This year, due to a grant from the Scottish Attainment Challenge, I was able to purchase manipulatives for the maths department. When they arrived, I was like a kid at Christmas. Even the fact that I'd messed up the order a little bit did nothing to dampen my spirits. Over the next year or so, the department and I will spend a significant amount of time looking at how we can use these manipulatives effectively but one of the things I've already start using after being inspired by this video from Mark McCourt @EmathsUK, is Algebra Tiles. I have used them with two classes so far, well that is after I let the higher class play with them, and the response was quite unexpected. My S3 class hated them. We used them to look at multiplying double brackets. I got lots of 'why can't you just tell us what to do'. That reaction was pretty surprising because I don't believe I ever just tell them what to do but apparently that's how they see my teaching. I persisted with the tiles for 2 periods getting them to set up an area model and use the tiles to create the rectangle in the blank space. By the end of the second period, I knew they'd had enough of the tiles but about 70% of them could explain why the double brackets multiply out the way they do and when we moved on to the more formal method, the majority of them opted to use an area model to demonstrate their working. The best thing happened today though when I gave them the quadratic and asked them to factorise it. I explained nothing as to how it was done. Some of them messed around with the algebra tiles to get it to factorise, others used the area model in their jotters and the rest were able to do it by inspection. It was pretty amazing. I've taught factorising a fair few times now but never with this ease. Maybe everyone else has this experience all the time but I was quite blown away by it. Of course, I know the test of how well they've learnt it is can they replicate it again in the future but I feel quite positive about their ability to do that. My S2s had a very different response. They were interested in using the tiles and having picked up on the things that tripped up the S3 class, I changed how I introduced them slightly which seems to have helped. The rest of the lessons were pretty similar. Setting up an area model and filling in the blank space. They were quicker than the S3 class to pick up what was happening and a lot more of them were comfortable multiplying the brackets out more formally. It'll be interesting to see how they take to factorising when we get to it but I'm pretty confident that they will pick that up with the same ease that they seem to have picked up multiplying brackets and of course, I'll test them in the near future to see if it has stuck.
I'm going to be honest, I never really experienced maths as a pupil in this visual way and until recently (last 3 years or so) have not understood the significance of a visual to maths teaching for the higher attaining pupils but as I'm learning to be a better teacher, I understand the significance of it more and more. If I had been taught this way, I definitely would have understood more as that's what's happening as I am teaching this way, and I also would have understood a lot more when my maths teacher said maths was about understanding patterns. I loved maths in school so she didn't need to convince me of it's awesomeness but I loved the logic and the structure of it. It's only now that I'm teaching it that I appreciate its elegance and beauty. I'd love to pass that on to my pupils.
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