I reckon that the ability to represent ideas in maths is something that most people underestimate or are even unaware of. Yet it is a crucial tool in a mathematician's backpack: it will help him or her gain a deeper understanding by thinking of a concept in a variety of ways. But it is a skill that I saw in action in a Grade 1/2 split class this week.
I showed students the pattern I created below and asked them to create a similar pattern using the shapes at their disposal:
All students came up with something like this. Some where initially concerned that the colours didn't match but convinced themselves that it was OK as it was still square, triangle, square, triangle. A lot of students also extended the pattern without being prompted to.
They were then asked to represent this pattern without using squares or rectangles and we got something like this from all the groups:
Then we narrowed the attributes and said that the had to represent the pattern again but this time only use one shape. I wondered if they would find this tricky but over half the students managed to get things like:
We allowed students to go on a scouting mission to see other students' solutions. The students who got stuck really benefited from getting the immediate peer feedback.
I then asked them to tell me how they could represent this pattern not with shapes but letters and they quickly gave me some examples.
We then agreed to call these patterns AB patterns.
But I wanted to push them further so I gave them some red counters and asked them to make an AB pattern with the red counters. Sure enough, many groups came up with something like:
We then asked the students to make an AB pattern using themselves. Firstly the organised themselves into boy, girl, boy, girl. Then after a little more thought, came up with stand, crouch, stand, crouch.
I then asked them to represent the AB pattern using sounds (Maths and music are so connected!) and this is something they really enjoyed:
By the way, I like to tell students that I call an AAB pattern 'We Will Rock You'!
And here's the thing which really toasts my crumpet. At the end of the lesson the teacher told me that the students who were the most successful today were her 'weakest' students!
Did I tell you how much I love my job?