This is essential. On commission from the UK in 2005, Malcolm Swan wrote a guide to great math teaching [pdf] that’s as good as anything I’ve read at this length. It is, explicitly, a collection of activities – full explanations of resources a teacher can use for floatation in her first year – but the document also goes into exquisite detail about what theory motivates those activities. It outlines excellent pedagogy while at the same time keeping your head above the waterline.

This is a fast read – big type, thin margins, lots of color, etc. – and from now on, it’ll be the first thing I recommend to new math teachers. I hope you’ll do the same. But help them make sense of it also. Some of this only may look so brilliant in light of my abundant early-career failure.