Graphics calculators
and mathematics education

Graphics calculators are around the same size as scientific calculators and include a graphics screen rather than only a numerical display screen. (Four current models, one each from the four current manufacturers, are shown on this page.) Consequently, with suitable software included in a graphics calculator, they can be used to undertake various kinds of mathematical work. The possibilities include graphing functions, tabulating functions, analysing statistical data and manipulating matrices in addition to various numerical activities such as computation, equation solving, numerical differentiation and integration, random simulation and financial mathematics. Graphics calculators can be programmed, so that users can customise the calculator to perform particular tasks of interest to them.

Not surprisingly, technology of this kind is of very considerable importance to secondary school and early undergraduate mathematics, since it has the potential of providing access to technology for very many more students than do microcomputers. In affluent countries like Australia, it is not unreasonable to expect that all students studying mathematics from around the middle of secondary school can be provided with personal access to a graphics calculator. (Already, a graphics calculator costs less in real terms than did a scientific calculator in the late 1970's, when they were first introduced to schools.)

Even in less affluent countries, the cost of a single computer and the cost of a class set of graphics calculators are comparable, and it is difficult to argue that a class of students will gain more educationally from a single computer shared among all of them than access to a personal and portable calculator with some of the above capabilities.

A good deal of my time recently has been spent on various aspects of the use of graphics calculators. The links below elaborate some of this work:

 

Algebraic calculators

In the past few years, graphics calculators that can deal with the symbolic manipulations associated with school algebra and calculus have been developed. Three current examples of these are those manufactured by Casio, Hewlett-Packard and Texas Instruments, each of which has a CAS (Computer Algebra System) incorporated into its design. Such calculators have been mainly directed at undergraduate and professional users, although the recent models have a sharper focus on the secondary school context. The interactive demonstration of Casio's Algebra FX 2.0 is a good example of this change of emphasis. At present, such calculators are not usually permitted in formal examination systems. (The restriction of calculators to those not having a QWERTY keyboard rules out palm-top and lap-top technologies from such settings. Thus, the Texas Instruments TI-92 was originally banned from the College Board's Advanced Placement Calculus examination, but the TI-89 is not, even though it has a more powerful CAS.) Consequently algebraic calculators are mainly of interest within schools for whom such a constraint is not an impediment to their use. It seems likely that the technology will become more affordable to many students and thus of more interest to schools in the near future. At the very least, the existence, and increasing affordability, of such calculators may provoke some reconsideration of the mature and purpose of school algebra and calculus, both dominated for many years by symbolic manipulation procedures. A paper of mine at the 1999 ATCM conference concerns several of these issues.

 

Need some help?
Beginning users of graphics calculators sometimes need a little help with calculator operations, and calculator manuals are not always clearly indexed (or even clearly written). I may be able to save a little frustration by offering a limited amount of help to beginners.