Graphics calculators in upper secondary courses

This paper has been produced on request of the Secondary Education Authority, as part of a process of considering the potential impact of graphics calculators on upper secondary school courses. The paper provides background on this matter for the Authority and for committee members, including syllabus committees that may be affected by the decision to permit the use of graphics calculators in Tertiary Entrance Examinations

Evaluating normal probabilities on a graphics calculator

One of the strengths of a graphics calculator is the potential it offers for students to explore mathematical ideas from a few different perspectives. A good example of this involves the normal probability distribution, frequently encountered in senior secondary courses involving statistics. This note describes a few ways in which the Casio cfx-9850G series of calculators can be used to evaluate normal probabilities

Graphics calculators and algebra

The personal technology of the graphics calculator is presently the only one likely to be available widely enough to influence curriculum design and implementation on a large scale. The algebra curriculum of the past is overburdened with symbolic manipulation at the expense of understanding for most students. But algebra is much more than just symbolic manipulation. Connections between some aspects of algebra: expressing generality, functions, equations and advanced algebra and some graphics calculator capabilities are briefly described. It is suggested that these kinds of connections need to be taken into account in developing the algebra curriculum as well as in classroom teaching

The design and use of eActivities for learning mathematics

The recent development by Casio of the hand-held ClassPad 300 device raises a number of important questions for the design of mathematical learning experiences for students. This paper provides a brief description of the ClassPad 300 and its mathematical capabilities, followed by a description of the idea of an eActivity, well provided for in the operating system of the device. As their name suggests, eActivities are electronic learning activities, designed to be used by a student with a personal hand-held ClassPad 300. Designing suitable eActivities requires decisions to be made about the suitability of various pedagogical approaches that might be accommodated. These approaches include exposition or authoritative presentation, controlled practice of skills, open exploration and discovery. The ClassPad 300 offers ways of connecting mathematical ideas together within an eActivity that can be taken advantage of with these various approaches. Examples of recent eActivities are presented and briefly analysed . Practical design issues are provided and illustrated through examples. The paper concludes with an assessment of the prospects of the idea of an eActivity for student learning of mathematics

Geometry meets the computer

In a rather short space of time, computers have changed in character from being large numerical devices that could only be communicated with obliquely to small visual devices that allow for much more direct forms of person-machine communication. We have gone from the roomfull to the pocketfull, from paper tape and punched cards to keyboards, mice and touch screens and from strings of binary digits to visual images. All of this has taken not much more than one (human) generation. The IBM Corporation confidently predicted in 1945 that there would never be a market for more than two or three computers in the world, and yet in affluent countries like Australia, there are already many households with more computers than that, depending a bit on how one defines 'computer'

The importance of being accessible: The graphics calculator in mathematics education

The first decade of the availability of graphics calculators in secondary schools has just concluded, although evidence for this is easier to find in some countries and schools than in others, since there are gross socio-economic differences in both cases. It is now almost the end of the second decade since the invention of microcomputers and their appearance in mathematics educational settings. Most of the interest in technology for mathematics education has been concerned with microcomputers. But there has been a steady increase in interest in graphics calculators by students, teachers, curriculum developers and examination authorities, in growing recognition that accessibility of technology at the level of the individual student is the key factor in responding appropriately to technological change; the experience of the last decade suggests very strongly that mathematics teachers are well advised to pay more attention to graphics calculators than to microcomputers. There are clear signs that the commercial marketplace, especially in the United States, is acutely aware of this trend. It was recently reported that current US sales of graphics calculators are around six million units per year, and rising. There are now four major corporations developing products aimed directly at the high school market, with all four producing graphics calculators of high quality and beginning to understand the educational needs of students and their teachers. To get some evidence of this interest, I scanned a recent issue (April 1995) of The Mathematics Teacher, the NCTM journal focussed on high school mathematics. The evidence was very strong: of almost 20 full pages devoted to paid advertising, nine featured graphics calculators, while only two featured computer products, with two more featuring both computers and graphics calculators. The main purposes of this paper are to explain and justify this heightened level of interest in graphics calculators at the secondary school level, and to identify some of the resulting implications for mathematics education, both generally, and in the South-East Asian region

Teaching and learning trigonometry with technology

Modern school classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of trigonometry in the secondary school. We identify some of the ways in which the teaching of trigonometry might be supported by the availability of various forms of technology. We consider circular measures, graphs of functions, trigonometric identities, equations and statistical modeling and focus on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with trigonometry, both trigonometric and circular functions. Many of these opportunities for learning were not available before technology development and access within schools we enjoy today. This paper suggests some of the avenues for exploration

Graphics calculator use in examinations: accident or design?

As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be used to help design examinations in which students are permitted to use graphics calculators as well as to interrogate existing examination practice

Understanding what you are doing: A new angle on CAS?

Powerful Computer Algebra Systems (CAS) are often used only with reluctance in early undergraduate mathematics teaching, partly because of concerns that they may not encourage students to understand what they are doing. In this exploratory study, a version of a CAS that has been designed for secondary school students was used, with a view to considering the value of this sort of student learning support for first year undergraduate students enrolled in degree programs other than mathematics. Workshops were designed to help students understand aspects of elementary symbolic manipulation, through the use of the Algebra mode of an algebraic calculator, the Casio Algebra FX 2.0. The Algebra mode of this calculator allows a user to undertake elementary algebraic manipulation, routinely providing all intermediate results, in contrast to more powerful CAS software, which usually provides simplified results only. The students were volunteers from an introductory level unit, designed to provide a bridge between school and university studies of mathematics and with a focus on algebra and calculus. The two structured workshop sessions focussed respectively on the solution of linear equations and on relationships between factorising and expanding; attention focussed on using the calculators as personal learning devices. Following the workshops, structured interviews were used to systematically record student reactions to the experience. As a result of the study, the paper offers advice on the merits of using algebraic calculators in this sort of way

Graphics calculators in the mathematics curriculum: Integration or differentiation?

Graphics calculators are examples of powerful technologies that we want our students to learn to use well. However if we use them in our courses only for learning, students will not regard them with due importance because they are not integrated into the assessment. On the other hand, if graphics calculators are integrated into both learning and assessment there are risks associated with students becoming calculator dependent, issues of equity arise associated with calculator access and there may be problems with setting an appropriate examination. We discuss this dilemma in the light of our experiences and the reactions of our students over the last two years