Recently, during the course of some random online reading, I discovered a technical term that neatly fits a set of observations I'm sure are familiar to everyone: "mathematics anxiety". This is not a new term, or a new phenomenon; a measurement scheme for maths anxiety was devised in 1972, and I'm certain every generation has among its members those who squirm when looking back on high school algebra.
Why though, does poor old maths deserve such special lexical attention? There is - as far as I'm aware - no psychometric test or technical term to describe a fear of learning geography, literature or law. What sets maths apart? Is the difference intrinsic or a result of our approach to teaching?
A recent conversation with a friend shed some light on these questions. This friend, a middle-aged electrician, was discussing his newfound interest in maths; an interest that grew after reading several popular-science books. He explained that in high school he had never excelled at mathematics, nor had he found it appealing in the slightest. His formal education in maths had seemed arcane and irrelevant: a set of intricate rules and techniques that were never explained, rarely applied, and quite difficult to memorise and implement. His recent experiences, he said, had been shocking precisely because they were so unlike his memory of the field. He described in particular how fascinating he found a book about the origin of mathematical constants such as Pi. In his words, he found it so enthralling that he "couldn't believe it wasn't taught at school".
Is this an accurate summary of the situation today? If so, what is being taught in the schools, if not the fundamentals my friend found so engaging? My personal experience indicates that not much has changed. From early high school the focus of maths education is to instil technical "competency". The focus is on techniques, breadth of study, and - to some degree - problem solving. A curriculum is judged to be acceptable if students are exposed to basic knowledge across numerous sub-disciplines, and positively brilliant if students are capable of solving "complex problems".
This is a curriculum that excels at preparing students for, say, engineering, or the statistics encountered in commerce and psychology, but fails utterly when it comes to inculcating an appreciation for mathematics. To find a subject interesting, engaging, relevant, a student must be made to understand "why" things are as they are, not just the "how". Regardless of how capable a student is at maths, it is simply impossible to garner any enjoyment from repeating "exercises" ad nauseam, or memorising formulae.
The first defence of the status quo is to claim that whether or not maths is enjoyable is a moot point. This viewpoint sees maths as a demanding field that is by nature not enjoyable, but a necessary tool, and inevitably an acquired taste. I take issue with this on a number of points.
First, I wonder whether these same individuals would make an argument for chemistry classes without practical demonstrations, distilling the discipline into masses of rote memorisation. Wouldn't it be boring? Intimidating? Impossible? It"s the equivalent of the mathematics education that is being advocated.
Second, to view maths as a means to an end, a tool for the natural sciences, would raise eyebrows (and tempers) among mathematicians. Many well-known mathematicians have claimed that the only mathematics they found appealing was often entirely useless.
What should be brought into the classroom to make mathematics understandable and enjoyable? In general, I would like to see a mathematics curriculum that does not march inexorably towards the goal of utility. Granted, calculus is "useful", the nature of infinity less so.
But for the majority of students who study typical senior mathematics courses, the rigour and technical aptitude instilled simply goes to waste. Only those students who go on to highly mathematical fields - engineering, econometrics - really benefit from their thorough grounding. Wouldn't a curriculum that reserved the rigmarole of technique for the extension subjects serve students better?
Basic maths courses could take the time to delve into some of the truly intriguing areas in mathematics that are now barely touched on. This sort of curriculum would not have to sacrifice anything in the way of "difficulty": the curriculum could simply be made difficult in the right way. Students could be challenged with problems of logic and understanding, instead of problems of technique-regurgitation. Most importantly, we could produce a generation of students who go on into their non-mathematical lives not with a head full of useless techniques, but an understanding and appreciation for mathematics as an art.