There are 132 tennis players in a knockout tournament. So what is the minimum number of matches needed to find a winner? If you've already reached for the calculator, or a pencil to start drawing diagrams of the tennis court, then you clearly haven't met Mike Jeffries, former headteacher and specialist in the teaching of thinking skills to children and school management teams around the country - and overseas, for that matter.
The question is typical of those he uses on in-service training for teachers - not so much a trick question as an illustration of some cognitive fundamentals.
"What happens, time after time, is that people immediately reach for the box marked 'mathematical problem solving' and start doing all sorts of adding and division tasks," he says."And they get immenselyfrustrated that these processes don't always serve them well."
In the end, the answer proves not to be as elusive as one might expect. Since it takes one game to eliminate every player and there is only one overall winner, then it must one fewer than the total, ie, 131. As with so many problems, Jeffries explains, it's often a question of looking at them laterally and disengaging from some of our more cumbersome educational baggage.
Since his days as head of the National Institute of Conductive Education more than 20 years ago, where he specialised in teaching children with motor impairments, Jeffries has been gradually building his case for putting "meta-cognition" - thinking about thinking - on to the mainstream agenda.
Some of his labours now show signs of paying off - particularly since the Qualifications and Curriculum Authority has made important changes to Curriculum 2000, its document reforming FE teaching. While it would be arrogant, he says, to presume they had acted on hisrecommendations, Jeffries' discussions with QCA officials last year seem to have been followed up with the late inclusion of "thinking skills" as an essential part of the revised curriculum; indeed, they are now on a par with such familiar staples as literacy, numeracy, communication and information technology.
Meanwhile, Transform, his cognitive design and development consultancy, is moving into a higher gear as news of hissuccess with meta-cognition starts to sink in.
"I think the time has finally come in this country when we're beginning to look very seriously at the development of children's thinking," he says. "There have been lots of fine projects over the years, which have created small pockets of interest, but meta-cognition has never really broken into the mainstream, as such. And this is a shame - especially when there are other countries around the world that have been developing thinking skills for some years."
One such is Singapore, where he has given presentations on strategic thinking. Singapore is undertaking a radical initiative, in which 30 per cent of thecurriculum in schools has been jettisoned to create space for a more direct approach to the teaching of thinking.
"They've realised that their future as an economy and a nation-state rests not on getting people to very high levels in some narrow field, but on developing creative individuals who are empowered in their creative thinking and their ability to create their own future," he says.
Not surprisingly, he has keenly followed the work of Edward de Bono, the Maltese psychologist and "lateral thinking" guru, as well as the mass of research on "multiple intelligences" by the lies of Howard Gardner and others in the United States. But he insists he is no disciple of any system.
More pragmatic than dogmatic, he is rather a bricoleur who has amassed a wealth of practical ideas and insights from worldwide cognitive research and adapted them to the unique requirements of individualclassrooms and schools.
One special area of interest he has brought to the cognitive classroom is the "thinking" that informs children's writing. Recent years have witnessed a new awareness of genre analysis, but he maintains that an essential ingredient is still missing. There may be no shortage of frameworks to support children's technical skills, he suggests, but there is still not enough "concretised" scaffolding to support children's thinking in this area. "Style models, genres, all these things have been important, but they still assume that the thinking is just there. How often do we, as teachers, say to children: 'Come on, just think a bit more about what you're writing' - often from our own frustration. But it's precisely in the thinking that the child needs support."
The decisive point lies, he suggests, in a more structured and analytical approach to preparation, which is where his project's strategic thinking and support techniques come into play, either by using customised, computer-generated planning formats or a range of pencil-and-paper "brainstorm and cluster" techniques, which he demonstrates in his own exemplar lessons.
"For one thing, we are finding that children are writing considerably more. Why? Because they realise they have a lot more to say. More importantly, they are demanding of themselves a greater level of sophistication, because the new ideas they have to communicate are, in themselves, more complex - and therefore put greater demands on children's linguistic abilities. In the end, it's about being more structured and disciplined in our overall approach to tasks - not simply saying,'Let's talk more about this'."
And if pupils are benefiting from the new insights arising from strategic thinking, so are the teachers in project schools, as the cognitive school makes increasing inroads into senior management planning and trouble-shooting. Invited recently into a school put into special measures after an inspection, Jeffries adapted his strategies to suit the needs of a management team with pressing problems to solve.
"What became clear was that these teachers were working extremely hard individually. But what they didn't have was a joint perception of what had to be done to get them out of special measures. In this case, we used a 'cluster and name' brainstorming activity, which meant that within less than an hour the management team could see - vividly, graphically - exactly what had to be done. At the same time, they had developed their own common vocabulary for approaching these actions. Often, it's this kind of insight that's most valuable - the kind that will never emerge otherwise - not even after six months of staff meetings," he says.
These principles of strategic thinking are, he suggests, just as relevant and applicable to developing corporate concepts in a multi-national bank as they are to trouble-shooting in the staffroom or approaching problems of basic literacy and numeracy with even the very youngest schoolchildren.
"At heart, I'm a teacher and what I'm about is enhancing and developing effective learning in the classroom - and the projects' aim is ultimately that," he says.
Transform, Mike Jeffries' cognitive design and development consultancy, can be contacted on Tel 01543 673798 email: firstname.lastname@example.org