ABSTRACT
Secondary schools in Europe as preparation for university studies started taking shape in the early 1800s as public, secular institutions; preparing for higher education, with a predominantly classical curriculum, taught by specialist teachers trained at the universities (Anderson, 2004). The models were the Prussian Gymnasia and the French lycées.
In 1805, the Danish State established the Royal Directorate of the University and the Learned Schools. In 1809, the former cathedral schools in Denmark were transformed from theological seminaries to schools offering general preparatory education for officials. Thus, organization of secondary education was transferred from the church to the state.
Bessastadir Learned School was established in 1805 as a merger of the two cathedral schools in Iceland. The Bessastadir School belonged to the Danish Learned School system, which underwent reforms of curricula in mathematics, science, and modern languages in the early 19th century under German influences (Poul Heegaard, 1912).
Björn Gunnlaugsson (1788–1876), son of a poor tenant known for inventions, studied mathematics at the University of Copenhagen in 1817–1822, and worked at land-surveying with Professor Schumacher in Altona during summers. Gunnlaugsson became a mathematics teacher at the Bessastadir School in 1822–1862. He raised the standard of mathematics teaching and initiated science instruction, using Danish textbooks, among them ones by L.S. Fallesen. During summers of 1831–1843, he made geodetic surveys as a basis for a scientifically drawn map of Iceland, published in 1844 by the Icelandic Literary Society.
During its time in 1805–1845, the Bessastadir School became a centre of culture and education in a country devoid of other schools or institutes. Its lecturers gave open lectures about classical works as well as modern sciences, such as the epic poem of Odyssey, the Icelandic literary heritage, astronomy, and land surveying. Their works were published by the Literary Society, whose goal was to further general education in Iceland and present the latest knowledge to Icelanders.
In 1865, the Literary Society published the first book in Icelandic on higher arithmetic and number theory. The book, Tölvísi, written by Gunnlaugsson, deepened topics in the Danish textbooks: divisibility by primes and methods of approximation. After introducing general arithmetic in whole numbers and fractions, Gunnlaugsson moved to Fermat’s Little Theorem. While Fallesen treated Fermat’s theorem in four pages, Gunnlaugsson went into details in its role in divisibility by primes, and its relation to periodic fractions. Then he explained chain fractions for approximation to infinite decimal fractions, quadratic and cubic roots.
Tölvísi proved an incomprehensive reading for most Icelanders. Only 400 pages were printed. The remaining topics: equations of first, second, and higher degrees, proportions, logarithms, interests, permutations, and combinations, might have been useful to the growing classes of merchants and craftsmen, but were never printed.
SELECTED BIBLIOGRAPHY
Anderson, Robert D. (2004). The idea of the secondary school in nineteenth-century Europe. Paedagogica Historica, 40(1–2), pp. 93–106.
Gunnlaugsson, Björn (1865). Tölvísi. The Icelandic Literary Society.
Heegaard, Paul (1912). Der Mathematikunterricht in Dänemark. Gyldendal.