Barry Kissane

In recent years, calculators have become common objects in primary school classrooms, as they also have in other places, including homes and shops. Being accessible to children is, however, no guarantee that calculators will be educationally beneficial, and some have even suggested that they might be harmful. An important part of the legacy of Derek Hurrell, reflected throughout this book, is that children might learn about mathematics if given appropriate tasks and opportunities to engage productively with them in a supportive environment...

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning about irrational numbers, of key significance to the study of the real number system, characterising lower secondary school mathematics.

Although scientific calculators are potentially useful for undertaking arithmetic computations, this is not their most important educational purpose, as claimed by Kissane and Kemp (2014) and Kissane (2015); other calculator roles of representation, exploration and affirmation offer important perspectives on the place of the calculator in student learning. Despite such arguments, it seems that many still regard the calculator as a computational tool, and not a learning tool; one purpose of this paper is to challenge that view…

Although advanced scientific calculators of recent years include many features intended for educational use, they are still frequently misunderstood as mostly devices for numerical computation. Following a model for the educational use of calculators, this article describes and illustrates several ways in which the use of a calculator facility to construct tables of values can have educational value in the secondary school. Examples include the study of linear and quadratic functions, algebraic equivalence, equations, sequences, series, limits, convergence, differentiation and integration. The article concludes by observing that the educational value of calculators derives from the experiences they offer students, not merely from their capacity to generate numerical answers.

Mathematics is often interpreted as a ‘useful’ activity, with limited attention paid to its potential to be significant for other reasons. While utility is of course important, it is of diminished significance if students are not engaged with, interested in or attracted to mathematics. Many mathematicians and others over time have drawn attention to the beauty of mathematics and its deep aesthetic qualities, and mathematics is connected richly to our collective cultural heritage. One of the broad aims of mathematics education is to develop positive attitudes towards mathematics; while syllabuses make reference to this broad aim in different ways, it is often hard to see how it is addressed explicitly in official documents. In this chapter, we first consider some ways in which mathematics is connected to a wider world beyond its practical applications. We address in particular the significance of some of the aesthetic aspects of mathematics and its cultural heritage, both its history and contemporary views of its place in the world.

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.

Mathematics is often interpreted as a ‘useful’ activity, with limited attention paid to its potential to be significant for other reasons. While utility is of course important, it is of diminished significance if students are not engaged with, interested in or attracted to mathematics. Many mathematicians and others over time have drawn attention to the beauty of mathematics and its deep aesthetic qualities, and mathematics is connected richly to our collective cultural heritage. One of the broad aims of mathematics education is to develop positive attitudes towards mathematics; while syllabuses make reference to this broad aim in different ways, it is often hard to see how it is addressed explicitly in official documents. In this chapter, we first consider some ways in which mathematics is connected to a wider world beyond its practical applications. We address in particular the significance of some of the aesthetic aspects of mathematics and its cultural heritage, both its history and contemporary views of its place in the world.

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