By Jo Boaler

MATHEMATICS should be one of the most useful subjects children learn in school yet thousands leave school each year unable to use simple mathematical methods. Or, worse, they are traumatised by their experiences in maths classes.

This unacceptable state of affairs means that many adults are left vulnerable, not only to financial ruin, but in any situation involving mathematical thinking or reasoning.

It should be the right of all children to be given a basic but sound mathematical knowledge and understanding. Yet thousands of students finish classes annually fearing or hating maths.

The reason for this is the way mathematics is usually taught in schools. Students spend hundreds of hours being shown a dry and narrow version of the subject that is nothing like the mathematics of the world and nothing like the mathematics used by mathematicians.

Maths exists in the petals of flowers, the rhythms of raindrops and the social networks that connect us; it is at the core of scientific and medical breakthroughs and it is a diverse and varied subject.

Ask mathematicians what mathematics is and they will generally tell you it is the study and exploration of patterns. Ask schoolchildren what mathematics is and they will usually tell you it is a vast collection of rules that have to be remembered.

Why are their descriptions so different? The reason is this: schoolchildren rarely experience real mathematics. Instead of posing questions, solving real and interesting problems, using and applying methods, and investigating patterns and relationships, children spend their time watching a teacher demonstrate methods and then practising them.

It is important for children to learn standard methods, but this is just one small part of a very broad subject, and it is the breadth of the subject that is generally denied to children, at great cost.

Children also suffer because they come to believe that maths achievement equals intelligence, and to fail at maths is a sign of being stupid. This idea serves to erode children's confidence in their ability to think, and it is the reason so many children feel traumatised when they don't do well in maths.

In fact, not wanting to engage in the narrow, fake version of maths often taught in schools is perfectly reasonable, if not commendable. Children who are subjected to dry and narrow maths classes need to know this and they need to be introduced to the real mathematics the varied and exciting subject that will help them for the rest of their lives.

Fortunately, parents (as well as teachers) can be powerful in introducing children to the real mathematics that they will enjoy and take with them into their adult lives.

Sarah Flannery, the young Irishwoman who won the European Young Scientist of the Year award for the discovery of a "breathtaking" new mathematical algorithm, revealed that her mathematical success was due more to the puzzles that she worked on at home with her family than all the years of maths classes she experienced in school.

There are many ways in which parents can help their children meet the real and exciting maths that exists in the world, and do well in maths at school. Here are just a few:

&149 It is really important that children know that everyone can be good at maths and everyone can reach high levels.

There is a pervasive view in the UK that only some children can do well in maths; this is wrong and damaging. Encourage and support children and never say "I was terrible at maths at school". Research found that when mothers said this to their daughters, their achievement went down.

- Introduce children to maths puzzles and games such as sudoku (there are many children's versions around), snakes and ladders (for early number work), Rubik's cubes, jigsaws, draughts, chess, dominoes, Connect 4 and any logic puzzles. They will all help enormously with mathematical work.
- Talk about maths together. Find a puzzle or problem that involves maths and discuss it with your children. Many parents read books to children every night but never discuss maths with them. My friend used to put a maths puzzle in her son's lunchbox each day. He is now a mathematician.
- Encourage children to develop a flexible view of numbers. For example, think about adding two numbers such as 96 and 17 in your head. This may seem tricky, but if you break the 17 into 4 and 13 then the sum becomes 96 + 4 + 13, which for most people is much easier.

Low achieving children do not treat numbers flexibly they try to count carefully, even when this usually results in mistakes, as they don't think they are allowed to break numbers apart. Give children lots of these kinds of problems that encourage the breaking apart of numbers. They can be addition, subtraction or multiplication problems, and they should be thought about mentally, without using pen and paper, with children being encouraged to find different ways to solve them. This has many benefits children learn a flexible view of maths, they learn that maths problems can be solved using different methods and they develop sharpness in mental maths.

Ask children questions as they work on maths, but when they say something incorrect, try to find the logic in their answer, even if it isn't the answer you were looking for. Rather than saying "No, that is wrong" find the logic in their thinking and build on it, saying "Oh, I see what you're thinking you're looking at it as if..."

If children are simply told they are wrong, they are likely to feel disheartened, whereas if they hear there is some logic in their thinking and there will be they will gain confidence, which is critical to success.

- Encourage children to see the maths that is everywhere in the world: explore petals and pinecones, try to find sequences of numbers on car number plates when on journeys, work out the time it will take to get to destinations using the speed and the distance, discuss the different shapes and patterns in your garden or park. Maths is all around us.
- Encourage children to think of themselves as great problem-solvers, and to see any maths problem as a puzzle they can solve through exploration and persistence.
- Last, but not least, if your child is not spending time in school working on diverse and varied mathematics, discussing ideas and problem solving, arrange to talk to your child's teacher or the school's maths co-ordinator and express your support for a problem-solving approach to maths.

Sometimes, this is all the teacher needs to hear to move to a more active, exploratory and real version of the subject.

Jo Boaler is the Marie Curie professor of mathematics education at the University of Sussex and author of The Elephant in the Classroom. Helping Children Learn and Love Maths (Souvenir Press).

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