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…

These analyses form part of a three-year project looking at mathematical thinking as a socially organized activity. We revisit data from a University Calculus class using tools from two theoretical perspectives, used increasingly in mathematics education research: (1) semiotic mediation; and (2) discursive practices. We highlight how different…

This paper presents preliminary hypotheses about the relationship between faculty goals for the introductory calculus-based physics course and their beliefs about student learning of problem solving. All faculties have problem solving as a major goal for their courses. There appears to be however, an instructional paradox. When discussing how…

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…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

Explores what kinds of calculus-related insights seem to typify calculus-related reasoning. Introduces "qualitative calculus" in which learning is focused on synthesis. Discusses the resemblance and difference between traditional calculus and qualitative calculus, advantages of learning qualitative calculus, and how understanding qualitative…

Describes the development and implementation of a Web-based calculus course at Texas A & M University. Discusses the course design, layout of content and the contrast with textbook structure, results of course surveys that included student reactions, and how students learn form Web-based materials. (Author/LRW)

The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

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…

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…