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Maple 'down-under' in Engineering Mathematics Education

GF Fitz-Gerald & G Keady
Australia

The ‘down-under’ word-play in the title of this paper alludes to the fact that Maple is embedded in a number of products: for example Matlab’s Symbolic Toolbox, Mathcad, MapleTA, AiM and WebLearn. Maple is also being used as a publishing medium: see, for example, the recent maple-10 eBook by Lopez, on “Advanced Engineering Mathematics”.

The purpose of this article is to review how Maple, and the related products listed above, have been used in the past, and to predict their use in the immediate future in supporting Engineering Mathematics teaching at some Australian universities. (Maple is of course not the only Computer Algebra (CA) package available, there being both commercial competitors notably Mathematica, and free open-source packages such as Maxima and AXIOM). There are many differences between teaching paradigms in Australian universities so the authors’ predictions are based on what they anticipate might happen in their own universities.

The authors continue to feel that, at least at their universities, expecting first year students do their own programming in a symbolic manipulation package is not such a good idea. They see the important task is to get students to think, and sometimes the minutiae of syntax difficulties, for example, might obstruct this. However, exposure to maths packages isn’t only about a student’s own use of them, but that a lecturers’ use, demonstration of their capabilities, use of graphics capabilities and so on, is essential. The appropriate message is that real engineers and mathematical scientists use relevant mathematics software when needed to support the modelling process. In many universities (and UWA is an example) it may be decided that students need not program CA in their first year. The CA support can be delivered in task-specific ways, for example using maplets delivered via MapleNet. In this way students have access to the relevant algebra without having to develop their own programs. Different universities will continue to make different decisions in connection with the level of usage of CA especially at first year level.

In the past, specifically 1988–97 (Australia’s bicentenary seems a suitable date to start the period) student computer laboratories were almost the only place for student’s to experience CA. From 1998, students’ home computers, and web-delivery of materials, began to take centre stage. Today, a minority of students are using their own notebook computers; and this minority is growing.

Many universities are investigating the possibility that, at least in the more technical areas, such as Engineering, a laptop computer (made more affordable by bulk buying) might be included as a part of the student’s tuition fees. As early as 1995, Rose-Hulman University in the USA had arranged this, so it certainly is possible. But, portable computing is possible in other ways too, and where the mass-market takes us in regard to integrated mobile communications and computing is anybody’s guess.

A range of developments in the use of graphics calculators in Higher Education (HE) and Secondary levels has been led by Murdoch University’s Education School, Swinburne University and Edith Cowan University. Some high-end graphics calculators include (limited) symbolic manipulation capabilities. All previous meetings of ATCM boast many workshops discussing such handhelds and scholarly papers describing their innovative use.

Maple is available for the Cassiopeia—Cassio’s WindowsCE hand-held computer but the authors are unaware of any Australian University using this product.

Nevertheless, it is these authors’ contention that computing power, screen size and pixel resolution of desktop and notebook computers affirms the choice of these platforms for serious Engineering work. The competitive price of low-end notebook computers also means that such technology is also now within the grasp of most students.

Symbolic manipulation is currently used in many institutions at all levels (Technical and Further Education (TAFE) as well as HE). (In Victoria, Mathematical Methods (CAS) Units 1–4 is now a parallel and alternative subject to the more traditional Mathematical Methods Units 1–4 offered at the Secondary level which is currently required for entry into most Engineering schools.) Their use currently ranges from none (including some Engineering Mathematics examinations for which any calculator is prohibited) to their complete use together with access to pre-developed worksheets.

There is an urgent need to get the balance “right” in all this. The authors of this article believe that symbolic manipulation packages are best considered as a tool to support the understanding and development of mathematical thought. Attempting to use the tool too early in the introduction of new topics, and as a replacement for genuine pen-and-paper calculations, is fraught with educational dangers.