Euclid’s Elements

My teaching style tends to rely quite a bit on the application of concepts first, and then filling in the details as we go. It seems to fit more naturally to the pattern of how people learn. I also try to give lessons a context to occur in. Games work well for this. If mental exercises become a game, then there is suddenly a powerful incentive to do them.

A few months ago, I stumbled onto successfully introducing my boys to algebra through an iPod app. My six year old especially, now has a good understanding of the basic principles involved. I am confident that when we get to seriously apply this knowledge some years down the track, it will all run uncommonly smoothly.

Following up on this success, we recently tried our hands at geometry. A friend of mine described geometry as ‘the fun side of maths,’ and I tend to agree with her. Breaking the world down into simple shapes makes it such a neat place. This is a commonality it shares with mapping.

The app we were playing with is called Elements, by DragonBox. Once I bought it, I thought it was probably a bit much for a six and a three year old, but they had seen that there was a new screen game, and there was no going back.

What I especially like about this game is that all the ideas involved are defined either by colours or symbols. There is no need for a child to understand degrees of a circle, add numbers together, write numbers down, read, or even count past four. It is purely conceptual.

The game begins by tracing around a couple of triangles. Things become increasingly harder from there. At the end of each level (there are seven of them), you get to fight an impossible to lose battle against evil spiders before finally killing off Osgard the Monster and freeing your magical tower through the power of geometry. This is all done to tension filled music, and is more important than it first appears.

There is about 120 puzzles. It took a couple of weeks and a bit of help for my six year old to get to the very end. After that, we reset it, and he then worked through all the problems by himself. I did not help him at all the second time around, and he finished it in three days.

My three year old runs out about three quarters of the way through. He can move circle radii around, and understands isosceles and equilateral triangles. He struggles with the idea of corresponding angles, though, and so has trouble defining a parallelogram or rhombus. Still, I am not complaining. It is a great achievement for a guy who cannot count past ten and technically has not started school yet.

This picture is one of the last puzzles. The idea is to demonstrate that the shape in the upper right quadrant of the screen is a square. To do that, my six year old had to understand that the radii of same sized circles is a constant, define parallel lines, show that opposite angles of intersecting lines are the same, understand and use the side lengths of isosceles and equilateral triangles to demonstrate the length and angles of adjacent shapes, have a clear understanding of corresponding angles, and use right angles. There is a lot going on here.

They put so much energy into learning things which are far beyond what is expected of them in such a short period of time, I was very curious as to exactly what was the motivating factor. I asked them what they liked about this game. Both boys gave the same answer. ‘Fighting the monsters.’