I've been a maths teacher for some time and a teacher-trainer, but have made little headway with the perennial problem of answering children's questions about the usefulness of maths. For example, when introducing the notion of unknownsvariables in algebra, where is there an application in which it is only possible to solve a problem through the use of early algebra?
I accept that there is a need for developing skills in combining like terms, and that's part of a requirement to practise skills in any subject.
However, where is the usefulness for 11 to 12-year-olds? How can they be encouraged to see that solving a simple equation represents something useful or applicable to their lives?
Algebra is used to calculate fitness levels, as well as making sure the Sunday roast isn't overcooked. I invited Professor John Mason of the Open University, who has contributed greatly to the debate on algebra in school, to make a comment. He made the following points.
* The curriculum consists of topics that someone thinks "can be learned" and hence "can be taught", strongly influenced by "what comes later", so that each topic is a preparation for the future as much as an end in itself. So there is an enormous amount of cultural history bound up in any curriculum statement.
* Literature provides vicarious experiences of deep emotions, which can provide the basis for juxtaposing reason and emotion, and even support preparation for difficult situations in the future. Encountering literature when young provides foundations for deeper understanding when revisited later in life. This theory of how meaningfulness arises includes a necessity for multiple exposures, including exposure to significant cultural influences.
This sets the scene for considering maths generally, and algebra in particular. Maths has been and continues to be a profound influence on our culture, hence the importance that young people experience and gain some appreciation of what it offers. Maths is a great deal more than arithmetic, and much more than a collection of techniques. It is the study of structure, whether it be the structure of the physical universe, of logic, of space and time, or of human thinking.
* The customer wants to know the price, as well as the qualities that are available. The entrepreneur needs policies to deal with multiple customers.
Arithmetic is sufficient for a customer in a particular instance; algebra is vital for the entrepreneur. The customer also needs algebra to make comparisons. There are many examples, from mobile phones to car rental and from mortgages and investments to shopping for food.
* To participation in society it is vital to be able to probe beneath the vague generalities and claims of politicians and the media. Appreciating what mathematical models can and cannot do to support reasoning and decision-making seems vital, otherwise we are at the whims of those who want to manipulate facts for their own ends.
* "Why am I doing this?" is often the result of being set repetitive tasks that fail to make use of learners' natural powers, whereas developing and extending those powers is actually pleasurable. When the teacher makes things too easy and clear these powers are not needed. Seeing the particular in a generality and the general through a particular are both fundamental human powers. Imagining possibilities and expressing those is also fundamental to the way humans work.
John Mason's website is worth a visit http:cme.open.ac.ukJHMFurthPartics.htm.
For some interesting artmaths crossovers visit www.mimetics.com and see the film clip of the virtual starfish that Richard Brown has created. The starfish moves towards you when you stretch out to touch it and if you touch it quickly it draws back. There is a real power in saying that this interactive virtual space would not have been born without maths.
Richard studied maths, further maths and physics, followed by a degree in computers and cybernetics. Later he did an Master of Arts in Fine Arts and this background is reflected in his work. Richard told me that he didn't know as an 11-year-old how useful his algebra would be in his chosen career.
* John Mason is the author (with Sue Johnston-Wilder) of Developing Thinking in Algebra, published by Paul Chapman Publishing (pound;19.99), which is the basis for an Open University course on teaching algebra at key stage 3 and KS4.