* Numeracy is usually defined as the ability to use maths at the level needed to get by in everyday life
* The term became common with the introduction of the national numeracy strategy in 1998
* Sats results have improved since then. About 96,000 more children now leave primary school with a level 4
* But their ability to solve 'real life' numeracy problems has fallen by 11 per cent, according to one study
* Poor numeracy rather than literacy affects how much you're paid
* Extra maths lessons account for more than half of all private tuition outside school hours
A report last year by a House of Commons committee suggested that as many as 15 million adults - around half the national workforce - have inadequate numeracy skills. The Basic Skills Agency puts the figure at around 6 million. Either way, a lot of adults are struggling with their decimal points and percentages. Is the next generation going to be different?
What is numeracy?
A 1980s school inspector described numeracy as "the sensible use of a four-function calculator". Nowadays, expectations are higher. Numeracy is usually defined as the ability to use maths at the level needed to get by in everyday life. But opinions differ as to what this means. To some people it means only a command of basic addition, subtraction, division and multiplication. Others argue that the mathematical skills needed in everyday life stretch well beyond simple arithmetic. Personal finances, for example, are increasingly complex: making an informed choice between a variable, capped or fixed-rate mortgage requires more than just a rudimentary grasp of percentages.
There's also the question of how we make sense of the ever-growing mass of statistical information available on the internet and in the media. Want to make up your own mind on global warming? Then it helps to know about statistical margins of errors and the difference between mean and median.
The Government seems to use the terms "mathematics" and "numeracy" almost interchangeably. "Numeracy is more than an ability to do basic arithmetic,"
insists the DfES framework, before listing a range of skills which exactly mirror the maths curriculum at key stages 1 and 2, suggesting that, at primary level at least, mathematics and numeracy are one and the same.
New word, old idea
While the word literacy was in use by the mid-1800s, its mathematical equivalent wasn't coined until 1959, when it appeared in a government report on 16-18 education. And it wasn't until 1998 that the term became common currency, with the introduction of the national numeracy strategy.
Even now, tapping out "numeracy" on a computer keyboard usually results in an angry red squiggle on the screen. Many educationists would like to see the word replaced by terms such as "functional mathematics" or "mathematical literacy" - which would include basic geometry and algebra - or by "number sense", which would refer more to arithmetic skills.
But while the word itself is something of an ugly upstart, the distinction between everyday maths and fancy calculus can be traced back to Victorian times. In 1868 the Schools Enquiry Commission recommended three levels of mathematics to be taught in schools. The upper middle classes were to learn classical Euclidian mathematics, the mercantile classes would tackle "practical mathematics", and the working classes could expect just a grounding in basic arithmetic.
Does numeracy matter?
It can seem as if there's not much need for basic mathematical skills any more; credit and debit cards mean you rarely need to check your change, and if you want to know how many miles to the gallon your car does, there is probably a button on the dashboard that will tell you.
But in the workplace it's a different story. An increasing number of jobs - teaching included - require employees to handle data, work with spreadsheets, and interpret statistics. In the US, it's been estimated that businesses spend more each year on improving employees' numeracy skills than the government spends on maths education in schools.
And while admitting to being "useless at maths" probably carries less social stigma than admitting that you're unable to read or write, poor levels of numeracy are a greater barrier in the workplace than low levels of literacy. A 1997 report for the Basic Skills Agency found that whereas 30 per cent of people with competent numeracy and poor literacy were likely to be "very low earners", 58 per cent of those with poor numeracy and competent literacy were likely to be in the same low wage bracket.
Maths is natural...
Scientists believe that all human beings are born with a mathematical instinct and an innate ability to understand concepts such as "more than"
or "less than". Even before babies can talk, their brains seem able to consider the question "how many?" In one experiment, infants matched the number of voices they heard on a recording with the correct number of faces shown on a screen. Nor is it just number sense which seems to be inborn; geometrical concepts such as symmetry also seem to be hardwired into the brain. Harvard researchers asked children from an isolated tribe in the Amazon rainforests to identify the odd ones out in a series of geometrical patterns. Even though they had no concept of angles or geometry, they were able to identify certain shapes as "ugly", and scored just as highly on the test as a group of US schoolchildren.
So why is it so difficult?
When children are quizzed about which subject they find hardest, maths always tops the poll. And extra maths lessons account for more than half of all private tuition outside school hours. So what's the problem? Some people who struggle with arithmetic may suffer from a condition known as dyscalculia - a mathematical equivalent of dyslexia - but this only affects a small percentage. It may be that the answer lies in the structure of the brain. Some scientists have suggested that the part of the brain responsible for mathematical calculations is closely connected to the part which registers anxiety. So any feelings of unease are likely to impede the ability to do maths, in turn causing more anxiety - or "maths panic", as it's sometimes known. Hence the reason many people experience a mental block. The situation is probably made worse by the fact that early years maths tends to be about right or wrong answers.
"Maths isn't any harder than history or geography," says Sue Johnston-Wilder, chair of the Association of Teachers of Mathematics. "But you have to prevent anxiety getting in the way. As soon as a teacher sees any sign of maths panic, they need to take that child to one side and do whatever they can to help them understand. If they press on, it's like asking someone to walk on a broken leg. It just makes things worse."
Has the national numeracy strategy had an impact?
Up to a point. The strategy (now part of the primary national strategy) was introduced in 1998, with ministers promising that "the new daily maths lesson will ensure children know their tables and can do basic sums in their heads". If that was the main aim, then the strategy has been a success; most teachers insist that today's classes are much better at mental sums than those of a decade ago. Sats results have also gone up. A further 1 per cent improvement last year means a 16 per cent rise over seven years; or 96,000 more children leaving primary school having achieved level 4 than in 1998. And the most recent international league table of numeracy (Trends in International Mathematics and Science Study, 2003) put the UK in 10th place, the most improved performer since the study was first carried out in 1995.
But not everyone is convinced that standards have risen. In particular, there's concern that children are taught to pass Sats, without being given a proper grounding in mathematical principles. For example, some pupils use inefficient methods, such as "counting up" one by one on their fingers, to add together two double digit numbers; a reasonable option for adding 11 to 16, say, but not for adding 98 to 75. And research at King's College London (KCL) which re-tested children using Sats-style questions one year after the official tests, found many performed less well than 12 months previously, even though they were a year older. "That suggests that the learning hasn't happened at a deep level," says KCL's Professor Margaret Brown. "I know of secondary schools that have setted children according to Sats results, only to abandon it because it doesn't reflect true levels of understanding."
Further research at KCL has shown that children's ability to solve problems about numbers "involving real life, money or measures" actually fell by 11 per cent between 1998 and 2003. If numeracy is the ability to use maths in real-life situations, it may be that the current generation of children is actually less numerate, despite their better grasp of mental arithmetic.
Dr Jonathan Solity of the University of Warwick believes that fundamental changes in the way early maths is taught could give children a better understanding of mathematical principles. His research has identified a set of three core skills which he believes are "every bit as essential to learning mathematics as phonics are to learning reading". The three skills are counting, understanding of the "equality principle", and mathematical language. He insists that the second of these, in particular, is often overlooked. "It's perfectly possible to learn to add three and four together without realising the principle at work," he explains. "Children need to be taught from the outset that 3+4=7 is an equation. It's balanced on both sides. The question might be 3+4=? Or it might be 3+?=7. It's the same question. If children understand this, then when they move on to algebra they shouldn't have any problems."
In Dr Solity's research group, children were not introduced to terms such as "double" and "half" until they understood the relevant principles of multiplication and division. They devoted a larger than usual amount of time to practising counting skills, without the use of number grids. And they were not prepared for Sats until the final few weeks, when they were shown how they could apply what they had learned to answer test questions.
The research group performed 20 per cent better than expected, with particular benefits for those at the lower end of the attainment range.
Onwards and upwards?
With the National Centre for Excellence in the Teaching of Mathematics scheduled to open in June, as well as plans to publish maths GCSE results separately in the league tables, and the possibility of numeracy tests for all school-leavers, the Government seems committed to keeping numeracy in the spotlight. Ofsted is also keen to promote numeracy across the curriculum to help make pupils aware of the practical applications of the work they do in maths lessons. At primary level, the framework for teaching maths is being updated, with new guidelines planned for the autumn. These are likely to reinforce the current emphasis on traditional methods and mental maths, and propose that times-tables should be learned earlier than at present, a move which some fear will put children under too much pressure, making maths phobia even more common.
And while guidance on calculator use has softened slightly from the early days of the numeracy strategy, which promised "a ban on the use of calculators up to the age of eight", critics argue that the new proposals still don't fully embrace modern technology. "In real life, the chances of being called upon to perform a long multiplication by hand are slim," says Margaret Brown. "Most children don't carry paper and a pen around with them, but they do carry their mobile phones, which often have a calculator function." Perhaps the biggest concern is that the new framework will mean an even brisker pace, with teachers being told what to teach for virtually every week of the school year. "There probably won't be much room for pause or recapitulation," says Sue Johnston-Wilder. "So some pupils could get left behind."
Fun and games
Despite all the attention, maths still has an image problem. Even though mathematical principles are behind every cool gadget from PSPs to iPods, and hundreds of careers from architecture to zoology make use of maths, it is often seen as useless, or just downright dull. Yet no other subject lends itself so readily to games and puzzles. Think of a number. Double it.
Add 4. Multiply by 3. Divide by 6. Subtract 2. Don't tell me... you're back where you started. It seems like a fancy trick, but once children figure out why it works, they realise it's just the magic of algebra.
Japan regularly tops international numeracy tables, partly because it has such a strong tradition of playing number games. Sudoku may be about logic rather than arithmetic, but it gets children used to numbers and problem-solving. Kakuro is even better. Here in the UK, there are bundles of "fun maths" resources on the market. One favourite is a mathematical version of Scrabble, where children use a mixture of symbols and numbers to build equations, while everything from darts to dominoes and blackjack to bridge make use of maths skills. Many schools are going all out to bust the subject's dowdy image with maths clubs, maths weeks, maths fairs, and family maths nights. "It's just so easy to have fun with maths," says "mathematical clown" Sue Brown, who takes her numbers show into primary schools. "Maths lessons may sometimes be boring, but maths itself isn't boring; it's something to celebrate. If children are having fun with numbers, the rest will come naturally."
* The Association of Teachers of Mathematics (www.atm.org.uk). Tel: 01332 346599.
* The Mathematical Association (www.m-a.org.uk). Tel: 0116 221 0013.
* The Advisory Committee on Mathematics Education (www.royalsoc.ac.uk/acme/index.htm). Tel: 020 7451 2571.
* DfES: www.standards.dfes.gov.uk/primary/ mathematics/www.standards.dfes.gov.uk/primary/publications/mathematics/math_ framework.
* Basic Skills Agency (www.basic-skills.co.uk). Tel: 020 7405 4017.
* National Centre for Excellence in Teaching Mathematics (www.ncetm.org,uk). Tel: 0114 219 1007.
* Spartacus Education (www.spartacus.schoolnet. co.uk/REVmaths.htm) has links to dozens of maths-related websites.
* Sue Brown, mathematical clown (www.hattiemaths.com).
* Nrich, mathematical problems, games and puzzles project run by University of Cambridge (www.nrich.maths.org). Tel:01223 764246.
* Beam (www.beam.co.uk). Maths resources and training. Tel: 020 7684 3323.
Summer conference, "Engaging maths, engaging minds", London (June 20), Leeds (June 27) and Bristol (June 30).
www.beam.co.uk/training/conference.htm. Also offers training in delivering primary Came, the cognitive acceleration programme developed at King's College London. http://www.beam.co.uk/training/pcame.htm.
* Number Partners (www.numberpartners.org) is a nationwide project that encourages adult volunteers to work with groups of upper primary and lower secondary classes.
* Mathematics Minus Fear, by maths teacher Lawrence Potter (Marion Boyars £7.99), is aimed at adults suffering from "maths panic".
* See Teacher to Teacher in this week's TESTeacher magazine for key stage 3 and 4 maths tips.
www.tes.co.uk/friday has direct links to these websites
Main text: Steven Hastings
Additional research: Sarah Jenkins
The Issue returns after Easter