During the last 10 years Danish university teaching has been confronted with several new challenges.
The classic well known university study tradition established by Immanuel Kant and Wilhelm von Humboldt and introduced in Denmark by the famous philologist Johan Nicolai Madvig (1804-1886) has now been replaced with other ideals (Flexner 1930, Gibbons 1994, Humboldt 1792, Huxley 1876, Jaspers 1923 and 1946, Kant 1798, Korsgaard 2004, Petersen 1993). In the classic tradition "the free academic study" with no narrow limitations and with an individually high degree of intellectual absorption the students could form their own academic personality. In this tradition famous Danish scientists such as Niels Bohr, Harald Bohr, August Krogh, Johan Ludvig William Valdemar Jensen, and B0rge Jessen were taught during their studies at the University of Copenhagen.
In the first half of the 20th century only a few per cent of the Danish population were educated at high schools and at the universities. The high school teaching and the university studies were for the few privileged, but in the 1960ies this changed considerably. Many more young people got a high school exam on a relatively high academic level and many more were matriculated at the Danish universities and got an academic degree (Damberg 2006). Still the university teaching was based on the tradition from Kant, von Humboldt, and Madvig.
After 1990 the high school teaching was changed in several steps. First of all many new subjects, that were not academic and were not taught at the universities, were introduced in high school teaching and at the same time the professional level in many subjects such as mathematics, physics and linguistics was reduced in a disastrous way (Damberg 2006). The students at high school were no longer trained sufficiently in basic academic and scientific methods, and when they started their university studies they got so many problems in their learning, that many dropped out very fast and many others were not able to pass their first year university exams. These problems increased substantially after the year 2000.
Also after 2000, and especially after 2003 when a new legislation for the Danish universities was decided by the Danish parliament, the classic ideals for university studies have been changed. The free study has been replaced with short well determined courses and many exams, such that the students should be able to obtain a university degree faster than before. But this also implies that the university education must be very efficient with very definite courses such that it has become difficult for the students to obtain a deeper and abstract understanding of their syllabus. At the same time the Danish universities were transformed from classic universities into mass universities with many students. The classic ideals were replaced with other ideals based on management principles. This is a development that is also known from other western countries (Damberg 2006, Kaufer 2000, and Olesen 2007).
The very increasing gap between the aim of the university education on a high academic level and the poor knowledge and the bad study ability the students now have from high school has become a more and more substantial problem for basic university teaching. In 2007 approximately 30 percent of the first year students at The Department of Economics were not able to pass their written exam in mathematics. This percentage has been only around 15-20 before 2003 and therefore something to prevent this catastrophic development had to be done (Olesen 2007). In this paper it is told how we managed this big problem in 2008, and it is also told how we are building up a new way of substantial academic teaching with future perspective for first year students.
Mathematics At The Department Of Economics
Mathematics is taught at several institutes at The University of Copenhagen. …