What is "doing mathtematics" now that technology is here?

Abstract

All over the world people say that mathematics is difficult and a problem. This is just as true in technologically rich countries as in others. "Doing mathematics" is widely perceived by the general population as carrying out simple arithmetic or as manipulating symbols. However it is much more than this, and rapid advances in technology give the opportunity to broaden perceptions of what doing mathematics is now.

Essentially "doing mathematics" may be seen as being about communicating ideas and ways of solving problems. Symbolic language is only one of the ways of doing this, but unfortunately this way is restricted to a minority of people. Many find this symbolism too demanding and too abstract, and consequently cannot use mathematical ideas which would be helpful to them.

Now that there is a wide range of powerful mathematical and other technology, both cheap and expensive, which support the mechanics of "doing mathematics" (such as CAS), we might ask what skills and knowledge remain or become essential.

Problems are often stated in words or pictures, so it certainly remains essential to be able to communicate in the sense of being able to translate from words into mathematical language and vice versa - in other words to formulate problems, and to interpret their solution. In fact while mathematicians require formal proof, most people will be happy with a persuasive argument. Thus the mathematical communication must be appropriate to the audience. Technology will always give an answer but just as important is to make sense of that answer and to validate it.

The whole range of technology is having an impact on mathematics, and not only specific mathematical machines and packages. Opportunities to apply mathematics are enhanced by digitised film, recorded sound, and easily used data gathering devices, now being integrated through packages such as Motion, Sound, TI-Interactive and the CBL/CBR. Thus numbers and pictures generate and motivate engagement with mathematical problems, as well as suggesting ways in which answers can be presented appropriately.

In this paper we describe some of our experience in modifying our practice to accommodate technology. We also raise some of the questions we are still having to ask, such as what constitutes the "basic skills" of mathematics, including basic symbolic manipulation skills, now and in the future.