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.


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:
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.