This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students' methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students'…

In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable…

Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

There is a call for change in College Algebra. The traditional focus on skill development is failing, resulting in withdrawal and failure rates that are excessive. In addition, too many students who are successful do not continue on to take a successive mathematics course. The Institute for Mathematics Learning at West Virginia University has been…

This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions involving…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

Most research in the area of Computer Algebra Systems (CAS) has been designed to compare the effectiveness of instructional technology to traditional lecture-based formats. While results are promising, research also indicates evidence of the steep learning curve imposed by the technology. Yet no studies have been conducted to investigate this…

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

New information technologies can act as a Trojan horse offering activities that will require major changes in the teaching-learning process. Computer aided learning applications are able to offer advanced students the opportunity to improve their skills and to maintain their motivation. In the spirit of "learning by doing", they are encouraged to…