Most Viewed Posts of 2016

I wrote 78 blog posts in 2016. That's an average of 1.5 per week. Here's a list of the ten posts that had the most views.

1. Classroom Photos - #mathscpdchat 

I wrote this post back in January to encourage people to take part in a Twitter chat about classroom displays, equipment and layout. I asked people to share photos of their classrooms because most of us like to have a peek at what's happening in other schools.

2. Divisibility Rules
My popular posts are normally about resources, but it makes me happiest when people read a subject knowledge post. In this post I talked about divisibility rules. These aren't taught as much as they should be. 

3. Classic Resources 
I was surprised to see a maths teacher on Twitter say they'd never heard of the Standards Unit. This prompted me to write a post about all the resources that I was taught about on my PGCE. It's really important that new teachers entering the profession know about these timeless classics.

4. GCSE 9 - 1 Revision Resources
In November I realised that teachers were struggling to help their students prepare for their mock exams because they felt that there was a lack of revision resources for the new GCSE. In this post I collated all the new revision resources that I was aware of - I will continue to add to this post over the coming six months.

5. A Level Revision Resources
Another popular post about revision - this one brings together exam preparation resources for A level students. It's a shame that it has a limited shelf life - most of the resources featured are designed specifically for the modular specifications, which are now coming to an end.

6. 5 Websites You Should Know... #1
My 'five websites you should know' series was well received. It was based on a presentation I did at a TeachMeet. I've written four out of the five posts so far, covering Corbett Maths, MrCarterMaths, MathsBot and MathsPad. 

7. Revision Clocks Galore
The revision clock idea originated from a geography teacher and was adapted by teachers in numerous subjects, including maths. This activity became very popular in the summer term. To help keep track of the huge number of maths revision clocks produced, I collected them all in one post.

8. Common Errors Made by Maths Teachers
A controversial post! After noticing a few misconceptions from trainee maths teachers at work, I wrote a post to discuss the fact that maths teachers sometimes get things wrong. We are all human after all! I was planning to crowd source a list of common errors and create a reference document for trainee teachers and NQTs. People are really sensitive about subject knowledge though, and after being accused of writing 'pedantic nonsense' I lost my enthusiasm for the idea. The post, and the extensive comments, are worth a read.

9. Five things you might not know about the new GCSE content #2 
10. Five things you might not know about the new GCSE content #1
My two most viewed posts of 2016 were about the new GCSE. The inspiration for these posts came from a tweet by Ben Ward. He spotted that graph stretches are no longer included in the GCSE 9 - 1 specifications, so I decided to find out if there were any other content changes that teachers might not know about. Across the two posts I featured ten bits of information that hopefully made teachers' lives a little bit easier. The popularity of the first post, which has currently had over 8,000 views, was probably due to the fact that Graham Cumming linked to it in one of his Edexcel Emporium emails.

I hope you found these posts helpful. They are my most viewed posts of 2016, though not necessarily the posts that I am most proud of - I will blog about those shortly!

5 Maths Gems #67

Welcome to my 67^th gems post. This is where I share the latest ideas and resources I've seen on Twitter. I used to write one of these posts every week but I now struggle to find the time, so this is my first gems post since November. I have some crackers for you today though!

1. Polygons
Ed Southall's (@solvemymaths) first video is well worth a watch. It explores the terminology, etymology and structure of naming polygons. I'm now eagerly looking ahead to when I next teach geometry so I can share this with my students!



2. My Favourite No
I first watched this video years ago but I've never put it in a gems post before. Thanks to Stephen Godwin (@stevejodwin) for reminding me about it after it appeared in Doug Lemov's recent blog post 'My Favorite No: Mistaking Knowledge Problems for Skill Problems'. Do watch the video below - it features a brilliant activity for exploring misconceptions.


3.  Primitives
I shared the lovely Furbles in Gems 21, but hadn't spotted the 'Primitives application' on the same website. This has been around for many years, but thanks to John G (@mathhombre) for recently sharing it on Twitter. This lovely interactive factorisation tool is really good for exploring numbers.

Primitives posters and teaching ideas are available from the ATM.

4. Euler's Number
Numberphile published a new video about e last week. I really enjoyed this video and plan to show it to my Year 13s next term.



5. Notepad Calculator
Colin Beveridge (@icecolbeveridge) tweeted about this excellent NotePad Calculator. I'm not sure whether I'll find it useful in the classroom but I love it anyway so thought it was worth sharing.

Update
I've published six blog posts since Gems 66. They're listed here in case you missed them:

• Highlights of 2016
• Merry #christmaths16
• Formative Assessment
• 5 Websites You Should Know... #4
• GCSE 9 - 1 Revision Resources
• New GCSE: Trigonometry Questions

Do check out Don Steward's blog too - he's published a lot of new resources lately.

You might also be interested in Dr Frost's revision advice for A level students and Colin Beveridge's exam technique tips for the new GCSE.

I'll leave you with this animation of the surface area of a sphere, shared by Damian Ainscough (@damianainscough).

Highlights of 2016

2016 has been truly awful... The best way to cope with so many terrible things happening in one year is to focus on the positives. In the world of maths education, there's been loads of fantastic stuff going on. Although we continue to face challenges relating to workload, behaviour, curriculum change and recruitment, there's still plenty to celebrate. In this post I share some of my favourite moments of 2016.

The Conferences
La Salle's conferences are always brilliant. I was gutted to miss their Leeds conference in June but I really enjoyed the Peterborough conference in March and the Kettering conference in October. La Salle are hosting even more conferences in 2017 (check out their dates and locations here) so if you haven't been before, do join us.

Pre-conference drinks in Peterborough in March

Teachers enjoying #mathsconf6 in Peterborough

Cake from Julia Smith at #mathsconf6
to celebrate my 50th gems post

Pre-conference drinks in Kettering
- we made Enigma machines!  

Rob Smith's tuck shop at #mathsconf8 in Kettering

The first researchED Maths and Science was held in Oxford in June 2016. It was excellent. I really hope to see this event return in 2017.

A wonderful venue for researchED Maths and Science

Maths teachers meet for lunch at researchED Maths and Science

In 2016 I attended a number of conferences as a presenter, including Edexcel's Warwick conference, the FMSP's London KS5 Network Day, and Coast2Coast TSA's maths conference.

Peter Mattock and I presenting at
Coast2Coast TSA's maths conference

Meeting my maths hero Hannah Fry at
Edexcel's Warwick conference

The Social Events
I really enjoy meeting up with maths teachers who I've chatted to on Twitter. A highlight this year was our trip to Bletchley Park in the summer holidays. We were so lucky to be treated to a tour of the grounds and a private demonstration of an Enigma machine.

Summer day out at Bletchey Park with fellow tweeters

Some of #teambletchley

La Salle organised their second summer meet up for maths teachers - Pie and Maths.

Summer drinks at #pieandmaths

I had a lovely time at one of Old Andrew's blogger curries.

Out for drinks with edubloggers, organised by
blogging legend Andrew Old

In December I hosted #christmaths16. 110 teachers got together for festive mathsy fun at the Science Museum followed by a night out at a Kensington pub.

Post-museum drinks at #christmaths16

Maths teachers enjoying #christmaths16

The Grassroots Events
This year I've attended a number of events at local schools. I presented at Maths in the Sticks which was an A level day run by Stuart Price, and I presented at Paul Collins' MathsMeet at Oakwood School. I also travelled up to Oldham to present at Lindsey Bennett's LIME event. I hosted my own event too - MathsMeet Glyn took place on a Saturday morning in March and starred one of my maths heroes, Don Steward.

Paul Collins at Oakwood School's MathsMeet

Ben Sparks presenting at Stuart Price's 'Maths in the Sticks' Event

With colleagues at lunch after #mathsmeetglyn

With Don Steward
at #mathsmeetglyn

The Websites and Resources
During 2016 the world of maths resources went from strength to strength.

Clarissa Grandi's artfulmaths.com is a beautiful new website, providing inspiration and resources for both classroom displays and creative maths lessons.

New website mrcartermaths.com is highly valued for its ease of use. Excellent websites such as mrbartonmaths.com, corbettmaths.com and mathsbot.com have continued to develop new content.

For A level teachers, undergroundmathematics.org arrived on the scene, providing high quality rich tasks from the team at the University of Cambridge. We also discovered the IYGB papers on madasmaths.com, providing a large bank of challenging exam style papers for A level students.

The prime game from Christian Lawson-Perfect provided hours of entertainment - and fierce competition - amongst maths teachers.

Throughout 2016 maths hubs all over the country supported teachers in both primary and secondary schools. The White Rose Maths Hub shared excellent schemes of work and assessment resources for Key Stages 1, 2 and 3.

Craig Barton's podcasts were a wonderful feature of 2016 - if you've not discovered these yet, they are well worth a listen. Look out for more of Craig's podcasts in 2017.

The Networks
Since joining Twitter in 2014, my career has been transformed. Its incredible network of teachers continues to provide an endless supply of support, advice, resources, ideas and encouragement. During 2016 I was fortunate to become involved with both the AQA Maths Expert Panel and the TES Maths Panel too.

Some of the AQA Maths Expert Panel members
sporting Christmas jumpers at our December meeting

School

I can't talk about my 2016 maths education highlights without mentioning my wonderful school and my awesome colleagues. They're a real pleasure to work with.

Lizzie and I with Year 13 maths students on their
last day at Glyn. They don't normally look so scruffy!

Celebrating results on the first day of the new
school year with colleagues Harry and Farah

With trainee teacher Sarah
at Glyn's staff Christmas party

With colleague Rachel at Glyn's
 staff Christmas dinner

Joint Heads of Maths Christina
and Catherine, with NQT Amelia 

Looking Ahead
2017 brings the first sitting of maths GCSE 9 - 1. The successful delivery of this new qualification will be something for maths teachers to celebrate. I worry about how the media and public will react to low grade boundaries and falling 'pass rates' though. I also worry about our poor 'guinea pig' year groups who won't be funded to resit if they get a Grade 4, even though it's likely they'll need a Grade 5 for future career opportunities.

2017 also brings the start of the new linear maths A level. Some of the specifications are not yet accredited, and it's with trepidation that I look ahead to the summer term. I expect that there will be a last minute rush to organise schemes of work, teacher CPD, resources and textbooks.

The Smith Report on post-16 education is due to be published any day now and I (nervously) look forward to seeing the recommendations.

There are many wonderful events planned for maths teachers in 2017 - see my event listings for details. I look forward to La Salle's next conference (11th March in Bristol) and I really hope I'll be able to attend the very exciting JustMaths conference at Alton Towers in June.

I'm positive that the many maths teacher networks, including our wonderful Twitter community, will continue to thrive in 2017.

We have a lot to look forward to.

Happy New Year, maths teachers!

Merry #christmaths16

I have a lot of people to thank! 

Thank you to all 110 wonderful maths teachers who came to my event yesterday. I hope you had a great time.

Thank you to Andrew Jeffrey, the brilliant mathemagician who performed a fantastic show for us.

Thank you to all the individuals and organisations who kindly donated prizes and freebies - this was very much appreciated by all.

Thank you to the Science Museum, particularly Roderick and Sergi at the Media Space Cafe and the awesome Dr Kenny Webster, Head of Learning Operations. They were helpful, generous, professional and welcoming and I couldn't have done it without them.

Finally, thank you to everyone who helped to make my event run smoothly, particularly Lizzie and Gareth who were absolute superstars on the day.

It's so lovely to see maths teachers enjoying themselves at Christmas.

The Galleries

I was really pleased that the Science Museum provided #christmaths16 guests with free access to the WonderLab, so we had two mathsy galleries to explore on the day. The WonderLab is where all the fun interactive maths and science stuff takes place. It was a lovely space full of excited children. If you're going to take a school trip to the Science Museum (you can take a whole year group at once, free of charge), you'd spend time in both the Winton Gallery and the WonderLab. They also run free 20 minute maths and science shows in the WonderLab.

I didn't get much time to explore the Winton Gallery myself (I was too busy organising things!) but I will return there in the New Year. Check out the tweets in this Storify to see lots of pictures of #christmaths16 guests enjoying both the Winton Gallery and the WonderLab.

The Reception
For the reception we all had a glass of bubbly and a couple of mince pies in the Media Space Cafe.

Everyone got stuck into my quiz (more about that in a minute...) while Rob (@RJS2212) was presented with a fantastic birthday cake by Julia (@tessmaths). Meanwhile, I spent some time fighting off members of the public who thought that they were entitled to free alcohol (!).

We enjoyed a brilliant magic show from Andrew Jeffrey, which involved tearing playing cards in half!

We finished with a calculator-assisted raffle, with loads of amazing prizes.

Quiz
If you weren't at #christmaths16 then you can have a go at my quiz here (last year's quiz is there too). There were some excellent and varied answers. It was a close call to choose the winners, but the glory goes to Lizzie, Amelia, Christina and Chris.

Pub
Quite a few people went to the Hereford Arms for dinner and drinks in the evening, with a brave few venturing out afterwards into the early hours of the morning. I got a taxi home and was in by midnight!

Thank you again to everyone who contributed to another successful Christmas event for maths teachers. Do check out my Storify here. If you didn't come, I hope you're able to visit the Science Museum soon to check out the all the mathsy goodness.

Merry Christmas everyone!

Formative Assessment

One of my roles at school is to present a short teaching and learning slot in staff briefing on a Monday morning. The Lead Practitioners do this on a rota, so I'm on every nine weeks. This is a challenge - it's hard to find good teaching ideas that can be clearly explained in a two minute time slot and are relevant to teachers in every subject.

In last week's briefing I chose to present on formative assessment because this is part of my teaching practice that I've improved significantly over the last couple of years. I've not perfected it yet, but I'm getting better.

I used to think that circulating around the room during lessons and looking at my students' classwork gave me a good insight into whether they'd learnt anything. In most lessons I'd conclude that enough of them were getting the right answers, and this meant that I'd taught the topic well enough to move onto a new topic. Later in the term they'd do a test and I'd be disappointed when they got the wrong answers. Had they forgotten the things I'd taught them, or not learnt them properly in the first place?

Over the last couple of years I've developed more effective formative assessment techniques, strongly influenced by Kris Boulton's excellent post 'How tests teach and motivate'. As a result I now have more reliable information on which to base my decision making and I'm able to act more quickly when a student needs support.

In my briefing presentation I talked about two techniques for formative assessment: exit tickets and low stakes quizzes. These approaches work well in maths and in many other subjects (though not every subject, as an art teacher pointed out to me after my presentation!). You may have already tried these techniques but in case you're not familiar with them, I will briefly explain how they work.

Exit Tickets

The idea here is that students spend five minutes completing a few questions individually at the end of each lesson and then hand their answers to the teacher as they leave. The teacher marks the exit tickets on the same day - this helps them identify misconceptions and determine what to teach in the next lesson.

Exit tickets capture information from every single student, allowing the teacher to instantly identify students who are struggling. This allows teachers to intervene at the right time, for example by emailing a video link or by asking a student to stay behind after school for extra support. Some teachers also use exit tickets for RAG123 - this is where students rate their own understanding and effort (you can read more about it here).

Using exit tickets does present some challenges. They are only effective if each student completes a ticket on their own, without conferring or copying. Whether or not you can easily get your students to work silently for five minutes at the end of the lesson depends on the behaviour and culture at your school. Exit tickets are best introduced at the start of a school year as part of a set lesson routine. Another challenge is in asking the right questions - the questions on the exit ticket must be very carefully chosen to ensure that they accurately assess students' new knowledge or skills. Some exit tickets just ask students to write a sentence explaining 'what they learnt today' - I think this is probably less helpful than actually testing their knowledge directly.

If you're considering using exit tickets, or if you're sceptical about their value, I recommend that you read Harry Fletcher-Wood's post 'Using Exit Tickets to Assess and Plan: 'The Tuning Fork of Teaching'. 

We are fortunate in maths to have access to banks of pre-made exit tickets. In Gems 38 I featured Lesley Hall's (@lhmaths) exit tickets and Emma Bell's (@EJMaths) exit tickets. The Algebra by Example resources that I featured in Gems 54 might be useful for exit tickets too. If you want to make your own exit tickets, MathsImpact on TES has provided templates.

If you use exit tickets in your lessons please comment below - I'd love to hear how they work for you.

Low Stakes Quizzes

Low stakes quizzes are have transformed my teaching over the last two years. I currently use them with both my Year 7s and my Year 11s and am considering introducing them at A level too. Every Friday I give my students a 15 minute test in the lesson. They do this in silence, but for my Year 11s it's an 'open book' quiz, so they may refer to their notes (this is partly to encourage good note taking).

My tests are multiple choice. Questions are drawn from diagnosticquestions.com, a fantastic website that contains thousands of questions for maths and a number of other subjects. Multiple choice quizzes are very quick to mark, and I could make that even quicker if I used an automated marking tool like Quick Key. Every Monday morning I return the quizzes to my students, displaying a slide similar to the one shown below (this example was for a Year 7 class).

My students have responded really well to these quizzes and genuinely seem to care about their results. They get a sticker when they get full marks and even my Year 11s love getting those stickers! Results are recorded on a sheet (Year 7s have this tracking sheet stapled into the cover of their exercise book) so they can easily see which topics need more work. I feel like I know my students really well since I started using these quizzes. I've blogged about this before in my posts 'Some Things I've Tried' and 'Going Well...'.

This technique is a bit less 'real time' than exit tickets as it's once a week instead of every lesson, but I find it easier to manage. Some teachers have expressed concern that it eats into teaching time too much, but I now consider it to be a vital part of my teaching. Running and returning the tests takes no more than 25 minutes of lesson time a week.

Further Reading
This post has provided a couple of examples of effective formative assessment techniques - there are many other techniques that I haven't mentioned here, such as questioning, mini-whiteboards, Plickers and Socrative. If you're looking to learn more about formative assessment in maths, the Mathematics Assessment Project has provided a full professional development module which includes links to books such the classic 'Mathematics inside the black box' by Jeremy Hodgen and Dylan Wiliam.

I'd love to hear about approaches used by other maths teachers. How do you assess your students' progress during lessons? How do you judge the right starting point for your next lesson? How do you know which students need a bit more support? Please let me know in the comments below.