Further Explorations with Algebra Tiles

Today I used algebra tiles with S3 to complete the square.  As I started the lesson, I almost forgot I could use the tiles but I'm glad I caught myself.  I'm aware this would be a more fun blog post if I had photos of the class using them so when I have the class again on Wednesday I'll try to remember to get some.  Also for showing the tiles on the board I used Jonathan Hall's (@StudyMaths) AMAZING MathsBot Algebra Tiles

To start, I gave the pupils a quadratic, all terms positive, and asked them to arrange the tiles into a square.  Quickly they worked out that the quadratic wouldn't make a perfect square and there were tiles left over (I know that I should have started with some that were - improvement for next time).  Next we looked at quadratics where they were short of tiles at the end.  Pupils were happy with these types of questions after a few examples.  At this point we were just playing with the tiles and we weren't writing anything down.  I will do that in the next lesson.

Where we are going to have to spend more time is quadratics with a negative x term.

I'll work through an example and attempt to show you the process I went through with pupils.

I'll use the quadratic

Once pupils have the correct tiles in front of them, they should attempt to turn the tiles into a square.

At this point, my pupils told me that they didn't have enough tiles to complete the square and that the answer is

What they had failed to notice was that the empty space that's left should be filled with positive tiles.

This is the point at which they started to get confused so we did and will be doing a lot of practice here.  Because I have added four positive tiles, I need to add four negative tiles so that I haven't changed the value of my quadratic.  I had to explain with multiple examples here that the positive and negative tiles have been added but they make zero so have not changed the value of my quadratic overall.  This is also why I've grouped them so that they look the same,

This means that my quadratic of

 in completing the square form.

I'm still very early in my use of Algebra Tiles but so far the experience has been very positive and the pupils are coming round to them more.  If anyone reading this is more confident with using the tiles and has a better method for using them for this purpose I'd love to hear about it.  I'm very keen to use them better and more effectively.

The Beginning of my Journey with Mainpulatives

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.

Book Recommendations and Reading List

The idea for this came from the conference yesterday.  We talked about professional reading and I wanted to put down my recommendations for what practitioners should read but also those books that are on my reading list.  This list will be updated and all the links will take you to Amazon.

Book Recommendations
100 Things Awesome Teachers Do - William Emeny
Mathematical Mindsets - Jo Boaler
The Elephant in the Classroom - Jo Boaler
I recommend the two Jo Boaler books not because I agree with her but because she is widely quoted for her research and opinions into maths education and if you are going to either defend or oppose her, you better know exactly what she is saying first hand.
Embedded Formative Assessment - Dylan Wiliam
Seven Myths about Education - Daisy Christodoulou
Seven Myths is possibly one of the best education books I've read.  It takes commonly held beliefs in education in the UK and clearly and succinctly presents the research that dispels them.  A must read for all teachers.

Reading List
Visible Learning - John Hattie
Outstanding Maths Lessons - Mike Ollerton
Getting the Buggers to Add Up - Mike Ollerton
Yes, But Why? - Ed Southall

What Does This Look Like In The Classroom: Bridging The Gap Between Research And Practice - Carl Hendrick and Robin MacPherson

Always on the look out for recommendations so feel free to send some my way.

Thoughts on #SMC2017

So yesterday I attended and delivered a workshop at the Scottish Maths Conference.  I've been pretty vocal about the fact that it was the best one yet.  I always enjoy the conference but this year it went to a whole new level.

Firstly our keynote speaker was Chris Smith @aap03102 - a practising teacher in Scotland.  In the 30 years of the conference, he was the first teacher to deliver the keynote.  What a statement about how highly Chris is thought of amongst the teaching community.  His address was on point.  All of the humour that you would expect from a moment with Chris and a snapshot of the calibre of teacher he is.  I've said it before but I'm even more certain of it now. HE is what the Scottish Government need to pay attention to if they want to raise the profile of maths across the country.

Secondly, I delivered a workshop alongside Julie Morgan @fractionfanatic on using Twitter to enhance professional learning (slides here).  It was so fun to deliver a presentation with someone who has benefited as much from Twitter as I have.  And thank you so much to our special community for their support with our presentation.  Hopefully we've encouraged a few more teachers to join us because there really is something quite magical about the way we push each other and the support we provide each other even in the most implicit way.  I really do love our community.  Speaking on a personal level, I am a better teacher for being part of the #ScotMTBOS but during the most trying time of my career the messages of support were invaluable and are probably the reason I didn't just throw in the towel.

Thirdly, I got myself along to see Chris McGrane @ChrisMcGrane84.  I am a HUGE fan of Chris' and I think the work he is doing at Hillhead is one of the most exciting things in Scottish Education right now.  I've been extremely lucky to spend a lot of time with Chris so was very familiar with a lot of messages that were in his presentation.  That being said, hearing it again, I still got so much out of it.  It's focused my attention onto different aspects of his curriculum development and will certainly be invaluable moving our own curriculum at Alness forward.  If you have not had the chance to hear Chris speak, you need to rectify that as soon as possible.  He will validate so many of your misgivings about current practices in schools and not just with his 'beliefs' but with hard evidence.  I will make the choice to see him speak again and again.

Fourthly, I finally got the chance to not only meet Michael Allan @mrallanmaths but learn from his experience of using OneNote with his classes and also for his own organisation. I'm highly impressed with the details that have gone into his use of OneNote.  His workshop was incredibly informative and I will be making changes to my practice based on his workshop.  Thank you Michael.

Finally, I had the pleasure of hearing Lee Gray @mrgraymath (he apologises for the lack of an 's') and his 'Making Learning Stick' workshop.  Although there were similarities between Lee and Chris' workshops, it was not a wasted 50 minutes. Lee focused a lot more on research but in a hugely engaging way.  He is an incredibly passionate practitioner working in a challenging environment.  His love for what he does was apparent but so was his frustration at how circumstances circumvent our hardest efforts.  The honest way that he threw out so much of what is educational policy was liberating and I definitely felt sighs of relief in the room when he had the evidence to back his opinion.

My absolute favourite part of the day though was meeting so many of my fellow practitioners, particularly the #ScotMTBOS community.  People who are so dedicated to our profession and maths that they would give up a Saturday to get better at delivering it,  So inspiring.

Things that were clear this year: we are moving to being a more evidence driven profession; we are going to start hitting back at silly policies with no educational benefits; and we are teaching maths in the most exciting time to be a maths teacher.  I am already so excited for next year.

A More Grown Up Blog

So I have moved my blog from Tumblr since this is a more grown up platform and hopefully more flexible with how I want to use it.  You can access my previous posts by clicking the link in this post.