The Kings College London Mathsoc has a weekend every year at Cumberland Lodge in Windsor Great Park, a large house dating from republican (Cromwellian) times but with many royal connections. As we were told, many of the discussions about the constitutional crisis provoked by Edward VIII’s abdication took place here, and the relevant scenes in the film *The King’s Speech* were filmed here.

This year, the students invited me to address them. On Saturday afternoon, I went for a stroll in the park with some of the senior Kings mathematicians, and afterwards a small group (Alice Rogers, Peter Saunders, Tony Barnard and I) sat in the bar and talked.

One idea that surfaced in our discussions concerns the fact that school mathematics education in Britan now, with its focus on syllabuses and testing, fails to communicate to pupils the real nature and excitement of the subject. Wouldn’t it be good if there were a series of books which provided such material, at a level accessible to good school pupils and their teachers, which would have no connection with the exam system but would give them a taste of real mathematics?

Could it really happen, or is this just one of those conversations which put the world’s problems to right but never make it into reality?

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I count all the things that need to be counted.

Totally agree that inspiration about the nature & excitement of maths is vital. But, depending on which level you are starting, are there not quite a few good books already (e.g. some by Martin Gardner, David Acheson, Tom Korner, etc)? Or am I misunderstanding what you had in mind?

Are these books actually used by teachers or bright pupils? Also, isn’t it possible that there are books just as good waiting to be written?

Are these books actually used by teachers or bright pupils?I think this is the key question.

Do you have in mind books to be used in schools for teaching purposes? Ar books to broaden the horizons of the interested student, out of school or at least outside main teaching time?

There are plenty of the latter type around, as Nigel says. (Indeed I’ve written a couple myself.)

If you’re aiming for the former, the question has to be what role these books will play in the life of teachers whose main focus is likely to continue to be getting students through exams?

Sorry if this comes across as negative – I certainly like the

idea– but I’m not quite sure where the gap in the market is.Can you spell out more how your fantasy books would be used?

My first thought was Paul Lockhart’s

Measurement, a fabulous book, full of good questions. I’d rather teach pre-calculus using his book than with a textbook. Of course I wouldn’t ‘cover’ all of the material I ‘cover’ now. But my students might be better prepared for calculus anyway.As a teacher in a UK state school I enjoyed your Gresham Lecture (via YouTube) and also this post. Richard is right, there are plenty, and they don’t nicely fit into hour long segments with a broad curriculum to teach. I lend mine out to interested pupils and discuss them after a week or two with those pupils. I tend to use interesting things from them to show where our 11-18 maths is heading, and in which areas it can be useful.

I agree the Lockhart’s book is great, but I haven’t found a way to incorporate it into my 120 lesson per year schedule, which is predicated on one topic per hour, learn, practice, explore.

I quite like Tony Gardiner’s Extension Maths series, though these are cast firmly in his mould. They do however involve and expose some real mathematical thinking with all pupils, but are only really accessible to the most able.

James Tanton’s books looks similar, and he has a series of YouTube videos.

Also as a high school teacher I read & encourage my students to read http://plus.maths.org/content/ (particularly relevant to this discussion would be the “about us” page)

Problems that we use in class are also available online at http://nrich.maths.org/frontpage