As the years have rolled by, the blackboard may have been replaced by a whiteboard, and then by a smartboard, but otherwise the formula has remained by and large the same: theory in the classroom followed by exercises for homework.
The idea of “flipping” the classroom, is to reverse this process. The insight is that in the age of youtube, today’s students can perfectly well take in the lectury bit at home — with the added advantage of being able to pause, rewind, and rewatch in their own time. This leaves lesson-time free for practice, providing the teacher with more time to go around talking to students individually or in groups, meaning more opportunities to help those who are struggling or to supply extra challenges to those who need stretching.
I have no experience of this method myself — all the same it immediately appeals to me as a way in which technology may really be able to improve the teaching and learning experience, rather than just adding bells and whistles. One person who is convinced by this new approach is Colin Hegarty, an old friend of mine from university, who I’m delighted to say has returned to the world of maths after a few years in finance, and is now expertly flipping classrooms in North London.
Even if you don’t have the good fortune to be one of Mr Hegarty’s students, you can still peruse the 611 (!) videos that he and his colleague Brian Arnold have created for this purpose, all of which are freely available on Hegartymaths, or on youtube. Judging by the 800,000 odd views their videos have gathered, it’s not only their own pupils who are benefiting from these experiments in flipping.
As a sample I’m embedding one in which Colin talks through the Chinese postman problem:
Simple City 
For a university level perspective, watching Eric Mazur’s lecture is eye-opening:
I wouldn’t have the guts to try it though…
This is the approach was also advocated by Salman Khan where teachers assign the videos to watch as homework and then do the related problem sets in class. He talked about it in one of his TED talks. (See khanacademy.org).
PostScript:
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By the way, I am a great fan of your 1001 Math book. Perhaps you can write on Origami Math someday. There was a recent documentary called Beyond the Folds that covered the varied aspects of origami in art, engineering, science and creativity.
@Matt – I watched that video of Eric Mazur – very interesting indeed – a little scary though!
@Jim -thanks! I have looked a little into the maths of origami. There’s an interesting paper about it here if you know some algebra:
Click to access Sheri.pdf