Jacob de Gelder (1765--1848) and didactics of mathematics (Q2785378)

The article starts with a short biography of Jacob de Gelder, who became a prominent figure in Dutch 19th-century mathematics teaching. Though not educated in neither a Latin school nor a university, he not only became a professor, first at the Military Academy in Delft (1815) and later at Leiden University (1819-1840): his didactical ideas were also backed by the government, in 1815 he was influential in making mathematics a compulsory discipline in the Latin school, and in 1827, again on his proposal, participation in ``colleges'' in mathematics didactics were made obligatory for future teachers of mathematics. NEWLINENEWLINENEWLINEThe larger part of the article presents de Gelder's views on the mathematics teaching and its purpose and the way these ideas were implemented in his teaching and in the textbooks he wrote. NEWLINENEWLINENEWLINEThe ultimate purpose he saw as the cultivation of the ability to reason. This view was connected to enlightenment ideals -- sound mathematical reasoning would lead to ``sound philosophy'' in general -- but it also followed from an enlightenment-rooted conviction that education founded on understanding was more efficient than learning by rote.NEWLINENEWLINENEWLINEDe Gelder's understanding of ``reasoning'', however, was not the belief in deductive logic which is mostly implied by this ``formal'' view of educational aims; he emphasized the need to adapt the ways to the individual level of students, to shape their understanding through systematic classroom dialogue. When teaching military engineers he replaced exact proofs by heuristic reasoning and argument from examples, but here as elsewhere he stressed the importance of precise use of language (in what seems to have been a somewhat pedantic way); the latter feature of his approach corresponds to a tendency in his textbooks to ``leave nothing to the fantasy of the reader'' (p. 261) and to make use of a very structured typography. NEWLINENEWLINENEWLINEFrench, German and English 19th-century ideas about mathematics education have received much attention in the literature. The present article is a welcome supplement.