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.

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.