In the 19th century, mathematics teaching at the Gymnasium was
centered on the goal of "general human education." Pure mathematics
and its formalisms were more important than applications.
On the other hand, arithmetic, including practical aspects of its applications,
together with the subject of German were the two main topics at the Volksschule.
Influenced by Felix Klein, the Merano conference in 1905 set
up several new guidelines for mathematics teaching, especially concerning
functional thinking, the genetic structure of teaching, and the integration
of pure and applied mathematics. A partial realization at the Gymnasium
took place in the syllabus of 1925.
In 1960, mathematics instruction was considerably reduced in order to
emphasize a more "Christian conservative" education. At the same
time, the U.S.A. began large programs, stimulated by the Sputnik shock,
to improve mathematics teaching.
Influenced by the Organisation for Economic Co-operation and Development
(OECD) recommendations of 1961 and 1964, a discussion began on the strengthening
of school mathematics.
The Deutscher Verein zur Förderung des mathematischen und naturwissenschaftlichen
Unterrichts, a teacher's association, established the Nürnberg
syllabus in 1965. The intention was to close the gap between school
and university by introducing the ideas of "modern mathematics"
in school. Therefore sets, structures, mappings, and logical concepts were
to be introduced in mathematics teaching.
At the same time the objectives of the Hauptschule were discussed
so as to replace the teaching of arithmetic and practical applications
by a more mathematical education. As a first step, elementary algebra was
introduced.
The most important change in mathematics teaching happened in 1968.
The Standing Conference of Ministers of Education and Cultural Affairs
of the states of the Federal Republic of Germany (Ständige Konferenz
der Kultusminister der Länder in der Bundesrepublik Deutschland,
KMK) passed the "Recommendations and Guidelines on the Modernization
of Mathematics Teaching at General Education Schools." During the
next four years, all states had to renew their syllabi for every type of
school according to the guidelines from 1968.
The recommendations are essentially general remarks on the importance of
mathematics. The progress in mathematics during the previous decades and
the use of "modern mathematical thinking" in fields important
for science, economics, and society had forced the modernization of mathematics
teaching. As one of the consequences, concepts such as the use of sets,
mappings, and structures should be fundamental ideas represented in all
suitable topics.
In 1976, some revisions were made that considerably reduced these specific
consequences.
During the 1970s each state tried to transform these guidelines into its
own mathematics syllabi. Since each state worked independently, the 10
states produced 10 different results. Several items were not accepted by
all states, and some topics were put into other grades.
Another problem was the differentiation among the three types
of schools. Some states (e.g., Hessen) created a common syllabus for all
schools that included some hints to the lower level schools for shortening
it. In general, different syllabi were developed.
The discrepancies described above initiated the development of new recommendations
for mathematics teaching by the teacher's association Deutscher Verein
zur Förderung des mathematischen und naturwissenschaftlichen Unterrichts.
These guidelines from 1988 were originally planned for all types of schools,
but finally they were basically formulated for the Gymnasium. The central
statement of the recommendations is a listing of leading ideas and goals
for mathematics teaching. Finally, some general educational goals are listed.
The recommendations conclude with a syllabus for the fifth grade to the
end of schooling.
Compared with the KMK guidelines and recommendations in 1968, the structural
aspects of mathematics are sharply reduced. Sets and relations are not
mentioned any more.
Curriculum changes in the former German Democratic Republic (GDR) were influenced by changes of the school system and the general goals of "Socialistic education". The introduction of the "Socialistic comprehensive school" (Sozialistische Einheitschule) from grade 1 to 10 meant teaching mathematics for all.
The resolution of the "Politbüro" from 1962 (Mathematikbeschluß) established measures for the improvement and the development of mathematics education. As a result, the syllabus was changed. It put now emphasis on "leading lines" (Leitlinien), e.g.:
A "settheoretical penetration" (Mengentheoretische Durchdringung) was typical. In geometry teaching the idea of symmetry became more important under the use of transformations. Compared with the Nürnberg syllabus it was more modest: Algebra was done without structures, and geometry without algebraic notions such as vectors, determinants, and matrices.
After the reunification of Germany in 1991 the new states had to organize their school systems and to develop new curricula. It was not a great problem to develop new syllabi in mathematics education, because the differences with respect to the contents were not very remarkable between the new and the old states. It was mainly probability and statistics which had not been taught in the former GDR.
Changes
in mathematics education through the reunification of Germany