A small group of six-year-olds at the Good Shepherd RC school JJin Hammersmith, west London, gather excitedly for their weekly dose of “thinking skills” with class teacher Amanda Ryall. “We play games that are fun,” says one child, “and the teachers don’t always get stuff right.”

The game this week involves a farm layout, on which the children arrange an assortment of tractors, trees, buildings and animals.

Each child pretends to be one of the animals, and tells the others two things on the board that this animal can see, and one thing that it can’t. The other children then have to guess the animal - using the kind of “concrete operational” thinking that involves putting yourself in another person’s position.

The point of the game is to improve their awareness of what it feels like to be in someone else’s shoes. Children find it difficult to realise that people in different positions won’t see everything from the same viewpoint.

Take the situation where two people are having dinner, and one has moved the salt so the other cannot see it. To realise that the salt is hidden from view for one person but not the other is a skill children need to learn. It is perhaps not surprising that some children struggle with this at first. But they all engage in useful discussion about how to work it out. One girl, already a successful concrete thinker, is even able to explain to the rest of the group that the boy opposite her has described not what his animal can see, but what he himself can see. “We had to really think in the game today,” says six-year-old Diana afterwards. “It’s a bit hard, and a bit fun.”

Diana’s class joined the Hammersmith and Fulham’s primary schools thinking skills project in autumn 2000. Masterminded by CASE (Cognitive Acceleration through Science Education) and funded by the Single Regeneration Budget, the project began three years ago and now incorporates 33 teachers and Year 1 pupils at schools in the borough.

It is related to a CASE programme, already well established with 11 to 14-year-olds in more than 150 schools around the country, which demonstrated that stimulating children’s metacognitive abilities - their ability to think about thinking - in early adolescence can lead to improved standards in maths, English and science.

CASE follows the psychologist Jean Piaget in identifying the years 11 to 13 as a critical window for accelerating the development of children’s thinking, from the concrete operational - where you consider other points of view - to the more formal and abstract, where you can manipulate a number of variables.

Similarly, the years from five to seven, explains Professor Philip Adey of King’s College London, represent the transition from “pre-operational” thinking - the child can consider only one thing at a time - to the more complex concrete operational.

Children who receive inadequate mental stimulation fail to make this transition. In the school context, this can make it so difficult for them to access the curriculum - for instance, when they are required to think about different points of view in English or history, or alternative explanations in science - that they lose interest and switch off.

Anne Robertson, a primary advisory teacher in Hammersmith and Fulham who is involved in the CASE project, says: “When I started teaching 25 years ago, this is how I was trained to teach - to get children thinking, to make lessons challenging. But what we have found in the project is that some younger teachers are so used to national curriculum strategies - presenting their objectives to the class, explaining them, going over them again and so on - that they find it difficult to make things challenging, and the children hardly have to think at all.”

In CASE lessons, by contrast, the approach is to hold back from telling children too much, so that they have to puzzle it out for themselves - sometimes even without arriving at a solution.

“The teacher has to accept that, at the end of the lesson, nothing has been formally delivered or covered, and the children may be a bit confused,” says Philip Adey. “But that is fine - as long as they’ve been puzzling away and their brows are furrowed.”

Amanda Ryall, at the Good Shepherd school, admits that she found it very hard at first to stand back and leave more up to the children. “Usually I am very didactic, and I see my role as a teacher to explain. But now I have learnt to keep quiet, at times - and I’m learning things from the children, because they look at problems in a different way from an adult.”

It also took her a while to get her head around “metacognition”, that crucial part of the CASE process where children have to reflect on their own thinking, to explain the reasons for their answers, and to consider whether they might be right or wrong, or whether they might even change their mind.

As this morning’s session demonstrates, a year on, the pupils have become adept at discussions of this kind. They try hard to explain, listen to one another with respect, and point out each other’s misapprehensions without being rude. “They have become more autonomous learners, and their self-esteem has risen, as well as their confidence to have a go at things,” says Amanda Ryall, who is now hoping to take the work on into Year 2. “At first they were terrified to say ‘I don’t agree’; now they’re happy to explain why something is wrong. They have really started to think for themselves, and to question their own beliefs.”

Although the CASE method centres on only one session a week for each group of six children, Amanda Ryall says it has influenced her teaching more generally, so that she will often ask the children what they are thinking and why. They also feel the benefits in many curriculum areas - for instance, thinking more about “why” and “because” in their written work, and producing better explanations of answers in mental maths.

Research tests last year on the first cohort of six-year-olds to start the project have also yielded very positive results, according to Philip Adey. After a year of CASE lessons taken by specially trained teachers, children were given a range of tests, including conservation (does the amount of water remain the same when poured from one vessel into another of a different size?), and seriation. The latter is a method of classification used to enhance the ways in which pupils think about mathematical concepts. If you give them blocks of differing shapes, colours and thicknesses, for instance, they will usually start to make houses or people rather than spotting characteristics (round, oval, triangle, blue and so on) that might link some of the blocks together. Over time, however, children become more able to distinguish features that are common to more than one block. Usually, teachers begin by asking children to spot just one variable factor among the many and then gradually to work their way through tasks of increasing complexity.

The children in the study were found to have made greater cognitive gains over the year than pupils in similar classes who had not experienced CASE intervention. Furthermore, there was evidence of a “transfer effect”, Philip Adey says, whereby children were performing better in some tasks that had not been specifically addressed by the CASE programme. “I would argue that CASE is having a general effect on their intelligence,” he says.

“It’s time for teachers to take a more holistic view of their pupils,” concludes Anne Robertson, “and to give them challenges just a little beyond what they are capable of - what Vygotsky called ‘the zone of proximal development’. This is what lights up part of the brain, and pushes the child into the next phase of thinking.”

CASE’s Let’s Think for primary schools is published by NFER Nelson in November. Information about CASE professional development courses from: Anne Robertson 020 8753 2882