Q1. What should the role of parents / families be in helping their children achieve in mathematics? What are the key obstacles / issues for parents and families in this regard? What more should and could we do to support parents and families in this area? What would you like the Review team to recommend in this area?

Parents, by and large, make very bad teachers. They lose their temper far too quickly; they shout too much; they expect their child to see that relations are 'obvious' - fractions, for example, or negative numbers - which were once dismissed by the most distinguished minds as absurd. They also very rarely realise that mathematics almost never deals with facts. Its applications may result in facts. It is itself mostly comprised of arguments: and arguments, in truth, which are often very highly contentious - and not just to children!

Two plus two equals four, for instance - or any similar combination - may be presented to the learning mind as if it is a fact. But the learning and inquisitive mind will not see it as a fact: for it is not. It is an argument, and an argument, furthermore, which depends on very delicate and questionable axioms. The child may see this; the parent, not. Result: explosion.

But many parents certainly do want to help. They can help by realising, as the child also needs realise, that learning is a complex process. Early experience is crucial. According to Baroness Susan Greenfield, one of the world's foremost neuroscientists: '… early experiences constitute an important factor in how well children assimilate information in more formal situations later on. .. Children's main sensory and cognitive learning achievements come from the own experiences in the course of the activities such as play, exploration, everyday talk, and social interactions with peers and siblings.'

Reporting on the success of the Head Start programme in the United States- and also on its superb cost-effectiveness - she adds: 'the experimental curriculum aimed to develop a whole range of physical and mental skills, including sharing and counting objects, fitting objects together, anticipating and remembering sequences of events, role playing, imitation, recognizing objects, playing simple musical instruments - and talking with others.' [Greenfield, 2003]

I have added the final emphasis. Children learn through talking. Here is a clear prescription for developing quantitative and qualitative skills in the early years; that is from 0 to 5 years of age.

To help children of six years and older to have more confidence in talking with others, it should not be a surprise that an advantage is for them first to be encouraged to talk aloud - carefully and thoughtfully - to themselves.

Many adults do this whenever engaged in particularly delicate tasks. It is a major assist to the brain. To encourage my own youngest pupils to try this at home - alone; with their younger siblings; with their favourite teddy; even, I told, them 'talk to your dog or your cat!' - I created a 30 page reading and colouring book called the 'Socrates Workbook 'for 9 to 11 year olds'. It was soon translated by senior pupils in my European School into five other European languages - most recently by the Qatar Foundation into Arabic.

There was a problem, however, one of the seniors told me, with the title. "It should read," he told me, "'for 9 to 19 year olds', because we all need to know what's in this book!"

Copies of this workbook in any of these languages (including Russian and Spanish) can be downloaded free from my website: www.gardenofdemocracy.org. All will be found under national flags in its 'Core Materials'.

It would of course be entirely feasible to revise the title to: 'for 7 to 19 year olds', for children can use this book, unaided, as soon as they can read. Its structure encourages them to read. In addition I have created a 'Teachers' and Parents Guide to the Socrates Method' with details from the National Literacy Trust statistics in support. This, too, can be downloaded free from the same 'Core Materials'.

Area 7: Primary Frameworks and EYFS