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…

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.

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.

Technology for learning mathematics and for STEM more generally can take many forms, but this paper argues that the most likely technology to have an impact for all students in many ASEAN countries is the scientific calculator. Integration of technology into mathematics education in the twenty-first century requires good technology, an appropriate curriculum, well-educated teachers and an assessment regime that recognizes how important technology is for mathematical activity. While popular misconceptions that a calculator is only helpful for arithmetic persist, a four-part model for understanding the educational potential of scientific calculators is described and exemplified, recognising the significance of representation, computation, exploration and affirmation. Alternatives to scientific calculators include online calculators with visual and computer algebra capabilities, which might be appropriate provided the educational environment supports their use in all aspects of education, including formal assessment. The paramount significance of the teacher for successful integration is highlighted.

Although officially approved for use in the Singapore secondary curriculum, including examinations, scientific calculators are still often misunderstood as devices solely for arithmetic computation and even at times regarded as unhelpful for students learning mathematics. Yet the development of calculators in recent decades has been focused on their use as educational devices, and the design of calculators has been heavily influenced by the needs of secondary school students. In this paper, we first consider the educational potential of calculators in education, drawing on a model developed for this purpose. We then focus on the educational design of tasks and activities using calculators for various educational purposes, including the development of mathematical concepts and important processes such as reasoning and modelling. Attention focuses on the design of experiences that incorporate modern calculator capabilities and their affordances for important learning goals, as well as the implementation of these in classrooms. Examples and analysis of some appropriate tasks are provided.

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 recognizing some calculator features not available to young 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.