Catering for the variety of learning styles - aural, visual and kinaesthetic - ensures maximum benefit for pupils. Learning - and teaching - maths needs a sense of active participation to make it exciting and enjoyable.
In "People Maths", people form the moving pieces of mathematical activities such as puzzles, sums, diagrams and demonstrations. Activities can have definite end-points, or solutions, which everyone can recognise.
Some methods of reaching the end-point will be based on efficiency - eg a puzzle that is solved in a minimum number of moves.
Activities can also demonstrate concepts. So, using pupils to shift along a number line provides a concrete representation of the addition and subtraction of integers, or can illustrate that decimal points don't move (the numbers move) during multiplication or division.
Similarly, people can be used to demonstrate the sum of infinite series, to represent loci, or to introduce Logo via a "human turtle". Shuffle games and position puzzles also lend themselves to this approach.
All these activities could be modelled by using counters or cubes; many can be completed individually using pencil and paper or a computer. What makes them better via People Maths is that they can all be initiated by using people in place of other kinds of resources, thereby encouraging discussion between pupils, as well as between teacher and pupils.
Such discussion makes using People Maths approaches in primary and secondary classrooms worthwhile. Learners become willing to take risks without fear of error or failure. Disaffected pupils become more motivated by being actively involved, pupils with English as an additional language develop confidence and language through working kinaesthetically and collaboratively, and all pupils gain experience of the need for proof.
Such approaches have historically been under-represented in the maths classroom. Schools like Collingwood College, Surrey, with an annual Year 67 maths afternoon, and Hounslow's "gifted and talented" maths days, are examples of how teachers and pupils appreciate these innovative approaches.
This view is supported by the experience of using them in schools, teacher training sessions and adult courses.
The national curriculum prefaces all programmes of study listings with "Pupils should be taught...". For People Maths the philosophy is that "Pupils should be actively involved in learning...".
Bob Vertes is a senior lecturer in education at St Mary's College and is co-author with Alan Bloomfield of People Maths Hidden Depths www.atm.org.uk