ABSTRACTS
Promotie Harm Jan Smid
Een Onbekookte Nieuwigheid?
(An ill-considered novelty? Introduction, extent, content and significance of
mathematics education on French and Latin schools 1815-1863)
Delft, April 22, 1997.
Abstract
In the second half of the nineteenth century The Netherlands underwent an
important change: from a rather backward country it became a more modern,
industrialized country. At the end of the century The Netherlands became also,
rather surprisingly, a leading country in physics, chemistry and astronomy; we
only need to mention names like Kamerlingh-Onnes, Lorentz, Zeeman, Van der
Waals and Kapteyn. One of the explanations often given for this remarkable
development is the creation of the HBS, a Dutch variant of the German
Realschule, founded in 1863. The creation of this type of school is
often described as something totally new, a creation ``out of the blue''.
Mathematics was the most important topic on this schoolsystem. In this study
we investigate the history of mathematics education before 1863, in order to
answer the question whether serious mathematics education really started in
1863, or that there was a more continuous transition from the old to the new
schoolsystem.
Mathematics education became compulsory on the Dutch Latin schools in 1815.
Then the new king, William I, issued a Royal Decree on the universities and the
Latin schools. One of the articles of the Decree stated that ``the principles
of mathematics'' should be taught at the Latin schools. That was something
new. In the eighteenth century, the Latin schools had confined themselves
almost exclusively to the teaching of Latin. Mathematics then was taught on a
limited number of so-called French schools --schools mainly preparing for jobs
in the trading business-- and on vocational schools: schools for sailors and
architects. In the eighteenth century French and vocational schools became more
popular in the Netherlands, while the number of students on Latin schools
declined. During the French period (1795-1813) the Latin schools were sharply
criticized for their one-sidedness. Several plans were proposed to modernize
these schools, including the teaching of mathematics. But nothing was
accomplished.
The Royal Decree of 1815 was on the whole rather conservative and brought
little renewal. The introduction of mathematics had not the intention to give
mathematics a prominent position on the schools, like the Von Humboldt reform
in Prussia had done. Mathematics was just something extra, to be taught at the
end of the daily lessons, by the same teacher who taught Latin and
Greek.
In 1826 the government took additional measures. It formulated a minimum
program for math on the Latin schools. Math teaching should at least
comprise:
- arithmetic; including decimal fractions and the decimal system,
proportions, root extractions and logarithms,
- algebra; mainly manipulating algebraic expressions, especially roots,
Newtons binomium and solving linear and quadratic equations,
- plane geometry; mainly the first five books of Euclid.
This program remained valid until 1876, when a new law on the universities and
the Latin schools was passed. Until 1863, the government did not take any
measures for the other secondary schools, the French schools. Formally they
belonged to the primary education system, but of course they did not fit into
that system. Due to the needs of the society a large number of French schools
of all kinds came into existence. Most of them just extended primary schools.
About a hundred French schools were more regular secondary schools and on the
most of these schools also mathematics was taught. In 1863 at last the
government passed a law on a Dutch type Realschule, the HBS, replacing
the French schools.
The introduction of mathematics in the Latin schools caused quite some
discussion, especially after 1826, when it became clear that math teaching had
to be taken seriously. Teachers of the ancient languages argued that Latin and
Greek could not go together with mathematics and that the latter subject
should not be taught on grammar schools. The advocates of math teaching, their
main proponent being Jacob de Gelder, a professor of math at the Leyden
university, argued that mathematics had a great formative value and that the
combination of Latin and math teaching provided the best results. The math
teaching on the French schools was for an important part dedicated to the
preparation of the military and engineering academies. The preparation for
selective entrance exams of these academies was a new, and also a much
discussed aspect of the teaching of mathematics.
In the history of mathematics education on the Latin schools from 1815 until
1863 we can distinguish three periods. In the first period, 1815-1826
mathematics had a difficult start. There was no generally accepted program and
in quite some schools the principal and governors opposed math teaching. In
the second period, 1826-1838, due to the Decree of 1826, mathematics was more
accepted and most schools followed the program prescribed by the government
and used the books by Jacob de Gelder, especially written for the Latin
schools and recommended by the government.
During the third period, 1838-1863, the Latin schools underwent important
changes. Combinations of Latin schools and so-called ``second departments'',
in fact French schools, were founded. The combination of a Latin school with a
second department was usually called a gymnasium. The first departments
of these schools were modernized Latin schools, were Latin and Greek, modern
languages, geography, history and math were taught. In the second department
no Latin and Greek was taught, there the emphasis was on math and modern
languages. The math program on the second departments consisted of the math
program of the Latin schools together with solid geometry, goniometry and
trigonometry and sometimes descriptive geometry. The teachers on the
gymnasiums were usually specialists in their field of teaching. The old
system of a class-teacher, teaching all subjects to the same class gradually
disappeared. Usually the math teacher had no university degree, but was a
schoolteacher from the primary school, who had qualified himself by
self-study and private lessons in mathematics. On those French schools where
mathematics was taught, the program was usually more or less the same as on
the Latin schools. On the schools that specialized in preparing for the
entrance-exams of the Military and Civil Academy, the program was usually the
same as on the second departments.
The results of this study show that mathematics education on the French and
Latin schools in The Netherlands in the first half of the nineteenth century
was not a negligible affair. During that period the French and Latin schools on
the whole were not so backward and old-fashioned as often is maintained. The
motives behind the rise of mathematics education were its supposed formative
value, and the use of mathematics as a selection criterion. These motives
exerted their influence already long before 1863. Our conclusion therefore is
that the introduction of the HBS in 1863, although it was an important
step forward in modernizing the school system, could build on foundations laid
in the time before.