Posts Tagged ‘reflection’

Symmetry and reflection

July 17, 2019 Leave a comment

This week I’ve been working on symmetry and reflection with my year 9s. As part of this we looked at creating some Rangoli style patterns that had symmetries. After discussing how to reflect shapes in mirror lines and drawing some reflections I shower them some pictures of Rangoli patterns and gave out some squares of squared paper with various mirror lines on and some coloured pencils and gave them some time to get to work.

I was interested to see some of the different approaches. Most just used the squares to create patterns in the first instance. Of these there were two basic approaches, A – complete a pattern in one quarter and reflect into the other quadrants. B – each time they coloured a square they reflected it. I would have opted for option B I think, but watching the class work it seems those who used method A made less mistakes.

There were a couple of students who didn’t just colour squares, they created some triangles, trapeziums and other shapes in their patterns. They all took approach A.

I’d be interested to hear how you would approach this.

Once we had some patterns we looked at them as a class on the visualiser, discussing their approaches, what we liked about each one finding mistakes, looking at the reflective symmetries and also discussing rotational symmetry too.

Here are some of the patterns:

This student did a quadrant at a time then shaded what was left in blue when I told them time was nearly up.

This student was doing 4 squares at a time. I like the fact each quadrant is symmetrical too. (I know technically it’s not a symmetrical pattern, but it would.have been had we had a minute or 2 more!)

This student did a bit at a time and reflected each bit in the diagonal line.

I liked all three of these, and they gave rise to a good discussion as they had all gone for more than 2 lines of symmetry and all had rotational symmetry too. More than half of the students had done this, and I wonder if that’s because the Rangoli patterns I had shown them had also done this.

Unfortunately a lot of the others opted to take their work home and I didn’t think to take photos first as there were some awesome patterns.

Categories: #MTBoS, SSM Tags: , , ,

Questioning Authority

March 1, 2016 Leave a comment

This post was first published here, on Labour Teachers, on 28th February 2016.

In life there are often many ways to reach a certain place. This is true in all aspects. You can take different routes when you travel to get to the same destination, you can solve trigonometric equations a number of ways, you can take many different routes into becoming a teacher, I’m sure there are plenty of examples from other subjects too.

Recently I was reflecting on the way I teach certain topics, and which method to complete them I think is best. This reflection led to a wider discussion and many of the contributers from that wider discussion stated that they preferred the method that they were taught at school. I found this interesting and it got me thinking about things.

I think there are a lot of instances where I am guilty of this. There are certainly topics that I have a preferred method for completing that stems back to the way I was taught, I’ve often suggested that I feel the PGCE is the best route into teaching – and it’s the route I took. I remember discussing with a friend the make up of exams when I was at uni and professing the belief that I thought a linear course was preferable at GCSE and a modular approach was preferable at A level – perhaps this discussion should have suggested we’d both end maths teachers! There are even examples in wider life when I drive home from a friend who lives near my old school’s house I always take a particular route that passes my parents,  and I think it’s because that’s the route my mum always drove me when I was a kid.

I have questioned all of these ideas to some extent. I now believe that different routes into teaching will suit different people and each has its merits and downsides. I now belive that a linear approach is preferable at GCSE and A level. I’m starting to use a different route from friends house that is actually quicker and my reflections gave led me to begin to question the methods I prefer.

It struck me as a blindingly obvious thing to do, but one that I had missed. I’ve become very good at challenging things I read and critically evaluating new things, it’s something I believe is vital and I’ve written on the topic before. But until recently I’d not thought to question some of the other things that stem from childhood – bizarre, perhaps, as I have questioned and left the religion I was brought up to be part of.

Young people take in things they are told by authority figures as hard truths. When we, as teachers, express the view that method A is preferable for solving trigonometric equations then those in our charge will follow that. We all know this, and often we need to ensure we are presenting an unbiased view on things (although trigonometry probably isn’t one of these…). What we sometimes miss, though, is that some of the things we learned as children may have been the opinion of our teachers,  and we need to critically evaluate those things too.

I intend to reflect on the topics I teach and the methods I prefer to ensure that I am teaching the what my students need to see.

A look back at 2014, and forward to 2015

December 30, 2014 7 comments

This time last year I wrote this post reviewing 2013 and looking to 2014. In the summer I looked again at it here, and discussed my year so far. Now, as the year draws to a close and I am reading all these #Nurture1415 posts it feels like a good time to reflect again.

My 2014

At home

I’ve had a good 2014, I’ve spent some great time with my family, watched my daughter grow from a baby/toddler into a real little person and seen a lot of other family.

Studies and the blog

I’ve continued to work on my masters, and to write this blog. Both of which have helped me improve as,a teacher, and both of which have been enjoyable. There has been a higher proportion of maths puzzles finding there way onto the blog this year. This hasn’t been a conscious decision, but I have really enjoyed working on them.


I’ve managed to read a few more maths books, and I have managed to get deeper into topology, as I had hoped to this year. I’ve also delved deeper into group theory, another old favourite of mine, and I particularly enjoyed exploring the tests of divisibility.


When I wrote the post last year, I thought I’d be in the job I was in for a long time to come. In reality I’d decided to move on and found another job by the end of February (I think). This was a massive change. I moved jobs, schools and authorities and there were some real challenges. I had a full set of new classes to build relationships with, and a full set of new colleagues to get to know. The new school is similar on many levels to the old one, but it is also infinitely different too. I feel I’ve joined a great team, and that I’ve already made some great friends amongst my colleagues. I feel that with most classes I’ve built up decent relationships and am making progress, and I feel I’m getting to grips with the new role.


I’ve been on some great CPD events this year. I’m on a Teaching Leaders course, I attended ResearchEd York, Northern Rocks, Maths Conference 2014 and teachmeets (I even presented at one!) The key messages for me is challenge everything, don’t just accept anything, ensure there’s something to back it up, and even then don’t just assumed it will work in all contexts.

Education in 2014

2014 will forever be remembered for that day in July when the news that Gove had gone shocked the nation. I wrote about my feelings at the time and you can read them here. I can’t say I’ve seen much difference in policy since he left, and I feel the move was made purely to detoxify the brand in the run up to the election.

It was also the year we got to see the draft maths A Level curriculum, which looks good, but not radically different, and the approved specifications for the new maths GCSE. I’m excited about the new GCSE as I think it addresses many if the short comings that the current one has, although I’d have liked to see calculus and Heron’s Formula make an appearance.

The Sutton Trust released a report in 2014 entitled ‘what makes great teaching”, it was my favourite type if report, one that backs up the things I thought with plenty of evidence. The crux of its finding being “great teaching is that which leads to great progress“. You can download the report in full here free of charge.

It also saw the first teaching of the new “Core Maths” suite of post 16 qualifications. We are a pilot school, and I’m quite excited by the prospect, although it’s not been without teething problems so far.

Hopes for 2015

Last year I hoped that the new curriculum would increase the rigour of the maths being taught and that it helps prepare learners for A Level. I still hope this, although I realise now it is a longer term hope. As is the hope that the new GCSE system will eliminate the threshold pass and the gaming we have seen with early entry and other such things. And I think it’s too early to tell if the new routes into teaching can bring down the high turnover we experience.

I still hope that the inherent inequalities present in the UK education system, and wider society, can be addressed.

I hope to find more time to spend with my family, to read and investigate further areas of maths this year.

I hope to continue to improve my practice and to get better at my job.

I hope to see an end to the ridiculous pseudo-context “real life” problems we often see in exams.

And I hope to make a real difference to the learners I’m in front of in 2015, to increase their maths knowledge and skill but also their respect for, and love of, mathematics. A number of my Y13 learners have applied for maths degree courses, and I hope they enjoy them.

I hope you have enjoyed reading this post, and have had a great year, and festive period, yourselves. Here’s hoping we all have a happy new year, and a fantastic 2015

5 reasons to go into teaching

October 30, 2014 3 comments

This post, like many others I’ve read over the last day or so, is inspired by Rob Carter (@robcarter2012) who wrote this post on a similar topic. It’s been a joy to read the posts which have provided much needed respite from the negativity pedal in some areas, such as the dreaded secret teacher.

1: You get paid to talk about your favourite subject.

I love maths, I love talking about it and I love doing it. All things that happen as a natural by product of my job. It keeps me engaged with a subject that had been vanishing from my life in the years between university and teacher training and it certainly keeps my brain sharp.

2. You meet a lot of amazing people.

Some jobs can be lonely, you can spend the majority of your time in a solitary relationship with your computer. Teaching is not like this, you spend the majority of your time with people, whether they be learners or colleagues. And I’ve met lots of amazing people who are both.

3. It’s a constant learning curve

No one is the finished product, we are all learning, all the time. There’s always a new piece of policy to implement, an impending curricula change or just a new pedagogical approach that might be worth a try. I’m currently studying towards a masters qualification, which I’m finding extremely interesting, but even without that there are tons of opportunities for continual development.

4. Making a positive impact

Every day I spend time working with young people to improve their prospects in the “real” world. The world beyond 18. This takes many forms. Teaching maths, obviously, equips some with the basic maths skills they’ll need in life, helps them achieve a qualification that will open doors and secures a good footing for the future. For some it goes further, inspiring take up of the subject at A Level, or higher education. I even had one student go on to do mathematics with QTS which has a knock on effect on a whole host of future pupils. It’s not just that though, helping with UCAS, helping learners decided what course in HE is best for them and writing UCAS references are equally important in making that impact. Then there’s listening, sometimes that’s all that’s required, and sometimes even imparting a little advice, when learners feel they need it.

5. An end to monotony.

When I think back to the time of spent in office jobs between university and teacher training I realise just how bored I was. I wasn’t being challenged intellectually and I wasn’t being challenged in any other way either. I had some good people around me, and that made the job enjoyable enough, but I would hate to return to that. I sat opposite a guy called Will who was great. He once said “do you feel your brain melting when doing this job?” we both decided a career change was in order. I followed nt long held dream to teach, and he followed his into the medical industry.

I’ve tried to keep this post fairly short and concise. I’ve written before in more detail about Teaching, why I would recommend it and what I think about the much reported downsides here.

If you’ve written a 5 reasons to go into teaching post, do post a link in the comments or send me it via twitter. I’d love to read them.

Related posts:

Keep up the hard work
Wasted investment

Half term 1

October 18, 2014 2 comments

Today my twitter feed is full of tweets from people in Southampton, at the teaching and learning takeover event (#TLT14). The event seems to be going well, and I hope to catch up on the day later via blogs and/or videos, but currently my house us full of the sounds of nursery rhymes, so I thought now might be a good time to reflect on the first half term.

Way back in August I started a new role at a new school. I’d never moved schools before, and as such was stepping into an uncertain world. That first week we went back a week earlier than everyone else which at the time was a tad annoying but is now paying dividends as we are starting a two week break.

Starting a new school is tough going. There’s a ton of new stuff to learn, new acronyms, new systems, new policies, new names for things, new colleagues and, of course, new pupils. This overload of newness hits you like a train, and it took me a while to get my head round it all.

I’ve enjoyed the first half term. There have been challenges, but I’ve learned from them and I think they have made me better at my job. I like my new classes, I like my new colleagues and I like my new role. On top of that I feel that the school are investing in my development and I am really glad I made the move.

As well as moving schools, I’ve also moved authority, and am now teaching in Bradford. The school is part of “The Bradford Partnership” which is a non-profit organisation which is wholly owned by its members (ie the schools). The mission if the Partnership is to improve education for all young people in the city and I think it’s a great initiative. There are opportunities to meet colleagues from other schools regularly and to share ideas and best practice.

This first half term is always a tiring one, as is the next, so I’m glad I’ve got two weeks off to recharge the batteries. I just hope my bodyclock realises it is the holidays, and allows me to start sleeping in a bit!

Categories: Teaching Tags: , ,

Happy New Year (2014/15)

September 8, 2014 1 comment

It’s funny that in most of the world the year starts in January, but in Education we start in.September. (Not to forget those finance types who start in April) But that’s how it is. My mind has always been set to a September new year. Probably because I’ve been around education for most of my life. I still work out people’s ages based on school years!

This time of year, for me, is one of new beginnings. I came across this post this evening. It’s last year’s happy new year post, and in it i set out some hopes and ideas for the year ahead.

This year is different, it’s not just a new year, but a new school. I do, however, have a similar feeling of excitement, perhaps more so.

Last year I wrote of wanting to ensure my lessons were as good as they could be, and I think I managed that on the most part. That’s not to say they were perfect, just as good as I could have made them. This year I want them to be better. I think that all teachers should be striving for those constant improvement. The way I plan to do this is to observe as many others as I can, to trail different things in my lessons, to use ideas I’ve seen and read about, continue to attend teachmeet and conferences (and any other CPD I can get) when given the chance and continue working towards my masters.

Last year I also spoke about wanting to read more. I have managed that, and the education books, journals and blogs I’ve read, and the Maths ones, have indeed helped my teaching. I even managed, fiction book! (Terry Pratchett’s collection of shorter writing entitled “A blink of the screen”, for those who are interested.) My “to read” list, however, is constantly growing, so I hope this year to be able to read even more from all categories, and hopefully these will improve my teaching too.

The new school brings with it a new role, and a move from TLR responsibility to leadership responsibility. This is exciting and I want to make sure that this side of my practice is as good as it can be too. My school have put me forward for a course which will help here and I have a lot of great people around to learn from.

Another exciting thing this year is purchased involvement with the core maths qualification. We are lucky enough to be a pilot school for the scheme and I’m excited by the prospect. We have a decent group of pupils who have signed up, and we are motoring along, even though there is, as yet, little information on the course. This new qualification is something that will be shaped over the next few years, and I look forward to being part if that.

All in all, I am excited about 2014-15, excited by its prospects and hopeful that I can improve myself, and the outcomes of the pupils in my charge.

Changing Schools

September 5, 2014 8 comments

I’d never done it before, changing schools. I had been to two schools as an ITT trainee, then moved onto employment at a third school, but that was that. I had been there since. When I left at the end of last term I had very mixed feelings. I was excited to test myself in a new classroom setting, I was excited to sink my teeth into the new role I had been appointed to, but I was sad to leave the place I had enjoyed working at so much. I was sad to be leaving my friends and colleagues, and I was sad to be leaving my classes. As summer drew on both these feelings remained. Had I made the right choice? Would I like it at the new school? Would I fit in to the department?

Now we’ve been back two weeks. That first week, when all the other teachers I know we’re still on holiday, was tough. But the thought of 2 weeks at October was certainly enough to keep me going! The first day was a training day, which was focused around the good results achieved last year and the challenges we face to keep them heading in an upward trend. I felt it was an exciting school to be at, and am exciting time to be here.

I get on with the others in the department, and there is a good team spirit which I already feel part of, so the worries I had there were unfounded. I’m still getting to grips with parts of my role, but I’m thoroughly enjoying the process and the challenges.

That leaves the lessons. The new school has promethean boards, not smartboards, so I had to get use to the new equipment and the software. The room layout is different too, so I’ve had to get used to that, but I feel I have made the switch well. I have met all my classes and I really like them. There have been one or two settling in behaviour issues, a by-product of being new to the school, but I feel that I’m on top of them.

All in all, I am enjoying my new role and the new chapter in my career. I feel I have made the right choice, and I look forward to the journey ahead.