This week I finally listened to a podcast I have been meaning to for a considerable time – Craig Barton’s podcast of his discussion with Anne Watson and John Mason.

As you can see from Craig’s notes the discussion is wide-ranging; so well worth a listen, this will leave you with plenty to think about.

I was particularly struck by Anne and John’s Big 3 (or Big 5!) (scroll down Craig’s notes). The only website they mentioned is Underground Maths; a personal favourite – Underground Maths pages here). John Holt’s How Children Learn was my first reading on my teacher training course decades ago – still a classic.

This morning, I have been distracted from writing watching Anne and John’s recommendation – Polya’s video “Let us teach guessing”. (Also on YouTube). To hear the man himself talking to his class is a joy. Not a traditional lecture – join in with his class as they guess!

Much food for thought – you can hear Polya’s summary of what is important in reasonable guessing at 54:16. Including the all-important reminder that we must test our guesses.

Polya Guessing from ihor charischak on Vimeo.

From the University of California, Berkeley see this summary of Polya’s problem-solving techniques – including a summary, in the Polya’s own words, on strategies for attacking problems in mathematics class from the book, How To Solve It, by George Polya, 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6.

For a useful document on cutting space with planes, the problem discussed in Polya’s class, see this University of Toronto resource.