Project Maths is in the news again with many claims being made for the ‘fact’ that it promotes a deeper ‘understanding’ of mathematics. Is this true? Unfortunately, it is very difficult to define what constitutes ‘understanding’. Ask any physicist what quantum mechanics means and they will shrug their shoulders. They don’t really understand it but they can apply the equations. All that Project Maths will ever tell us is that students have attained proficiency at applying certain types of mathematics in certain (predictable?) contexts.
So what are the origins of the Project Maths initiative? I think one of the main drivers is the almost religious belief of many education theorists in the Problem Based Learning concept. The idea of ‘learning by doing’ is widespread in education, perhaps inspired by the famous quote by Confucius: “I hear and I forget. I see and I remember. I do and I understand”. I think what Confucius actually meant is that we consolidate and strengthen our understanding by practicing whatever we have been taught – not just plunging into doing things with superficial background knowledge, or none at all. As the great Seve Ballesteros said: “To give yourself the best possible chance of playing to your potential, you must prepare for every eventuality. That means practice.” For me, the idea that you can do any meaningful mathematical modelling without spending a lot of time practicing your mathematical technique is nonsense. This is true of lots of things in life, sport being a good example. All sports people spend long hours practicing – they don’t improve if they only compete. In fact, they get worse because they accumulate bad habits that can only be fixed by practice.
I think that one of the fundamental problems in all of this is the fact that T&L has been hijacked by those with a view that education should be ‘engaging’ and ‘relevant’ at all times. In fact, learning a subject like maths requires spending long periods practicing alone. ‘Doing the problems’ has always been the cornerstone of mathematical education but as a supplement to more conventional learning. This is real ‘problem based learning’.
Two more things come to mind when thinking about this whole debate. First is the vaguely expressed link between higher level maths and the ‘knowledge economy’. This is very easy to say and it has a ring of truth about it but what level of maths is routinely used in industry and business? Of course, engineers do a lot of tough maths at college but how much do they use in practice? Who’s solving differential equations out there? Or is it just general numeracy that we are talking about. Is the use of advanced maths quite rare and confined to specialised industries? In other words, do we really need loads of people doing high level maths or should we be worrying about improving the basic mathematical literacy of the population – the ordinary level cohort? These questions need to be answered precisely because there is a lot of waffle going on about, God spare us, the ‘knowledge economy’.
The other point that makes me pause for thought is the prevalence of a utilitarian view of mathematics. There seems to be no sense that maths is worth pursuing for its own sake. Nobody obsesses about the relevance of History or Art or English Literature. Some of mankind’s greatest intellectual achievements are in mathematics. School kids may soon be denied any exposure to many of these achievements and that is sad, especially for those with an innate interest in mathematics for mathematics sake. They seem to have been forgotten in all of this.