I had a conversation with a colleague about why people find mathematics difficult. We agreed that this question could only be answered by first understanding what mathematics is. People engage in mathematical activity all the time. They can distinguish one thing from another, appreciate the relationship between doing and undoing, they can see that ordering fish and chips is the same as ordering chips and fish (in the same way that a + b = b + a) and that an empty salt pot won't change the taste of their dinner (in the same way that a^{2} + 0 = a^{2}). So if people can do this why can't they do mathematics? Well, perhaps the thing that people find hard to do at school IS NOT mathematics but the way in which it is presented  as a meaningless set of rules and procedures to memorise and use whenever needed.
Mathematics can be described as a community of practice defined by particular ways of being, seeing and communicating. To be a mathematician one is expected to master these ways of being, seeing and communicating which the mathematics community attaches to that position. These ways of being, seeing and communicating are of course created by mathematicians as they do mathematics. Mathematics is what mathematicians do and mathematicians are human beings. The point here is that mathematics is a human activity, it exists because there are human beings who constantly create and shape it.
Mathematics can also be described as what mathematics does. It is concerned primarily with what can be accomplished by reasoning. But why should one reason? Mathematics, more than any other human endeavour relies upon reasoning to produce knowledge. The primary purpose of all mathematical work is to help humanity study the environment, and in this endeavour mathematics cooperates with science. This does not necessarily mean that mathematics is merely a useful tool and that the real pursuit is science. Through reasoning mathematics has made and makes known the secrets which would otherwise not have been revealed. The fact that mathematics is of central importance in the study of environment reveals almost immediately several values of mathematics. The first is the practical value: the construction of bridges and tall buildings, the harnessing of the power of water, coal, electricity and the effective employment of light, sound and radio in illumination, communication, navigation and even entertainment.
The success of mathematics in the study of the environment has inspired another value: the mathematical study of human nature. Mathematics has not only contributed to the very practical institutions such as banking, insurance, pension systems, etc. but it has also supplied substance, character and methodology to other sciences like economics, politics and sociology. Number, quantitative studies and precise reasoning have replaced vague and subjective speculations.
As we celebrate the National Mathematics Week we should realise that mathematics is not just interesting, but it is important for human development and a crucial part of human culture. It is unfortunate that in the popular conception, 'mathematics' is synonymous with 'number' and various forms of computation. Mathematics is a living and changing discipline and has roles beyond the basic functionality associated with numeracy. It is a powerful language for sharing and systematizing knowledge and also an important part of human existence. While part of the mathematics is its utility, mathematics is also a discipline in its own right and a part of our cultural heritage. The usefulness of mathematics lies not just in its 'application' but in the 'thinking tools' it provides.
The biggest challenge for the mathematics education community is to ensure that students appreciate mathematics for what it is, what it does and what it can enable them to do and be. I believe that all students can be successful in mathematics. Success in mathematics is of course more than 'getting the answer right'. It includes the ability to use mathematics in different situations and the ability to apply mathematics in new and original ways. There is no doubt that 'getting the answer right' is good for a moment and a mark, but it is not all there is to mathematics. The motivation to just 'getting the answer right' is what pushes many learners towards memorising rules without reasons when learning mathematics. As I have been arguing, mathematics is much more than just rules, procedures and algorithms, it involves "knowing what to do and why". As a mathematics learner at school I was fortunate enough to have a teacher who was not just impressed with knowing the rules but always emphasised the fact that we should be able to justify our answers and the procedures we used to solve problems. As a mathematics educator, I learn a lot from interacting with other mathematics educators through the Association for Mathematics Education of South Africa (AMESA), the national association of mathematics educators. AMESA encourages and assists its members to strive towards making mathematics more meaningful to the learners.
For more information on AMESA and its activities visit http://www.sun.ac.za/mathed/AMESA/
