Barry Kissane

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…

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.

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.

Scientific calculators are sometimes regarded as important only for obtaining numerical answers to computational questions, and thus in some countries regarded as inappropriate for school mathematics, lest they might undermine the school curriculum. This paper argues a contrary view that, firstly, numerical computation is not the principal purpose of scientific calculators in education, and secondly that calculators can play a valuable role in supporting students’ learning. Recent developments of calculators are outlined, noting that their principal intention has been to make calculators easier to use, align their functionality with the school mathematics curriculum and represent mathematical expressions in conventional ways. A model for the educational use of calculators is described, with four key components: representation, computation, exploration and affirmation. Examples of how these might impact positively on school mathematics are presented, and suggestions are made regarding good pedagogy and curriculum with calculators in mind. The paper concludes that scientific calculators represent the best available technology to provide widespread access to some ICT in the mathematics curriculum for all students in the SEAMEO region.

Although the term is often used to denote electronic devices, the idea of a 'technology', with its origins in the Greek techne (art or skill), refers in its most general sense to a way of doing things. The development and availability of various technologies for computation over the past forty years or so have influenced what we regard as important in mathematics, and what we teach to students, given the inevitable time pressures on our curriculum. In this note, we compare and contrast current approaches to two important mathematical ideas, those of square roots and of integrals, and how these have changed (or not) over time.

Calculators have been around for about forty years or so now. There are many different species of them. Some are used in offices, some are built into devices, such as cash registers or rulers, some are on phones and some people even have them on their wrists in the form of a watch. There are online calculators, home loan calculators, superannuation calculators and the bank manager will probably pull out a financial calculator if you enquire about a loan or an investment. There is an almost uncountable number of calculator apps available for high-tech devices like tablets and smartphones. What these calculators have in common is that they calculate answers to numerical questions. That's why they call them calculators, and it's also probably why so many people only think about them in only one way...

Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have been designed to support secondary school mathematics education at various levels, including much more powerful ways than merely providing numerical answers to arithmetical questions, and continue to be one of the few technologies designed expressly for educational purposes. In light of economic realities, it is argued that calculators provide the most affordable mechanism for developing countries to provide students with access to technology in mathematics. A major element of calculator use involves individual exploration of mathematical ideas, for which a personal technological device is ideally suited. Support for the work of teachers is recognised as critical for integrating technology into the mathematics curriculum.