Algebra at the age of four

21st July 2006 at 01:00
Can you solve x + y = 4, where x

y? Warwick Mansell watches in amazement as infants work it out

It is the first lesson of the day, and Natasha Dorrington's primary class is grappling with the fundamentals of algebra.

In front of the children are sheets of paper on which many outlines of snails have been drawn. On the tables are tubs of coloured crayons. The children are given two rules on what to do next: they have to colour in four snails, and the number of brown-coloured snails must be more than the number of yellow-coloured ones.

I watch amazed as around a quarter of the class get the task right without any help, most colouring one snail yellow and three brown. The shock comes from the age of these pupils: they are in reception and are just four or five.

This is algebra in its earliest stages, admittedly, but the problem can be written as two simultaneous equations: x plus y is four, and x is greater than y. The staff argue that such fun exercises will make written equations easy in later years.

It is part of what looks, for England at least, like a revolutionary approach to maths teaching and professional development being piloted in around 20 primaries.

The Mathematics Enhancement Project attempts to stop pupils passively working through written exercises and emphasises problem-solving. It also makes extensive use of group discussion, with pupils encouraged to challenge each other's answers, to explain their thinking, and to argue with the teacher.

During a visit to Downton primary, near Salisbury in Wiltshire, for a lesson that also covered geometry, I saw this happen repeatedly. Ms Dorrington deliberately made mistakes and then defended her position as the enthralled children joyfully explained why she was wrong.

The approach was developed at Exeter and Plymouth universities by David Burghes, now head of the Government's National Centre for Excellence in the Teaching of Mathematics. The centre is also supporting it.

It is based on teaching methods developed in Hungary, long seen as a leader in maths education. Schools adapt the national numeracy strategy to run it.

Teachers at Downton say they are already seeing results, a year into the scheme. Alison Duckham, the deputy head, said that some previously struggling pupils in her Year 5 class were making far more progress this year than last and were now almost guaranteed to get a level 4 at key stage 2 tests.

Exercises for Year 1 pupils (see box, right), look challenging. Ms Duckham said the teacher would work through the problems with the children, rather than having them try to solve it on their own.

The other innovative aspect of the programme is its approach to professional development. Training is modelled on a Japanese system, in which, once a term or so, two or more teachers plan a demonstration lesson together, teach it, then review it.

Mike Hindle, who co-ordinates the project with Professor Burghes, said that teachers working together to build knowledge was the key to its success.

For details, go to or email

Another voice 16

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