Barry Kissane

Advanced scientific calculators, developed in recent years, include more sophisticated capabilities than original models, including some of direct relevance to elementary calculus. In this paper, some relevant calculator capabilities are described and their potential use for students and teachers of elementary calculus are illustrated and evaluated, against the framework of a model for learning mathematics with calculators. Despite the name of such devices, calculators derive their educational value from processes other than mere calculation. Key ideas of continuity, convergence, limits, differentiation and integration can be both represented and gainfully explored on an advanced scientific calculator, supporting student learning in powerful ways not otherwise available to many students in Asian countries.

This paper identifies a problem that calculators are often interpreted as devices whose sole purpose is to undertake numerical calculations, with the result that their educational significance in secondary schools is not understood well, in contrast to other forms of ICT, for which the software capabilities are recognised as the key features. It is suggested that the potential for educational use of calculators in many Asian contexts is undermined by this limited understanding of their capabilities. An important use of calculators in secondary schools beyond mere calculation involves mathematical exploration, which is described in the paper. Several examples of ways in which features of scientific calculators might be productively used for mathematical exploration are outlined, to indicate the range of contexts of relevance. Ways in which such features might be used in schools are described

Over the past two decades, graphics calculators have been prominent in many discussions of technology in mathematics education. This paper describes how they have become part of teaching, learning and assessment in school mathematics in each of three different countries: Australia, Singapore and the United States of America, as well as directions for future use. Critical issues associated with effective implementation of graphics calculators into the school mathematics curriculum are highlighted, including the nature of school mathematics, examination practices, Computer Algebra Systems, the support of teachers and students, curriculum change and development, the focus on learning, dealing with inherent limitations of graphics calculators, school and university differences, future technologies.

It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation, calculation, exploration and affirmation) is highlighted and illustrated, mostly with relatively unsophisticated modern calculators such as those widely accessible to students in Years 6–10, but also recognising some calculator features not available to younger Australian students. Intelligent use of calculators at these levels of schooling offers many opportunities for students to develop a solid understanding of key aspects of mathematics through their own actions, provided our apparent obsession with calculators as merely ‘answering devices’ is overcome.

Calculators can be used effectively for mathematics education in a number of ways, although frequently they are regarded merely as devices for undertaking computations. In this analytic paper, we describe and illustrate a four-part model to understand more fully the potential role of calculators for learning mathematics. The four elements of the model include representation, computation, exploration and affirmation. Effective use of a calculator by students learning mathematics will often involve more than one of these four components. The model has been derived from analysis of educational materials developed to support rich calculator use.

Calculators have frequently been regarded only as devices to perform calculations and thus often regarded with disapproval by mathematics teachers. With the availability of sophisticated technologies in many settings, it seems that the potential for scientific calculators has been neglected recently, and developments in this technology not adequately exploited. This is of particular significance in developing countries, where resources are limited. In this analyti c paper, we highlight some opportunities created for conceptual development with regular access to a modern scientific calculator. The focus is on the development and deep understanding of mathematical concepts, widely recognized as of prime importance to student learning. The analysis is illustrated with examples related to the multiple representation of concepts and to the use of an advanced scientific calculator to provide numerical experience of important mathematical concepts .

This paper describes and analyses some of the discontinuities observed as students move from senior secondary school mathematics classes to undergraduate studies in a range of quantitative disciplines, with a view to understanding the sources of these discontinuities and the associated teaching and learning practices. The major vehicle for the analysis concerns practices related to the use of technology in formal assessment, particularly the technology of calculators. The paper explores how decisions are made by university staff regarding the use of technology in assessment, and how this is related to the use of technology in teaching and learning. The paper draws on two data sources. The first of these is an Australia-wide survey of assessment practices in universities related to the use of technology by students. The second involves a case study of assessment practices related to calculators in university examinations at one particular university. The paper concludes by offering advice on strategies for improving the coherence of teaching, learning and assessment in universities regarding technology use and for reducing some of the discontinuities in practice between schools and universities.

Developers of mathematics curricula make choices regarding the kinds of technology that are to be used by students, which in turn influences the work of both students and teachers to learn and teach mathematics. This paper analyses the potential relationships between calculators and the mathematics curriculum, drawing implications for what can be learned through student access to different levels of calculators. Three different levels of calculators are considered in detail in the paper: scientific calculators, advanced scientific calculators and graphics calculators. Significant consequences of these choices are described and exemplified through a consideration of a number of mathematical topics that are commonly taught in many curricula in Asian countries.