teacher education through the reunification of Germany

Since 1982 teacher education in the GDR was a single-phase 5 year course at the university for secondary teachers or at teacher training colleges for elementary school teachers. Responsibility for the school practical education in the 5th year was taken by the university or the teacher training college. The student trainees were watched by the tutors in the schools. The tutors themselves were supported and trained by the universities. The studies led to the degree of the Diploma (Diplomlehrer). The training as a whole was carried out in accordance with a uniform and central study curriculum that organized all subjects in a chronological order for all parts of the training. The components of the teacher training were the following:

• education in two subjects,
• one educational subject (pedagogy, psychology),
• Marxism-Leninism,
• didactics: theoretical and practical parts, with a wider range than in the old states of Germany and in the new curricula at the universities of the new states.

The studies also included

• physical education/ sports, Russian, culture theory and English as a second language.

Each study subject was accompanied by a uniform study programme. This programme offered information about

• aims,
• contents of education,
• detailed commentaries on the organization and structure of the education itself. In addition to that advanced studies and specific main fields of research were included.

Positive aspects of this system were: a fruitful teamwork between university and school, connection between theoretical and practical elements in university education study, and teacher training as academic professional training.

Nevertheless this system had to be given up under political pressure. In all the new states of Germany teacher education is now carried out in two phases (with temporary regulations), as has been the practice in the old states.