The list goes on

Another item for the list:

XI. Computing

When I was a kid at school I got into programming in Basic. It was mathematical in ways that maths lessons weren't. For instance, the only time I ever asked a teacher how to do something that hadn't been taught was when I needed a bit of maths for a program I was writing.

"How do I stop this weather data looking so spiky?"
"You need a moving average."

When I did my teacher training at the Roehampton Institute back in the early 80s, computing was as you know in its early days, not quite as early as when I was at school (there was a screen for instance!) but early days:

But there was a book I really enjoyed, and found captivating, Seymour Papert's Mindstorms. The idea of using Logo in the classroom to program a turtle was a really inspiring one, where you really needed to get to get to grips with maths to get a lot of things done. This short video from the time gives you some idea of what was starting:

Over the years, I've used Logo a lot. You know the kind of thing: forward 10 right 90...
I used the Microworlds  environment quite a bit. Now I use Scratch. It can have too many knobs on, too many attractive features, and I think the simple maths of Logo is the best; it continues to be a great way of really needing a lot of maths to achieve an end. I never seem to get quite far enough with it to get on to the wealth of exciting possibilities, but I think this might be changing with the new emphasis on coding in the computing curriculum. I'm using code.org's great resources and courses with my kids, and encouraging the whole school to develop this kind of coding, and although the finely-grained steps of the courses are mainly convergent, I think they provide a great preparation for wonderful divergent work.

It's this sort of blank slate tool that I like best of all. I use other packages that aren't blank slate (Education City, mymaths.co.uk) and there are lots of brilliant websites for developing skills, but the tools I like best are the powerful ones where it's down to the students to make something of them. (Geogebra is another brilliant example, one I used today for instance to get the students to generate lots of different kinds of hexagons.)

Here's a great tribute to Papert: