The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

Apprenticeships for adults are one of the policy solutions to the need for supporting adults willing to train, while broadening the skills base of the working population across Europe. According to Cedefop estimates, there are around 128 million adults with potential for upskilling or reskilling in the European Union (EU). EU Member States have…

This short description contributes to better understanding of vocational education and training (VET) in Germany by providing insight into its main features and highlighting system developments and current challenges. Learning on the job is traditional in German education. Work-based learning (WBL) features in most secondary and tertiary VET…

We propose a theory of education curricula as horizontally differentiated by their paces. The pace of a curriculum and the preparedness of a student jointly determine the match quality of the curriculum for this student, so different students derive different benefits from learning under the same curriculum. Furthermore, a change in the curricular…

This paper looks at the importance of mechanisms that give formal recognition to vocational skills acquired through work-based learning and how such mechanisms might be developed. It describes how skill recognition can benefit individuals, employers and society as a whole, and identifies in which contexts skill recognition has the highest…

In instructional multimedia design, it is often recommended that text accompanying pictures be presented in a personalised style to promote learning. The superiority of personalised over formal text is may be explained using social agency theory (Mayer, 2005b), but it has not been investigated empirically whether such effects are valid in…

The title of this document is a deliberate play on the title of the biennial reports on the progress of Bologna produced by the European Students' Union, "Bologna With Student Eyes." It is a way of paying tribute to student involvement in the Bologna reforms, and marking a parallel student working participation in the state system…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

This paper describes the architecture and discusses implementation issues of a scalable Internet-based teaching and learning system (SKILL) being developed at the University of Essen (Germany). The primary objective of SKILL is to cope with the different knowledge levels and learning preferences of the students, providing them with a collaborative…