23 July 2017

What did I miss?

Hello summer! We made it.

What a year... During term time it can be hard to keep track of what's going in maths education because we're all too busy planning lessons, teaching and marking. The volume of mock marking this year was insane, with many of us having to mark 200 GCSE papers. In this post I summarise some of the things that busy maths teachers might have missed during school year 2016/17.

Lots of new resources have been made available to maths teachers this year. Piximaths.co.uk launched in September, and websites such as Mr Carter Maths, MathsPad, MathsBot and CorbettMaths have continued to grow (see my series of posts about these websites here). The White Rose Maths Hub continues to provide high quality resources, assessments and schemes of work for primary schools and Key Stage 3, and the exam boards continue to provide helpful GCSE resources (such as Edexcel's new content resources which were published back in September).

Although TES has experienced difficulty with plagiarism this year (teachers selling other teachers' resources, which is appalling), it is still an excellent source of teacher-made resources. Quality varies and there's an awful lot to search through, so the TES Maths Panel pulled together four recommended resources for every single GCSE topic here. When working on this project I discovered Dan Walker's resources which I absolutely love.

Don Steward continues to be one of my favourite resource authors, and on the @team_maths1 Twitter account I share all his new resources when they are published. 

The maths community's collection of displays for maths classrooms and corridors has grown significantly this year. New displays include Clarissa's Faces Behind the Formulae, Nicole's Challenge Display and Hannah's Maths Words of the Week
I'm finished! What shall I do? by @BaileyMaths

Other developments in the world of maths resources included:

Do check out my resource libraries for recommended resources by topic for Key Stages 3 - 5.

This year many teachers have used long commutes or lazy Sunday afternoons as an opportunity to listen to Craig Barton's brilliant podcasts. These are well worth a listen.

To keep on top of the latest education research, check out Craig's research page where he summarises findings from a maths teacher's perspective, and the series of Espressos ('a small but intense draught of filtered research on mathematics education') from Cambridge Maths.

I went to all three of La Salle's maths conferences in 2016/17 and they were excellent. These take place on Saturdays and are very affordable - if you've not been to one before, try to come along to #mathsconf13 in Sheffield in September. You can read my previous conference write-ups here.
Ed Southall, Craig Barton and me
(enjoying pre-conference drinks at #mathsconf9)

There were loads of fantastic events in 2016/17, including Christmaths, Maths in the Sticks, two Mixed Attainment Maths Conferences and the JustMaths Conference. There were also local events organised by Maths Hubs, LIME and ATM/MA branches. There is always a lot going on for maths teachers - I've pulled together conference listings for 2017/18 on this page.

Ed Southall's book 'Yes, But Why? Teaching for Understanding in Mathematics' was published in March and has been a huge success both in the UK and overseas. You can read my review and have a peek at some extracts here.

I launched my new CPD project 'Topics in Depth' in June - I will be doing a lot of work on this project over summer so watch this space.

Me presenting my first 'topics in depth' workshop at a ATM/MA London branch conference

Blog posts
There have been lots of blog posts about maths education this year that I highly recommend to maths teachers. These include Mark McCourt's series of posts on mastery, Jemma Sherwood's posts on times tables and feedback, Dani Quinn's post 'Under Pressure', Kris Boulton's post about conceptual understanding and procedural fluency and Ed Southall's response to secret teacher. There are many others that I haven't listed here, and a good way to keep track of them is to follow @MathsEcho on Twitter.

Popular posts on resourceaholic.com included my post about maths anxiety in teachers, my post about what's working well in my A level teaching, and my two posts about my folder experiment. See my blog archive for a full list of posts.

The new GCSE
The first sitting of GCSE 9 - 1 was a really exciting moment for maths teachers, after years of preparation. In the run-up to exams lots of teachers shared helpful resources, included Mel's exam preparation slides and her 'questions by topic' pages, my revision resources post, and the 'best guess' papers and revision lists produced between exam papers by a number of helpful resource makers. The collaboration in the maths teaching community was outstanding.

Other highlights
It's been such a busy year in maths education - here are some other highlights you might have missed:
  • The maths teaching community celebrated the life of the late Professor Malcolm Swan on #malcolmswanday. Teachers shared their favourite Malcolm Swan resources and activities. It was lovely. 
  • To banish the January blues, I ran a World Cup of Maths where teachers voted for their favourite topic to teach at GCSE.
  • The Education Team from Bletchley Park visited schools for free as part of their Ultra Outreach Programme, to the delight of students and teachers all over the country.
  • The new Maths and Further Maths A level specifications were accredited. I've recently published my new A level support page and will continue to blog about the new A level over summer.
  • Maths education received a lot of news coverage. This included my article in Schools Week at Easter and TES's coverage of the MA's poll on A level uptake.
  • After a long delay, the Smith Report was finally published!
  • Times Tables Rockstars featured on BBC Breakfast. My school sent a team to the London Rock Wrangle for the first time, and they loved it.

My team at the Rock Wrangle!

There's plenty going on over summer. No doubt there will be press coverage of maths on GCSE results day. Book now for #mathsconf12 in Dunfermline on 19th August, and for my #summaths event at Bletchley Park on 27th August.

It's been a busy year! If you missed anything, I hope this post has helped you catch up.

17 July 2017

Strength in Numbers

I've finally rejoined the Mathematical Association! It's about time. I've not been a member since I was a trainee teacher. Over Easter I read a fascinating chapter on the history of maths education and was struck by this paragraph...
"The emphasis on Euclid, and a growing feeling that it was outdated and inappropriate, led in 1871 to the creation of the Association for the Improvement of Geometrical Teaching (AIGT), probably the world’s first subject teachers association. As its name suggests, the AIGT argued for a replacement for Euclid, an aim already dismissed by a committee of the British Association set up in 1869 (including Cayley, Clifford and Sylvester) which thought nothing so far produced ‘is fit to succeed Euclid’. The AIGT produced its own course, but it was not to prove a success or be widely welcomed by universities. Undeterred, the AIGT broadened its interests to other branches of mathematics teaching and in 1894 published the first number of its Mathematics Gazette, before changing its name to ‘The Mathematical Association’ (MA) in 1897."
The oldest subject teachers association in the world! After reading this I wondered why on earth I wasn't a member of the MA. As a maths teacher, how can I not support an organisation that has played such a key role in the history of mathematics education? Particularly given the terrible recruitment and retention crisis we're currently facing, maths teachers need to stand together.

Importantly for me, the MA doesn't push a progressive agenda. Its representatives don't tell teachers that they're doing it all wrong - they are never patronising or dismissive. They are supportive, encouraging and knowledgeable. The MA's Twitter feed is excellent - as well as keeping maths teachers well informed, it listens carefully and joins in our conversations. The MA is well positioned to present sensible, timely and representative views about mathematics education in consultations and in the media.

There are numerous benefits to joining the MA. Publications and branch events are the key mechanisms through which it has an impact in the classroom. Shortly after joining I received a parcel full of exciting stuff - I particularly like the fantastic resources featured in the Mathematics in Schools journals. And what good timing to receive a set of puzzles to get stuck into over the holidays!
The main benefit of joining the MA comes from being part of a network. I'd like to see more and more teachers joining the MA over the year ahead, so that it grows to become even more representative and influential. I'd very much like to see the MA's publications have a far-reaching impact on teaching and learning. Please join - and contribute your ideas - to make this happen!

Another way you can make a difference is to sign up to present at BCME 9. This is going to be huge! Instead of the usual separate ATM and MA conferences next Easter, BCME (British Congress of Mathematics Education) is taking place in April 2018, bringing all the members of the JMC together for a joint conference. I'd like to see as many maths teachers as possible standing up and sharing their ideas and experiences. If you'd like to speak, submit a proposal by the end of July.
I strongly encourage all maths teachers to consider joining the MA this summer. It's logical isn't it? Strength in numbers. Together, let's make the MA the biggest and the best subject association in the world.

11 July 2017

The Folder Experiment... Revisited

Back in October 2016 I wrote a post about how I was trialling folders instead of exercise books with Year 11. I promised I'd write a quick update at the end of the year, so here it is.

I've decided that I will be using folders with my Year 11s again next year, as I believe it was a successful trial. I'm not saying it had any impact on attainment - I'm not sure how I'd measure that - but it's still something I want to keep doing. In case you're planning to do the same, here are my key observations:

Folder Type
By Christmas the ring binders were falling apart because they were overflowing. Sometimes a student would pick up their folder at the start of a lesson and their nicely organised notes would fall all over the floor, which was very frustrating. I suggested that my students each buy their own lever arch file during the Christmas holidays, but only a handful did so.

I'd like to use lever arch files instead of ring binders from the start of next year but I can't because:
  1. lever arch files are too expensive
  2. 34 lever arch files are too heavy for me to keep moving around (I teach in multiple classrooms).
So a possible solution is to use 68 ring binders instead: one for the autumn term, and another for the spring and summer term. This may be expensive though.

Here's a flick through one of the better folders so you get an idea of what my students' classwork looked like:
Worksheets and Printing
I made a one page sheet for every lesson which included all the lesson tasks, plus space for notes. 
In number and algebra lessons this was straightforward, but in shape lessons it was more challenging to limit the material to two sides of A4. I managed it though, and now it will be pretty quick to plan my Year 11 lessons next year because all the materials are ready to go.

The only problem is the printing cost - at 2p per side, that's 20p per week for each of my 34 students, costing over £250 in printing per year. Bear in mind though that I don't need exercise books or glue, and I probably would have still done around half that amount of printing even if my students had exercise books, so it doesn't work out that much more expensive.

Organisation and Pride
At my school (all boys) we do find that quite a few students don't take much pride in their work. If you glance through a randomly chosen exercise book you'll probably see untidy handwriting, disorganised work, poor use of space, doodling and maybe even graffiti... Switching to folders didn't automatically fix this, but I did see some improvement. My students often told me that they liked having folders instead of exercise books. Visitors to my lessons always noticed on how well organised the folders were. I'm certainly not saying that folders would work for every class, but they worked for me and I'm looking forward to using them again next year.

Spotted in a student's folder: a section for
'random interesting maths' -  not prompted by me!

3 July 2017

5 Maths Gems #74

Welcome to my 74th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Area Mazes
Two years ago I wrote about Area Mazes in Gems 36 . Last week Nicke (@NEdge9) told me about the lovely website areamaze.com which I'd never seen before. This simple, user-friendly website presents a series of increasingly difficult area mazes for students to work through online. Helpfully, students are able to draw workings on the diagrams while they reason their way through the puzzles.
2. Animations
Tim Brzezinski (@dynamic_math) has been tweeting some brilliant online geogebra stuff lately. I like to use things like this in lessons as part of my explanations. No Geogebra skills are required! For example Tim has made excellent collections of animations for exterior angles and interior angles of polygons and a tool exploring linear growth vs exponential growth. Follow Tim on Twitter for lots more like this.
Another clever animation that I spotted on Twitter this week was one by Kendra Lockman (@klockmath). Kendra has created a tool in Desmos: 'Adding Integers on a Number Line' which is worth a look.

3. Angles in Polygons
Ed Southall (@solvemymaths) has been finding out about maths education over in Japan and will no doubt share lots of blog posts and articles about what he's discovered. He's already tweeted about multiple approaches for finding a formula for the interior angles of polygons.
Most teachers go with the first approach here, but for a while I've thought that the second approach (triangles that meet in the centre, leading to the formula 180n - 360) might be more intuitive. It's worth discussing.

4. Odd One Out
MathsPad has published a new set of Odd One Out resources. Students need to find matching pairs from nine items in a box, and then circle the odd one out. These activities are designed to draw out possible misconceptions. There are currently nine topics available to MathsPad subscribers and two topics available for free: Reciprocals and Simplifying Surds.

5. End of Term Quiz
My post 'End of term resources' lists maths activities that are helpful when you have a half a class or half a lesson. I believe it's very important to keep teaching maths right up to the last day of term - I never give in to students' requests for films or games! But sometimes lessons are disrupted by school events, meaning that teaching a new topic becomes difficult. This presents a good opportunity for maths enrichment.

Thanks to Richard Tock (@TickTockMaths) for sharing his End of Year Maths Quiz. This quiz is very mathsy and is written specifically for summer 2017.
This Maths Pub Quiz Pack by @SE_Education is also worth a look.

I'm very pleased that exam season is over! It's good to have some gained time, though I'm really busy writing UCAS references, sorting out displays ahead of open evening, and finding resources for the new A level. I will be blogging about new A level topics soon.

Last week I was appointed to the role of Acting Joint Head of Maths at Glyn School (it's just maternity cover, and I was the only applicant, but hey - it's nice to get a temporary promotion). It's going to be a challenge but I'm delighted to be given the opportunity.
A third of Glyn Maths Faculty enjoying prom last week

In case you missed them, my recent posts were:

I'm presenting my Angles in Depth workshop at the ATM & MA London Branch conference this Saturday so if you're based in London, do come along.

In other maths news, MEI launched a new app (Bundles of Graphs) and Simon Singh launched his Parallel Project for keen high attainers. Also, MEI have launched some excellent new A level resources on Integral, including helpful revision summary sheets.

Don't forget to book tickets for my #summaths event!

I'll leave you with this lovely activity 'Ab-surd!' from Underground Maths - I love surds!

28 June 2017

JustMaths Conference 2017

I love the summer term for CPD - I've been to two conferences in four days!

I'm very grateful to the JustMaths team for inviting me along to their first annual conference. I don't normally attend events on school days, but because all my exam classes have left I didn't need to set any cover for this one. It was a great idea to hold this conference after the end of the exam period.

I attend quite a lot of conferences and always pay my own travel and accommodation - although it's financially challenging, I think it's worth it for all the ideas, insights and networking.

I got the train to Stoke after school on Monday and was very grateful to Emma (@El_Timbre) and Laura (@LauraCodd1) for collecting me from the station. Once I'd checked into the Alton Towers Hotel I went along to pre-conference drinks, where Jenny (@MsSteel_Maths) was busy painting nails with mathsy designs (the templates can be bought here, and hopefully Jenny will be doing nails for charity at #mathsconf13 in Sheffield).
The Alton Towers Hotel was full of quirky features. The children's entertainment went on surprisingly late, with dancing toddlers everywhere at 10pm!

On the Tuesday morning, I enjoyed collecting bits and pieces from the conference exhibition including A level SAMs from AQA, GCSE problems from Edexcel, and stationery freebies from ypo. Ypo had some good Brain Booster packs which each contain 50 cards giving teachers ideas on how to use manipulatives in the classroom.
I was surprised to see a BBC stand as I've not seen one at a maths conference before - they told me about their new maths videos for use in the classroom.

The conference venue was beautifully decorated. I was surprised by the size of the event - it was much bigger than I expected. There were around 300 delegates - many were at their first ever maths conference. I normally see lots of familiar faces at La Salle's conferences but this was a totally different crowd - it was really nice to meet so many lovely new people. Some teachers had travelled from overseas to attend. The majority of teachers I spoke to had never heard of resourceaholic.com, so I guess I still have a lot of work to do (but I make no money from my website, so my marketing budget is non-existent... I rely on word of mouth, so was very grateful to Mel for mentioning my blog during the conference).
There were lots of nice surprises throughout day - including a huge number of prizes (I was delighted to win a bottle of champagne in the prize draw!), and a free JustMaths marking bag and fidget spinner for every delegate.
The day was organised a bit differently to conferences I've been to before - instead of choosing smaller workshops, we all stayed together for the whole day and listened to six sessions - one from each of the exam boards, one from Ofqual and one Q&A at the end. It was a shame not to have a session from the excellent Mel and Seager of JustMaths (it would have been good to hear what they do at their school that earned them TES Maths Team of the Year last year) but they did an awesome job of hosting the event and were very entertaining.
In the exam board sessions it was good to look at exam questions and to hear about some of the resources available to teachers (such as OCR's check-in tests, Edexcel's Access to Foundation Tier resources, and Eduqas's takeaway menus).

The absolute highlight of the day was Craig Barton's session for AQA. I've seen Craig speak at a few conferences before and it's been fascinating to see his approaches develop over time. Craig has read tonnes of research recently, and has very helpfully summarised it for maths teachers on his research page. In his session he discussed how teachers often rush ahead to complex exam questions before students have developed fluency in the each of the individual skills involved, and he said (controversially...?) that students shouldn't be doing a full GCSE paper until the March before their final exams.

Craig's suggested approach was the catchy 'IDAP': 1. Isolate the skill, 2. Develop the skill, 3. Assess the skill, 4. Practise retrieval later. He showed us examples of resources that worked well for skill development in novice learners.

The thing that stood out the most for me was what Craig said about 'non-problems'. At the moment, many of us teach Pythagoras and then give students a load of Pythagoras questions in different contexts and guises. These problems have the same deep structure (Pythagoras) but different surface structures, like these:

Students don't have to work out that they should use Pythagoras in these questions, because it's obvious if the lesson is all about Pythagoras. An alternative approach would be to give a set of questions with the same surface structure (eg an isosceles triangle) but different deep structures (eg not all involving Pythagoras). This makes a lot of sense.

I kept a tally of how many times Craig said the word flippin' - I got to 15, but I may have missed a few as I was very busy taking notes! It was an utterly awesome session and I'm really glad I was there to see it.

At the end of the conference all delegates had free access to the theme park - including a period of exclusive access to the big rides. I was really excited to try out a few rides but, annoyingly, I had a train to catch. By the time Craig and I got off the monorail and walked around the park, we didn't have any time left for rides because I had to rush off and get my taxi. But at least I had a good catch up with Craig!
I bet that everyone who stayed for the rides had a fantastic time! What a fun way to end an event.

Well done and congratulations to Mel, Seager and Fize from JustMaths - I can't imagine how much work is involved in pulling together such a big event. The next one is on Thursday 28th June 2018 - save the date!

25 June 2017


Yesterday I attended #mathsconf10 in sunny Essex. I'm very grateful to Mark McCourt and La Salle Education for another fantastic day of maths CPD and networking.

I started the day by meeting up with Lisa Winer, a math teacher from Florida who is visiting Europe for a couple of weeks. She's written a blog post about her trip here. We travelled from Central London to Essex by train and had plenty of time to check out the exhibition before the conference started. The format of the day was slightly different to previous conferences - because there were so many workshops, there was an additional session added to the programme and no keynote at the start. This worked well - it was good to be able to choose five workshops, though choices were as difficult as ever.

In the first session I presented my 'Angles in Depth' workshop. This is the first in a new series of workshops where I look at a topic in depth (misconceptions, explanations, resources etc). I feel quite strongly that this is something that maths teachers need, though I think it will take me a while to convince people of this! I blogged about it here.
Apart from the uncomfortably hot room and the glare on the screen, I think my session went well. I focused specifically on two angle facts - adjacent angles on straight lines and angles in a triangle. After my workshop, lots of members of the audience told me stories of their experience teaching angles - the misconceptions they'd seen and the approaches they'd used - which was brilliant.

Lots of people at the conference requested that I share my session online. It makes a lot more sense if you actually hear me talk through it, but here you go:

Links and sources are in the notes at the bottom of each slide.

Once I've made a few more of these I'll put them on a separate page so they're all in one place.

The idea is that these slide packs are shared with trainee teachers the first time they teach these topics. My next session, at Sheffield in September, will focus on angles in parallel lines.

After my session Charlie Dawson showed me a brilliant manipulative which is really simple to make:

In the second session I attended Mark McCourt's workshop on the history of maths education. I did a lot of research on this earlier in the year because I ran a session on it for my SCITT trainees, but I felt that I had some gaps in my knowledge so it was worth attending Mark's session to find out more. As expected, this was a really interesting session. It's fascinating that maths education keeps swinging from progressive to traditional and back again.

I then went to Andrew Taylor's session where he talked about his personal history of problem solving. He shared some lovely Malcolm Swan problems, including Skeleton Tower from the blue box.
When he shared the marking guides for the old maths GCSE coursework it made me very happy that I became a teacher after coursework was removed from GCSE. Tilly's tweet about this really made me laugh:

Andrew spoke about the reasons that coursework was discontinued and how exams now try to test problem solving skills, though of course we know that conducting mathematical investigations under time conditions is not ideal.

During this workshop a lot of people attended the lovely Jemma Sherwood's session on feedback and came out saying that they were going to start using exit tickets and wanted to know where to find some. I think exit tickets are a great idea - I don't use them but some of my colleagues do. I blogged about them last year here and included some links to exit ticket resources (though, arguably, an exit ticket should only take a few minutes to create so teachers may be better off making their own tailored exit tickets instead of using pre-made ones).

At lunch I popped along to the tweet-up and tried (unsuccessfully!) to make a cobra weave stick bomb with Lucy Rycroft-Smith.

After lunch I attended Rachel Horsman's session 'Geometrical Gems'. This was a lovely session full of practical activities. My favourite part was the Area Game, which I played with Martin Noon. The idea is to take it in turns to draw lines inside a rectangle to form triangles. When you form a triangle you claim it by colouring or labelling it. Each line you draw must start where the previous line finished and has to meet the other side of the rectangle. The person with the biggest total area at the end wins.
It's obvious now, but whatever you do you'll end up with a draw - because you'll both have the length of the rectangle as your total base, and all the triangles have the same height. Clever!

In the final session Dani and Rose headlined with a workshop on workload. I didn't go to this session because I feel that my workload is as under control as it can be. Most of the big drains on my workload (UCAS references, mock marking etc) are unavoidable. A lot of the tweets mentioned quizzes, which I've been using for a couple of years now and absolutely love. Regular low stakes quizzes are one of the best changes to my practice that I've made in recent years and I cannot recommend them enough (I blogged about it here). A level marking and feedback for a giant class of 28 is the main thing that's caused me ongoing workload issues this year - I'm not convinced that quizzes are a suitable alternative at A level, but I suppose it's worth considering.

Instead I went to Peter Mattock's session 'Opportunities for Reasoning' in which he shared lots of interesting activities and resources, including this from the Standards Unit which requires students to explain what's happening in each step:
He also shared his lovely fractions activity which you can download here.

I stayed for a couple of drinks after the conference and had a lovely chat with fellow maths teachers. Overall it was a great day and I look forward to the Sheffield conference in September.

In case you're interested, my previous maths conference blog posts can be found here:
#mathsconf9 (March 2017)
#mathsconf8 (September 2016)
#mathsconf6 (March 2016)
#mathsconf5 (September 2015)
#mathsconf4 (June 2015)
#mathsconf2015 (March 2015)
Gems 8 (September 2014)

I'm going to the JustMaths Conference on Tuesday (two maths conferences in four days!) - if you're going, see you there.

16 June 2017

Topics In Depth

This year I've been responsible for running subject knowledge enhancement sessions for five trainee maths teachers. Over the course of the year, I realised something: maths teachers spend a lot of time talking about general approaches and strategies, but very little time looking at specific topics in detail.

Examining a topic in depth prior to teaching it is incredibly powerful. Even if we've taught that topic many times before, we still benefit from taking a step back and thinking about misconceptions, approaches, explanations and resources. If we had more time then we'd be able to do this with colleagues on a regular basis. We could draw on some of the excellent topic specific resources available online, such as the National Strategy materials, the NCETM's Departmental Workshops and Colin Foster's Instant Maths Ideas. What a shame that we are so busy teaching, we rarely get time to do this.

It's very clear to me why Ed Southall's book 'Yes, But Why?' is Sage's bestselling book of the year. Rather than sharing general ideas for how to teach maths, it goes into detail on individual topics. This is what maths teachers need.

My Project
I'm excited to launch a new project! My aim is to create a series of 45 minute sessions on the entire range of topics in secondary mathematics (this will probably take me years to complete!). The sessions will cover subject knowledge (the facts, the 'why', the misconceptions) and teaching ideas (approaches, resources, good questions for assessment, how to stretch and challenge etc).

I hope that my sessions will be useful for trainees, NQTs and non-specialists preparing to teach a topic for the first time, and also for experienced teachers. These sessions could be used in schools - for example if all Year 8 teachers are about to teach indices, then they could get together and run through my (yet to be written) session on indices.

I've spent many hours pulling together the very best animations, questions, resources, examples and puzzles for my first two sessions. My first session - which I'm presenting at #mathsconf10 - is on angles, focusing mainly on adjacent angles on straight lines and angles in triangles. My second session - which I'll probably run in Sheffield - is on angles in parallel lines. I'm really excited to present what I've found. It's amazing how much there is to say on each of these topics if we really look at them in depth. I believe it's worth taking the time to do so.

13 June 2017

New GCSE: Done!

Over the last couple of years we've all been working incredibly hard to deliver the new GCSE. It feels quite surreal that after all the uncertainty, nerves and excitement, the first sitting is now over and done with.

Most teachers felt that the exams were as expected, pitched at a similar level to the mock exams and providing good coverage of the full range of topics on the specification. We knew that the exams would be harder than the legacy GCSE, and they most definitely were. We knew that the hardest questions would allow us to better identify the very best mathematicians, and it certainly looks like that will happen. We knew that some students would find the exams inaccessible. We still have a long way to go.

Now we're impatiently waiting for results day! And we're continuing to teach our Year 10 classes, but with more resources, experience and certainty than we had this time last year.

Looking back over the last few years, there are some people I'd like to thank for their outstanding contributions to the successful delivery of the new GCSE across the country.

Mel Muldowney - JustMaths
Mel's individual contribution has been absolutely amazing. She has written blog posts providing detailed information and resources for new topics, she has represented the views of maths teachers in discussions with Ofqual, she has collated questions by topic (I used these almost every single day!), and she's done so much more. Mel has worked tirelessly to support the maths teaching community. She deserves a massive thank you for everything she's done.

The Exam Boards
I know it's their job to deliver the new GCSE, but kudos to the awarding bodies for the excellent support they've offered over the last two years. They've done a brilliant job of keeping us informed - I've been particularly impressed by their instant responses to queries on Twitter. They've also provided quality resources both for teaching and assessment. Special mention to AQA for their Teaching Guidance, to Edexcel for their new content resources and to OCR for their Check-In Tests. Our competitive awarding bodies strive to deliver excellent customer service and quality materials, and us maths teachers have certainly benefited from this over recent years.

The Resource Makers
This time two years ago I was worried that new GCSE topics were woefully under-resourced. But thanks to the hard work of teachers who generously share their resources for free, there hasn't been a single lesson in the last two years where I haven't used high quality resources. There are too many individuals to list here, but they know who they are! Social media has enabled maths teachers to collaborate nationally like they never could before. Thank you to everyone who has made that happen.

The Teachers
I know we're still waiting for results, but I really think that all maths teachers across the country deserve a pat on the back for delivering the new GCSE. We didn't ask for a new qualification, and we weren't happy about the rushed implementation. Admittedly, we've moaned a fair amount along the way. We've been anxious and uncertain at times, but we've gone into classrooms everyday and delivered maths lessons with expertise, professionalism and enthusiasm. Today we should take a moment to celebrate. Job done.

And now... let's do it all over again!

4 June 2017

5 Maths Gems #73

Welcome to my 73rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. GCSE Paper 2 and 3
So, we've had the first new GCSE papers! Like everyone else, I was full of nerves and excitement on the day. Years of preparation and it finally happened. Many teachers will see their Year 11 students for revision sessions at some point over the next two weeks. If you're looking for resources for those sessions, check out Adam Creen's post where he has collated all the practice papers for Edexcel that were made after Paper 1. There's a lot to choose from! If you're AQA then head over to corbettmaths.com for practice papers. Students should continue to revise all topics, even if they appeared on Paper 1, but these resources are helpful for focusing specifically on topics that haven't yet come up.
2. GCSE Workout
Sticking with GCSE revision - a lot of people (including me) used @Adam SmithMathsnon-calculator Higher workout with their Year 11s the day before Paper 1. It took my students a good 45 minutes to complete, and uncovered a number of gaps in their knowledge. I've now made a calculator version - you can download this Higher GCSE workout from TES. Thanks to @onechriswhite who has made a helpful tip sheet to go with this resource

I've also created two shorter calculator workouts. These are intended to be used in pre-exam breakfast revision sessions and should each take 15 - 30 minutes. You can download my breakfast workouts from TES.
I've mentioned before that intermediate papers are a good source of GCSE practice questions, and it turns out that an intermediate question from 1997 was reused in this year's Edexcel Paper 1 (both Foundation and Higher) - thanks to Jo Weaver for spotting this. This is something to bear in mind for future years - old intermediate questions probably won't be used again, but intermediate papers remain a helpful resource for GCSE students.

3. Parabolator
On the odd occasion that I make my own resources, I sometimes need an online tool to sketch a simple graph. When I made my quadratic inequalities resource I used graphsketch.com, but even that isn't quite as clutter-free as I'd like. I'm pleased that @theshauncarter has now made a lovely user-friendly tool called Parabolator. With this tool you simply move a parabola to the required position and mark some points, then the sketch is instantly available to paste into resources. Read Shaun's post for more information.
4. A Level Summer Work
I find that setting summer work for students before they start A level maths is a bit hit-and-miss, particularly given that some students don't decide they want to do maths until the first day of Year 12. But, like many schools, we do have A level induction days coming up and this is a good opportunity to set some kind of preparatory tasks for our Year 11s who plan to take maths next year.

It's worth reading Kim Pitchford's (@ms_kmp) post 'Pre-A level skills boost'. She has produced a booklet full of enriching maths-related activities that students can do over summer, including playing Sumaze and watching Numberphile videos.

Another tool that's worth a look is Bridge It! which is an excellent MEI quiz game to support preparation for post-GCSE maths. Students register and then work their way through a series of levels ranging from basic arithmetic to trigonometry and vectors. 
5. Problems Booklet
Sandra from mathsbox.org.uk has shared a free booklet containing 55 maths problems.
This prompted me to tidy up my Problem Solving Resources page where you'll find similar resources for both primary and secondary school students.

In case you missed them, here are my recent posts:

Over the coming months I'll probably be blogging a fair amount about preparing for the new A level. As soon as I get some gained time it will be my main focus. There's lots to do - schemes of work, resources, content splits and so on. I'll be preparing to teach mechanics for the first time too.

I'm speaking at two conferences in the coming months - #mathsconf10 in London and #mathsconf11 in Cardiff. Both are on Saturdays and only cost £25 so do come along if you can. My workshops are part of a new series of talks where I will look in depth at specific topics, speaking about approaches, misconceptions and resources.

I will also be attending the JustMaths Conference on 27th June which I'm really looking forward to.

Tickets are currently on sale for my exciting summer maths teachers' event - check out summaths.weebly.com for details.

On my @Team_Maths1 account I've shared some classic resources over half-term, so if you're on Twitter do check it out.

Finally, I'll leave you with a nice puzzle shared by @solvemymaths via @sansu_original. I don't often make time to try random maths puzzles but I had a quick go at this and enjoyed it! What's the ratio AB:BC?

25 May 2017

New A Level Timings

After exam season is over, I expect that Heads of Maths and Key Stage 5 Coordinators all over the country will be making plans for delivering the new A level from September.

Timings at A level always make me nervous. I hate having to rush my teaching. Linear A levels are meant to improve the situation, but I'm not convinced that there will be much chance to slow down.

My school (a suburban comprehensive school with a large Sixth Form) has nine hours a fortnight teaching time at A level. I recently did a poll on Twitter to find out how this compares to other schools. Here are the results:
At my previous school I only had eight hours a fortnight and it worked fine, mainly because the vast majority of my students got an A* in their maths GCSE. I now have a lot of students who got a B in their GCSE, so the start of the year has to go at a relatively slow pace. Instead of briefly revising surds, indices and quadratics, many students need these topics taught from scratch. The same will probably be true of grade 6 students starting A level maths this September.

Later in the year, time is lost to internal exams - at my school we have multiple rounds of 'PPEs' (pre-public exams), amounting to at least six weeks off timetable over the course of Year 12 and 13. Although I do see some benefits to formal internal exams, I'd prefer to see more of this assessment happen during lessons so that loss of teaching time is minimised. 

If a fire alarm goes off when I'm teaching A level I want to cry! The time pressure is such that every lost hour is a worry. Lessons are also lost to inset days, bank holidays and school events, so a degree of flexibility has to be built into schemes of work. 

By my calculations, I will have approximately 270 hours in which to deliver the new A level over two years. This assumes that I will teach right up until the end of April 2018. 

Edexcel's scheme of work recommends 360 hours. So I'm 90 hours under. Eek.

Daniel Fox (@danielfox66) told me that his school has applied a two thirds reduction to all of Edexcel's suggested teaching times in order to make things fit. I think my school will probably have to do something similar. Hopefully that will also leave some time for revision and in-class assessment throughout the two year course. 

Having looked through the scheme of work, there are some topics where I definitely wouldn't want to reduce Edexcel's recommended timings. But, for example, their suggestion of seven hours in Year 12 on binomial expansions could easily be reduced to four hours. We will need to go through the scheme of work in detail, topic by topic, and work out where hours can be cut. I think it's feasible, it just requires a bit of work. 

Once the timings are sorted, the next task is to work out how to sensibly split the content between two teachers.

I'd like to hear how other schools are approaching timings, schemes of work and content splits. It makes a lot of sense for schools to share what they've done, so that we're not all re-inventing the wheel. Please get in touch through Twitter or by commenting below.

23 May 2017


Today is #malcolmswanday - a day for members of the maths education community to celebrate the life of the late Professor Malcolm Swan. Peter Mattock's blog post explains how you can get involved. I did not have the privilege of meeting Malcolm Swan myself, though I was lucky enough to be introduced to his awesome Standards Unit resources during my PGCE. Since then I have blogged a number of times about his resources, including my posts 'Classic Resources' and 'The Hidden Treasures of Shell Centre'. If you're not familiar with the work of Malcolm Swan, I recommend that you read his obituary in The Guardian and this lovely tribute from MEI.

In this post I share four examples of my favourite Malcolm Swan resources - those of the Mathematics Assessment Project. This project was based in America but I find that many of the resources work well in my classroom, from Key Stage 3 through to Key Stage 5.

1. Describing and Defining Quadrilaterals
I used to dislike teaching quadrilateral properties - I couldn't find any good resources that helped me assess my students' understanding. Then I discovered Describing and Defining Quadrilaterals from Malcolm Swan and his team at the Mathematics Assessment Project. The lesson materials include discussion prompts and assessment tasks. As in the Standards Unit, misconceptions are highlighted...

...and some elements of the lesson are scripted.

The resources provided are excellent, including this lovely activity:

2. Using Standard Algorithms for Number Operations 
This lesson is intended to improve students' conceptual understanding of why and how written methods of arithmetic work (such as column addition) and develop procedural fluency. Again, the lesson materials include questioning prompts and potential misconceptions. Tasks include 'Getting it Wrong':

3. Classifying Equations of Parallel and Perpendicular Lines
This lesson works well at both GCSE and A level. I remember giving the task below to my Year 10s for a homework last year and being surprised by how hard they found it.

The lesson materials are packed full of excellent tasks, including this:

... and a collaborative task in which students have to group equations of straight lines according to their properties.

4. Applying Angle Theorems
In this lesson students are presented with four alternative methods for solving this angle problem:
The task requires students to make sense of the different methods and evaluate each approach.

There are loads of excellent resources to explore on the Mathematics Assessment Project website, from full lessons to short assessment tasks (which work really well as homeworks). Do explore this website if you haven't already - Malcolm Swan was an absolute legend, and his resources are a testament to his brilliance.