Searching through an old computer back up recently, I found this foreword I wrote for a colleague’s book over ten years ago, back in 2004. I found that I still felt I agreed with these earlier views, and that it might be useful to others:
There is a relationship between the human mind, the modern computer and mathematics which is often misunderstood. Indeed over centuries, humankind has used the developing concept of the computer as a metaphor for the mind, and the growing knowledge of the human mind as a metaphor for the computer, and it is now unclear which was the chicken or the egg. This interchange of conceptions suggests a central place for the computer in our culture, that the often heard, but rather dismissive remark, “it’s just a tool”, can underestimate.
It can be persuasively argued that tools and technology have been at the heart of intellectual endeavour since the stone age, and that the sciences and mathematics owe a debt to tools, rather than the reverse, as a source of intellectual development in our culture.
Since mathematical concepts and logic lie at the heart of the computer’s function, it comes as no surprise that the study of mathematics and the use of ICT may be profitably intermingled. The concepts of algorithm, function, operation and set all have concrete manifestation in the world of computers to parallel their abstraction in mathematics. One consequence is that the computer, through the spreadsheet, database, LOGO programming and modelling & simulation environments, has the delightful capacity to make concrete of the otherwise abstract ideas of relationship and process. For example the mathematical variable in algebra is often a mysterious object: “Please miss, tell me how much x is?”. The same (but subtly different) X on a computer, although capable of varying, can always be known as a value at any given time. A spreadsheet cell containing a function always shows an answer, for the moment. Suddenly, elusive mathematical ideas become tangible and may be played with, bringing dead algebra to a ‘what if?’ life.
So far so good – it seems that there is already an impressive case for doing mathematics, practically, with a computer.
But in fact, there is even greater scope, because the computer has added to this capacity for logic and computation a unique facility to integrate and generate visual and dynamic material – multimedia – and to portray the most aesthetically pleasing visual and musical outputs based on mathematical data. Using LOGO and other software to discover geometry empowers us to pin down elusive abstractions with concrete experiences. LOGO also encourages us to benefit from our kinaesthetic, body-centred capacities when solving problems by acting ‘turtles’ ourselves.
In all of these ways, mathematics and the computer can combine to appeal to our multiple intelligences and raise the stakes for capability in learning mathematics.
But sadly, the potential identified here is often missing – why? – perhaps in part because such experiences have not been lived by many of today’s teachers. Hence the purpose of this book: to begin to unlock the genie in the bottle and promote creativity in mathematics teaching and learning through practical advice and relevant detail.
Such advice is legion in this book, with valuable commentary to reassure the inexperienced teacher so that they may tackle both statutory and unspoken expectations, from the National Curriculum and the Numeracy and Literacy Strategies, with carefully explained and justified lesson ideas.
Pupils will also benefit from the appropriate deployment of ICT in Mathematics advocated here: the handling of data and creation of graph & chart which may come from speedy ICT tools and the teacher’s knowledge, enhanced by this book’s exposition, coupled with the generation of their own data and purposes conspire to make the exploration of mathematical concepts both meaningful and relevant. Genuine ‘what if?’ questions may be asked and answered, alternatives judged and genuine inquiry fostered – the ‘quantitative’ improvement in the speed of production brought about by ICT begins to change the ‘qualitative’ nature of engagement with mathematics.
With the confidence that this book will inspire, the truth and beauty that excites successful mathematicians may begin to be appreciated by a much wider audience of teachers and learners, and the symbiotic relationship between our society and its most powerful tools may be continued, to all humankind’s benefit.
Reader, Ultralab, Anglia Polytechnic University