There is growing concern in Europe that some students are not well-equipped to start a Bachelor's or Master's programme, especially when the programme has a strong mathematical focus. In particular, attention is drawn to problems with mathematics in the transition from secondary to higher education. Higher education expects a certain level of…

This paper discusses the theories of conceptual change and how they explain the difficulties in mathematics learning, especially in enlarging the number concept. Two studies are presented, one of which examines the research questions: What is the role of prior knowledge in students' answers to questions about the density of rational and real…

The planning of an introductory calculus textbook in classical mechanics is shown as an example of an approach to textbook design that uses four main cognitive categories: sources of learning, instruments of learning, processes of knowing, and mechanisms of knowing. The aspects, domains, description, and elements of each section of the textbook…

Reports on the design considerations involved in the development of a series of interactive videodisc modules in pre-calculus mathematics. Topics discussed include math deficiencies and anxieties at the college level; videodisc and microcomputer technology; instructional design; learning theories; and the results of two field tests in secondary…

This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In…

In the late 1990s failure rates in a first-year introductory calculus course at the Norwegian University of Science and Technology reached peak levels. This paper reports on findings from an action research project that was set up in 2002/2003 to improve the situation. The study confirms that students approach their tasks differently which…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…