(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

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.

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

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