I don't know about you, but I've always found it hard to get my head around stuff like
As a boy, I'd chew my pencil and stare out of the window and wish I was playing with my kite or riding my bicycle. With dreams of being a navigator I would need not just to pass maths, I'd need an A.
Easty (we called him that because his brain had gone west) failed to capture my imagination. The chalk squeaked on the blackboard, and some days tears would well up as I tried to get to grips with it all. Mr Kirkwood's class was a slight improvement, we plotted parabolas on graph paper. We weren't sure what parabolas were for, but at least there was a physical manifestation, a drawing on a piece of paper. Not until I was 17, and attending sea school, did it all start to make some sense, because now there was a globe, and angles subtended at the centre of the earth, and arcs described on the surface of the earth. Arcs along which you could steam a ship.
But now, in second childhood, I am happy playing on my Chromebook. I have just grabbed 3D Function Graphics from the Chrome Web Store. It's free, so I didn't even need to think about it. Click. Done. It's obvious how it works. All I need now are some cool 3D functions (if I was at school my maths teacher would be writing them on the board). In another tab I go to Google and put in the obvious search string "cool 3d functions" and I land on the Physics Forum page 'Cool 3-D functions for graphing' by LPHY.
I try a few – you just enter the function in a text box at the top of the page – and the one I like the best is
It makes an object that looks like this
I wonder… what would it look like if I … put this?
Wow, look what's happened to the corners!
Now, I didn't tell you that another thing I've found in the Chrome Web Store is Pixlr Editor. I'm wondering if I could turn my object into a character. There's an 'export as image' feature in 3D Function Graphics, so it's easy to get these 2D snapshots of my object (viewed from any angle) Pixlr Editor. I try a few filters, and then hit on this one… that's one mean duck. Quack! Quack!
Since discovering 3D Function Graphics I'm taking a lot more interest in functions. All this fun has put me in mind of Ed Catmull, the brains behind many of the algorithms that powered Pixar and gave us Toy Story, and Finding Nemo, and Cars. It seems that all those numbers can be an enormous amount of fun. Serious fun. Hard fun.
I think what I'm trying to say is this: When you see a student idly playing around in their Chromebook, fiddling about with something, don't be in too much of a hurry to pull them back on task. They may be learning something very important and personal to them.
Number 6 of CORE Education's 10 Trends 2013 was 'Thinking 3D'. I think you can unpack that in many ways.