5 Maths Gems #203

Welcome to my 203^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Diagram Builder

I absolutely love this game changing diagram builder! mathfigures.com is the best I've seen. Thank you to @harryzafar for drawing it to my attention. 

It's incredibly easy to use. If you want to make a diagram for a lesson, resource or assessment, you can create one in seconds. 

I like the way the box plots update automatically as you add data, which means it can be used as a teaching tool too.

Built by the team at teacher.dev, there are also versions for chemistry and physics so share these with your science department. And the physics diagrams will come in handy for A level mechanics.

2. Two Minute Math

Colin Foster is incredibly good at explaining maths concepts. His new videos at Two Minute Math present mathematical concepts in bite-sized videos, mostly around 2 or 3 minutes long. You could show these videos to students, but they are also brilliant for teachers' pedagogical subject knowledge development. If you're about to teach, for example, significant figures or perpendicular bisectors or bearings, then watch Colin's videos so you know how to introduce these concepts really well. There's a wide range of videos, including some for A level topics like logarithms. I wish I had time to just sit down and watch all of Colin's videos! They are excellent. I plan to use them in department meetings this year. 

3. Maths Habit

@themathshabit.co.uk is a secondary maths teacher who has built a free website themathshabit.co.uk featuring Key Stage 3 and GCSE resources: full lesson decks, worksheets built on faded scaffolding, puzzles and end-of-unit tests. I think there may be a lot of useful resources on this website so do check it out. 

There's so much content I can't list everything here, but it includes 'Aiming for the next grade' exam questions.

And Key Stage 3 Assessments...

The walkthroughs are a clever idea - students could stick them in their book before starting a practice task. 

There are loads of worksheets, like this Trigonometry Perimeters Codebreaker.

There are resources for formula sheet practice.

There are also loads of tools like an exam timer and printables. So much to explore!

There's been a large number of new websites and resources appearing recently - this is definitely one of the best I've seen.

4. A Level Resources

Two of my favourite task designers - Amanda Austin and Nathan Day - have been busy making A level Further Maths resources.

On @draustinmaths.com's Further Maths page there are new resources for Maclaurin, momentum and complex numbers.

And @nathanday shared some CP1 vectors questions and a method guide, plus a great Core Pure 1 revision mat.

I found a task in Heylings that helped me introduce Matrix Transformations. 

@jamiewoodmaths made a really good tool for understanding the order of operations for combined graph transformations. Try it - it's so clear! I have a related resource on combined transformations that I made back in 2014.

And finally, some challenging questions from @andrewmaths1 on surds and indices (and many other topics) aimed at TMUA/ESAT candidates but suitable for others too.

5. New Websites and Tools
It's ironic that I'm a huge AI-sceptic (mainly because it pains me to see people increasingly unable to write a letter or plan a lesson by themselves) but I receive a lot of emails telling me about free websites and tools for maths teaching built with the help of AI. I know there's value in these websites so I'm sharing some of them here for my readers to explore and decide what they find useful:

• School Ninja - past papers, mark schemes, revision notes and topic questions, plus cute little jokes. It includes papers from AQA, Edexcel, OCR, WJEC, Eduqas and Cambridge.
• Edexcel IGCSE 4MA1 Past Paper Solutions - full worked solutions for IGCSE papers.
• From @Pencil201, a lesson explanation generator for Key Stage 3. Download this one to access it.
• Wonderlattice.com - a set of 27 small interactive experiments with big mathematical ideas.
• eclassroom.org.uk - a collection of free GCSE and A-Level maths revision resources including printable PDF topic worksheets with full worked solutions, interactive practice engines for online practice, an exam paper builder and an interactive starter of the day. It also has a Maths Skill Tree system which almost 'gamifies' learning maths - the goal is to master all topics.
• milomarwick.com - 3D spatial reasoning puzzles which may be helpful if you're teaching plans and elevations.

Update

I'm now off school on a two week half term break which is a great relief after a busy six weeks. I'm very much looking forward to BCME next weekend. Apart from that I'll have a relatively quiet couple of weeks in which I will mainly be catching up on school work, filming CPD videos for HoD Space, taking a short trip to Liverpool (my daughter is a big Beatles fan), and watching Traitors (still great, even after what happened to Hannah!). I'm also going to see Leslie Odom Jr at the London Palladium on 31st October for my daughter's 15th birthday. So lots to look forward to!

I'll be delivering a workshop at #mathsconf42 in Barnsley on 14th November. I'm excited that it's a new talk from my topics in depth series, this time on simultaneous equations. I've been doing a lot of research from old textbooks and I have loads of very cool stuff to share - way too much, in fact! So this is another job for half term: working on my mathsconf presentation. I'm really looking forward to sharing what I've found.

HoD Space continues to be a brilliant place to get support and share ideas and resources. Free trials are still available so join now at HoDSpace.com. Craig and I record podcasts every two weeks in term time where we share some of the things that are being discussed - listen to our latest episode here.

I had a lovely day out with my team at an Inset Day last week. I particularly enjoyed the keynote from Rob Eastaway 'Much Ado About Numbers' - if you haven't seen this talk, make sure you see it! Or buy the book. Then try his Elizabethan Maths Quiz.

Finally, I've been asked by Simon Singh's Parallel Academy to share their tutoring opportunity. They currently support 1,000 bright and enthusiastic secondary students at UK state schools (including students from my school). These students receive weekly online tutorials and they need strong tutors - you can apply via this link. 

That's it from me - I hope to see lots of you at BCME, or if not then at mathsconf in November.

And if you didn't watch Hannah Fry's video on the maths of Traitors, recorded before she went in, then do have a watch. 

HoD Space

When you get promoted to a new role in a school, whether it's as Key Stage Coordinator, Head of Department, Head of Year, or a Senior Leader, you probably don't get any training on how to do that role. If you're lucky the previous job holder is around to show you the ropes, but sometimes you just have to wing it, all by yourself. 

For the last couple of years I've been increasingly keen to offer training courses for newly appointed Heads of Maths. But in order to start a training business I'd have to stop being a Head of Maths, and that's not going to happen (I love my job!). I do already support Heads of Maths from across the country all the time - through my blog but also through email - over the last two months I must have received over fifty emails asking about my scheme of work. But it's very labour intensive for me keep sending advice and resources to individual Heads of Maths. So I was in need of a big idea to solve my problem - how to better upskill and support Heads of Maths - and along came Craig Barton, who always has good ideas. What if I delivered my Head of Maths training online, and provided resources to download directly, and we created a community where Heads of Maths could connect and help each other? Like Twitter used to be, with the constant sharing of advice and ideas and resources, but better - without the adverts and the politics and the hate. Craig introduced me to the Circle app, which is exactly what we need. We genuinely believe this is going to be a game changer, so we've invested in it and we're now ready launch our exciting new project: HoD Space. 

I've only been using the app for a week myself, and we only have a few members at the moment, but already I'm absolutely loving it! You can join too - the more members we have, the better it gets - and it will cost your school less than the cost of a training course. But it's so much better than a training course. You get my training, my resources, a weekly podcast where Craig and I will discuss the big topics that are coming up in the forums, and you get an entire year of expert support instantly available. Imagine being at work and knowing you have access to expert mentoring in your pocket. People who you can ask for help with difficult decisions, difficult conversations, or even the routine stuff - how do I decide on GCSE tiers, how do I set up my department tracker, how do I go about recruiting a new member of my team?  The impact is going to be huge.

Let's have a quick tour... I'll show you some screenshots from the app.

It's ridiculously easy to navigate. When you first join, read the welcome section then add a post in the introductions section and either me or Craig will say hello. Also complete your profile so we have information about your role and your school (this will come in handy later, when the community is large and you want to connect with people who, say, offer the same qualifications as you). 

There are various spaces where you can post questions. Sometimes there will be a quick answer, sometimes a lengthy discussion. If something causes a lot of debate, Craig and I will pick it up in our weekly podcast (we've just posted our first podcast episode). The space running the department is for the practical side of the job. Examples of questions might include:

• Where do you put your non-specialist teachers, and what support do they get?
• How do you structure TLRs in your department?
• How do you handle movement between sets during the year? 
• What's the best thing you spent money on this year?
• What do you do for Year 11 intervention?
• How do you handle a teacher whose behaviour management isn't working?

If there's something you'd rather ask without your name on it, you can send it through an anonymous question form, and we'll post it on your behalf.

There's a similar space for curriculum and teaching, where questions might be about schemes of work, feedback, marking, qualification delivery models, enrichment, and so on. With upcoming curriculum tweaks, and perhaps even more significant shifts in curriculum on the horizon as proposed by the new prime minister, there will be a lot to discuss here over the coming years.

There's also a space for recommendations and things to celebrate (I love this - a space where you can share things that have gone well at work - something most of us never do in public on social media).

There's also a surveys section where I will regularly gather information that we are all dying to know about each other's schools! Like the old Twitter polls that we all loved. I've started with two surveys on curriculum time (Year 7 and 11). Now I just need everyone to sign up to the free trial and complete my surveys!

In my video library I'll share two CPD videos each month, each one around 10 to 20 minutes long. I've already posted videos on planning September Inset meetings, setting Year 7, what to do on Results Day, and communicating with your team. I've also recorded videos on communicating with parents, setting up department trackers, scheme of work design, recruitment, and seating plans - these will all be published on the app soon. I have loads more videos in the pipeline, including assessment design, Year 11 intervention, running UKMT competitions and so on. 

Anyone can post in the resources to magpie section. I've already put some stuff here, and there's more to come from me in September. Soon I hope it's full of content shared by hundreds of Heads of Maths.

The members section is where networking happens - find HoDs in local schools, find HoDs who offer the same qualifications as you or have the same challenges, connect with them directly, maybe even visit them. There are literally thousands of Heads of Maths in the UK - imagine what we could do if we all joined forces. This is networking at its smartest. 

And what might come next for HoD Space? I can imagine in-person events (HoD Space conferences?), HoD Space for English and Science... So many ideas! So much potential.

I want join! What should I do?
Join today on a totally free trial. If you join now, you'll get full access for four weeks at no cost (free trials are normally only two weeks, but we're offering four weeks this summer only). We won't even ask for your card details up front. Then when you go back to school in September, ask your school to pay for your membership from the school's CPD budget. Given the impact it will have on the maths department, it will be very easy to justify. And if they won't pay, don't worry - you can take your career development into your own hands - we offer a cheaper membership if you're paying with a personal card. 

This isn't just for Heads of Maths - perhaps you're a 2ic, a TLR holder, or an aspiring Head of Maths. This is for everyone who wants to learn how to run a maths department, wants support for the department they already run, or just has an interest in what we're doing - join us on a trial to see if it's right for you.

Sign up today at hodspace.com. If loads of you sign up to the free trial and start posting questions or joining the discussions, it will start working really well. I need lots members so everyone can see how good it's going to be! Make sure you download the Circle app to access it - the app is brilliant. 

I'm really looking forward to chatting to you and sharing ideas on HoD Space. See you there!

 

Tasks for the Summer Term

I like the summer term.  

At my school Year 11 are in lessons until half term, but Year 13 went on study leave on 8th May, which means my teaching timetable has already lightened and will soon reduce further (this year I teach both Year 11 Maths and Year 11 Further Maths so I'll gain a lot of time when Year 11 leave). With all the gained hours in a day you would have thought the summer term would be relatively easy. But, surprisingly, it always feels like the busiest time of year. School work still extends into evenings and weekends in June and July in the same way it does in every other month. But, with my Head of Maths hat on, the summer term workload is distinctly different – fewer lessons to plan, but far more administrative tasks. A lot of the job becomes about preparing for the next school year.

As I’ve been Head-of-Mathsing for a good few years, I thought it might be helpful for inexperienced Heads of Maths if I share some of the things that they should be thinking about this term to make sure their department hits the ground running in September. If you’re an experienced Head of Maths then you will already have all of this on your radar, and perhaps other things I’ve missed. The idea of this post is just to give some ideas to Heads of Maths who are new to the role.

Curriculum Development
It’s a good idea to ask your team for feedback on whether your curriculum is working well. Perhaps there are times teachers feel rushed or the order of topics doesn’t quite work. Get this feedback now – if your curriculum needs a re-write it’s a big job. Also consider exams analyses from previous years. If your school’s A level or GCSE results showed underperformance in certain topics (compared to national performance) then you might need to make some changes. For example, one of the topics we were weakest on in a previous year’s GCSE was product rule for counting, so this year I’ve reviewed when we teach that and how long we give it, and I’ve done some department professional development on how to teach this topic.

If your scheme of work is working well then the only thing you need to do is adapt the timings to fit next year’s calendar. I usually need to move a couple of topics around to make things work, but changing the placement of topics has knock-on effects on resources and assessments which is a pain. The timing of the 2026 August Bank Holiday means a lot of schools are going back later than usual this September - for us, the first half of the autumn term is going to be a week shorter than it was this year, and the first half of the summer term is a week longer.  So everything still fits but some rearrangement is needed. My schemes of work look like this (each link on the schedule takes you to a topic page where a possible lesson breakdown is provided, but teachers don't have to follow this exactly - they adapt it for their classes):

I can’t do any work on curriculum timings until my leadership team confirm the dates of next year’s assessment windows (they in turn have to wait for the MAT to confirm the dates – I never understand why the MAT waits until so late in the school year to decide the following year's assessment calendar). It means I can’t do all my curriculum work until the last couple of weeks of the summer term. And it’s not just rewriting the scheme of work – website documents have to be updated too, and I need to load the curriculum for each year group onto Sparx which is a big job.

Sparx will look a bit different for our Year 11 next year - previously we’ve set normal Sparx homeworks right up until Easter but we’re going to change that. We like the new GCSE revision tool on Sparx so we're going to set that from February half term of Year 11, instead of topic-based homeworks.

Assessment Writing
We write new mid and end year assessments for Years 7 to 10 every year. This is partly to ensure students don’t get hold of the previous year’s assessments and memorise the answers. An advantage of writing new assessments every year is that we can use previous years' papers as revision material. I enjoy writing assessments, particularly searching for (or creating) novel questions to challenge students. But it’s such a huge job that it’s hard to get in done during the busier periods of the school year, so I try to make a start in the summer term where possible (I try to – but it requires a lot of focus which is hard to achieve at school, so I normally end up doing most of it in the summer holidays or October half term).

This year we wrote Year 13 mocks from scratch for the first time. Last year we used Edexcel’s secure mock papers (which are excellent) but students had clearly managed to find these online, or perhaps through tutors, so we ended up with lots of inflated predictions. It was so frustrating to waste time marking mock A level papers for students who had clearly seen the papers in advance. One boy got 100% in his mechanics mock (!) – his solutions were flawless, seemingly written by a mechanics genius – but he went on to score 62% in the mechanics paper of his actual A level exam in June... We’d had enough of all this cheating so this year we gave up on the secure mocks and instead made our own A level mock papers using questions from a variety of sources. It worked very well, so we’re making one more set. My colleague Linda will do this during her Year 13 gained time – this is an excellent use of time in the summer term.

Resource Improvements
We use warm booklets for retrieval practice at the start of our lessons, and at the end of each topic we give a test (we call these ‘snapshots’). All of these are teacher-made - sometimes they were made in a rush six years ago but get re-used every year. The summer term is a good opportunity to review and improve these resources. For example our snapshots are sometimes a bit short of space so some re-formatting is needed. Here's an example taken from one of my own Year 11 snapshots - in the top image there wasn't enough space for students to present their work clearly. The bottom image is an improvement. 

Improving the quality of shared resources is a good task to direct my team to complete after Year 11 have left. 

Subject Knowledge Development

The summer term is a good time for teachers to prepare for any new courses they're teaching next year and to develop their subject knowledge in the courses they already teach. 

The day after GCSE and A level exams have taken place I hand the spare papers out to teachers of those qualifications and expect everyone to complete the papers themselves. We become experts in the qualifications we teach when we regularly complete exam papers.

As well as completing exam papers I also hope to spend some time this term reading Colin Foster's new website bigmathematicalideas.org. 

Timetabling, Groupings and New Staff Induction
I’ve already done the class allocations for next year (i.e. deciding who will teach each year/set) and now we’re waiting for the timetabler to run it all through the system and we’ll see what comes out the other side. My hope, as always, is for minimal split classes. I have a rule that no classes of low attainers should be split between two teachers, so when the timetable comes through I’ll probably have to make some tweaks to ensure this happens (I don’t like any class being split but it's less of a concern for classes of high attainers).

We’re lucky that every year our timetable is ready for new staff induction day, which is on 29th June this year. On this day I run a department meeting after school (joined by new members of staff) where I hand out provisional timetables and set out the big picture and expectations for the next academic year. It's important that new staff go home from their induction day knowing exactly what they're teaching in September.

Another one of my big jobs in the summer term is allocating students to maths sets for next year. It’s important to get this right (particularly when it impacts GCSE tiering) so it takes time – it’s mainly spreadsheet work but I also need to get input from teachers. Our setting is based on performance in formal assessments (mid and end year) but we also take into account classwork throughout the year. I have to wait until Key Stage 3 assessment results are ready before I can get started on this job, and I have to wait for SATs results before I can start grouping the new Year 7s (these are released on 7th July but there’s always a delay getting all the UPNs we need - so this is another job that ends up being completed right at the end of term). I also get heavily involved in groupings in other subjects (careful allocation of students to bands is a key strategy for behaviour management) - all of this happens right at the end of term when there's lots of school events going on (I'm leading two Year 7 trips in the last week of term!) so it gets a bit crazy. Don't ever let anyone tell you that the summer term is quiet!

Preparation for September
There’s a lot of preparation for September that needs to be done in advance. In August I have to spend a lot of time checking papers for A level and GCSE candidates who were close to a grade boundary so I've learnt from past experience not to leave my September planning until August.

I encourage my team to start preparing their resources for September in July (as soon as they know their timetable then they can get started). This includes hole punching exercise books, printing warm up booklets and preparing first lessons. I do this for my own classes too – September Inset Day is always very busy so I know I won’t have time to plan lessons then.

There’s also stuff to prepare for September as Head of Maths – the big one is the maths department meeting on September Inset Day. This is the most important meeting of the year so I always spend a lot of time preparing it. I also need to produce and update posters and slides for my team to share with students in September – for example slides on how to use Sparx (there are new features we need to tell them about) – see my post September Routines for more on this. And of course there’s loads of housekeeping to do in the final weeks of the summer term – updating corridor displays, tidying classrooms and offices, and placing the annual ‘big stationery order’.

***

This isn't meant to be an exhaustive list of ‘things to do in the summer term’. In all schools there's a lot going on at this time of year (for us it's things like Year 6 transition interviews, Year 10 work experience calls, vast quantities of UCAS references, Open Evening, trips, induction days, assessment marking and plenty more). This is just a post about ‘things Heads of Maths should be thinking about at this time of year’, in case you’re new to the role and not sure where to start. I hope it helps!

#mathsconf40

Mathsconf40 took place in Derby yesterday. I thought it might be helpful to write a quick post to update my readers on some stuff I learnt.

I enjoyed Joe Berwick's (@berwickmaths) session on teaching statistics at A level. My degree was in Statistics at UCL (I actually did SORMS, which is similar to MORSE at Warwick - a popular course amongst our Year 13s) so I teach a lot of statistics, including FS1. Further Statistics 1 is a great choice of module for A Level Further Maths. It's particularly beneficial to students wanting to study economics at university (a popular choice) and numerous other courses. And there are many great career options for keen statisticians, such as Data Science and Actuarial Science. Our students who have studied GCSE Statistics (which they don't love) are always pleasantly surprised that they enjoy FS1. Joe also talked about the benefits of teaching FS2 - students get to learn confidence intervals which feature in many university courses. 

The majority of Joe's talk was on teaching the statistics content of A Level Maths. He talked about how the large data set includes the Great Storm of 1987 - I remember this very well (I was a very scared 6 year old living in an area with lots of big oak trees, many of which fell down). Coincidentally I'm telling my Year 12s about this tomorrow, and sharing some photos of me in the aftermath of the storm (in the first photo I'm with my mum and brother - we took these after the roads had been cleared of trees).

Joe talked about how he teaches correlation hypothesis testing first, before he teaches normal and binomial hypothesis testing. This gave me something to think about. He has very helpfully shared some of his lessons slides on berwickmaths.com. Joe made a lot of good points about things that I too have noticed - for example, that the Edexcel textbook has a single exercise on Discrete Random Variables but it comes up all the time in exams, and the questions are very different from those in the textbook (for example they include questions on the sum of two DRVs). I noticed this too and did a lesson on it with my Year 13s last week. I wasn't aware that OCR is a great place to get DRV questions for modelling and practice (see the OCR Paper 2s here - full of great questions that I can use in my Year 13 revision lessons in the next three weeks).

In the second session of the day I presented on how we engage and challenge Key Stage 3 mathematicians at my school. I think our strong GSCE results and the high uptake of our maths GCSE option (last term over one third of Year 9 students chose our course - which I blogged about here) are both down to what we do at Key Stage 3. I spoke about our curriculum, department professional development, and our assessment strategy. In particular I'm interested in research that suggests some students aren't exposed to 'novel' maths in Year 7, and I showed examples of what 'novel' might look like.

In the next session there were a number of fantastic talks on offer but I was still buzzing from running a session so I took the opportunity to have a break and catch up with my mate Dr Ed Southall. I also picked up some freebies from the exhibitors and enjoyed my bag of tuck from Rob Smith's excellent tuck shop. I learnt about the Unit Award Scheme offered by AQA which is great for schools who manage to teach students part of the L2 Further Maths course but not enough for them to enter the full exam.

Did you know that Ed is co-chair of the BCME 10 committee? BCME (British Congress of Mathematics Education) is a big research-based residential maths education conference, attended by lots of academics. I'm considering presenting at BCME this October, but only if lots of teachers attend the conference as my presentations always written for teachers. I had a great time at BCME 9 back in 2018 (blog post here) when I was lucky enough to receive a bursary. Teachers - I urge you to sign up to either speak or attend - the website is bcme.co.uk. 

After lunch I went to Matt Man's (@mr-man-maths) session on international exam papers. Matt was responsible for providing me with 'officially the most helpful bit of information I have ever picked up at a mathsconf' (see my post about mathsconf37) which was to explore different specifications on ExamWizard to find fresh banks of questions (I have recently found International A level very helpful for my Further Maths lesson planning). In Matt's session yesterday he talked about a range of qualifications and we had the opportunity to try some questions from those qualifications. 

Finally I went to Ed Southall's workshop on problem solving where he talked about what problem solving is (this will feature heavily in maths curriculum reform in the next few years). We also had a go at some different types of problems. This is part of the work Ed does at Maths Horizons which you can read about here. 

I missed Tim Dolan's (@timdolan) session on online maths tools. I often use online tools for demonstrating concepts - for example my daughter was practising for the Junior Maths Challenge last week and there was a question on rotational symmetry. She didn't know what that was so I used MathsPad's rotational symmetry tool (login required) to explain it to her. I also use a lot of animations in my teaching (gifs inserted into PowerPoints), for example when teaching constructions. I love it that Tim has collated loads of great online tools in one place on his new website mathsindex.uk. Tim invites teachers to contribute ideas for additions to the website. 

I had a nice train journey home with Megan Guinan and Jamie Frost. It was a great day overall, and it was delightful to see that there were many teachers attending mathsconf for the first time. As always, the best part was the networking, chatting about maths teaching, and catching up with old friends. Thank you to La Salle for running the conference and to City of Derby Academy for hosting it. Attendees of the conference will be able to access all the PowerPoints when La Salle shares the link in a few days. In the meantime, I'm always happy to share my schemes of work and/or assessments - just email me. See you at the next one!

Conferences and Catching Up

I’ve been out and about over the last couple of weeks, doing my usual rounds of the summer term maths events. I’ve been quiet on my blog in recent months, partly because relatively few new resources have been shared on social media, and partly because my day-to-day workload continues to be relentless, leaving very little time for hobbies like blogging - I’m sure many other Heads of Maths and teachers can relate to this. As it's been a while since I've blogged, I thought it might be worth writing a quick post to tell my readers what I’ve been up to lately, and what conversations I’ve been hearing in maths communities.

TES Awards
My first event of the summer season was the TES Awards. My school was nominated for a technology award, mainly for the huge amount of brilliant robotics we do (in robotics competitions we’re mainly competing with grammar and independent schools). As head of a STEM subject they kindly let me tag along to the event – I’m not directly involved in robotics so I really appreciated the invitation! We didn’t win our category but we had a lovely evening. It took place in a fancy hotel on Park Lane and was attended by over a thousand teachers in their finest attire. The event featured a performance from Hercules and a brilliant comedy set from Tom Allen. It was an unusual and enjoyable night out!

MathsConf
The day after the TES Awards I travelled to Birmingham for Mathsconf38. I always love a mathsconf – it’s great to catch up with friends and meet new people. I presented on some fun maths from old textbooks, mainly with a focus on surds.

AQA Panel
On Tuesday my timetable was clear (I taught a lot of Year 11 and 13 this year!) so I had the opportunity to attend the AQA Maths Expert Panel Meeting in London. I very much enjoyed this day (not just because it took place in a delightfully cool office on the hottest day of the year, a welcome relief from the furnace that is my classroom). It was great to catch up with lots of people who I haven’t seen in a while including Julia Smith, who is writing a book about maths teaching, Danielle Bartram, Colleen Young, Jamie Frost, Peter Mattock and Tom Bennison. We had some excellent discussions about AI, GCSE Maths, GCSE Stats, A levels and All About Maths.

MEI Conference
The MEI Conference is always brilliant. It’s my favourite event of the year. I was teaching on Thursday morning but travelled up after lunch, arriving in time for the excellent conference dinner on Thursday night. If you’ve not been before, you might not know that this conference dinner always has a free bar, paid for by the lovely people at Casio. A free bar is a rarity in education so it feels like a real treat. Dinner was great and I particularly enjoyed catching up with Anthony of thechalkface.net who I used to chat to loads on Twitter back in the day, and David Bedford who always has wise words and interesting stories to share. The after-dinner speaker this year was Rob Eastaway who did a brilliant talk on viral maths problems which I very much enjoyed.

I loved all the sessions I attended on Friday. Bernard Murphy ran a fantastic workshop called 'Exam questions that give more than they ask'. If you've ever been to one of Bernard's sessions then you'll know that they always feature a very high level of challenge for delegates! Thinking deeply about difficult maths the morning after drinking a lot of Casio-sponsored wine was hard on my brain but I really enjoyed it. For example, Bernard shared this relatively simple question from the 2018 AQA AS Paper 1...

but talked about how -4x + 6y = 0 is a linear approximation to the circle as you get close to the origin. This led down a rabbit hole that I won't attempt to explain here, but was fascinating.

We also looked at some interesting aspects of this question from the 2021 AQA A Level Paper 1:

Students found this question particularly challenging because it didn't tell them to solve the differential equation - they had to work that out for themselves. Again, Bernard took us down a rabbit hole of maths relating to this question.

We looked at a number of lovely questions in this session, and two of them stood out as being useful early in Year 12. When we have students who start Year 12 with a really strong understanding of GCSE content, particularly those who have studied Level 2 Further Maths, sometimes it can be difficult to challenge and engage them in the early lessons on indices and quadratics. So it was great to see a couple of questions that we could use in these lessons to get students thinking. This one is from the 2019 OCR(A) A level Paper 2:

And this one is from an OCR AS Paper. This was my favourite question of the day - there are at least six different methods that would work here!

My next session was 'Getting to grips with interviews' with Tim Honeywill. This was incredibly useful and well timed for me. At my previous school I didn't get involved in Oxbridge applications because we had a very wise and experienced maths teacher who specialised in supporting students with this. Now I work in a new school that's just had its first Year 13 cohort, and we have absolutely no experience and expertise in this area. This year I had to write two Oxbridge references - one for economics and one for engineering - and students asked me to help with both interview preparation and STEP preparation. Luckily the AMSP came to the rescue with the STEP support, and interview support was provided by someone in the MAT. But I realised that I seriously need to upskill in this area so I can support my students better. Tim's session was enlightening and I now have a far better understanding of what happens in these interviews and how to support students preparing for them. 

In the next session I delivered 'Strategies for Challenge'. I had a lovely group of delegates who asked lots of good questions, so I enjoyed running this workshop.

After lunch there was an excellent keynote from Sarah Hart, writer of the book Once Upon a Prime. 

In the final session of the day I learnt how to use the CG100 for statistical analysis. I have no experience with graphical calculators so it was good to have a play with Casio's latest model. We don't use them at my school - I really struggle with the idea that students who spend more money on technology have an advantage in their A level exams. It upsets me that this situation is allowed to exist. Maths should be a level playing field for all. It's such a dilemma - I don't believe that money should be able to buy you a better grade, but by insisting that I won't make my own students buy graphical calculators, I increasingly feel that I disadvantage them. 

Ethical dilemmas aside, I enjoyed the session and it was good for me to finally make a start in understanding how to use these calculators. I now feel ready to explore my CG100 on my own. Casio were incredibly generous, giving a free CG100 to anyone who attend a Casio session. They were also handing out amazing goodie bag as always. I will take pleasure in sitting in my Casio hoodie, drinking from my Casio mug and using my Casio pen from my Casio pencil case!

Shout out to Integral too for the top quality goodies (I love the mechanical pencil!). 

If you’ve never been to the MEI Conference then give it a go next year. It really is brilliant. It's fun to stay on a university campus, the facilities and catering are excellent, the sessions are always top quality and the people are really nice. There’s lots of A level stuff but there’s plenty for Key Stage 3 and 4 too. There are always lots of teachers there whose school or college have paid for them to attend – so it’s worth asking. 

Talking Points

I may be quiet on social media but I’ve always got my ear to the ground so I can keep on top of what’s going on in maths education. Here are some of the things maths teachers have been discussing lately:

• Edexcel's A level papers caused a stir this summer. It seems that Paper 1 used very similar questions to 2022 (schools pay a lot of money for top quality original exam papers to be written every year so this is disappointing). It meant that students could easily predict what would come up on Paper 2. Edexcel reacted by using their back up replacement paper for Paper 2. This meant it wasn't a match with Paper 1 - there were topics like Binomial and Integration by Parts that didn't come up on either paper! But it also seems that Edexcel may have screwed up - though they haven't admitted to an error - the modified papers for visually impaired students were not replaced (did they forget about them? or was it too late to make modified versions of the replacement paper?) meaning this small group of students did the originally intended Paper 2. So Edexcel will need a separate set of grade boundaries for this tiny cohort. This has caused distress - I heard of a student with a reader who read different questions to those on the paper in front of her. What a mess. Read more about this in Schools Week. 

• We've known for a while that students can use AI to do their online maths homework for them, and we are starting to develop ways to identify who's doing this and address it as best we can. They key is to help students understand the value and long term gain that comes from completing their homework themselves, which is harder than it sounds! This is a frustrating issue for maths teachers. Read more about this in Craig Barton's Eedi newsletter.

• A similar issue is that the improvement of search engines using Google's AI has made it incredibly easy for students to find secure mock papers online. We have always experienced problems where students have got hold of secure mock papers through tutors, but the problem seems to have become much more widespread this year. We used Edexcel's Mock Paper 4 for our End of Year 12 assessments (that's the super secure mock set that's not even on Emporium) but when we marked Paper 1 we felt that many of our students had seen the paper before. It was hard to tell who'd done well because they'd worked hard and understood the content, and who'd done well because they had predicted that we would use mock papers and found them online. As we need robust data for UCAS predictions, we did an emergency re-write of our Paper 2 (a bit like Edexcel did!), ensuring we used questions that students can't find online. This worked, but made us realise that if we can't use mock papers anymore, we will have to write every internal A level exam ourselves going forward which is a huge workload - and very difficult to do (every school independently writing A level Further Maths mock papers from scratch every year...? No thanks!).

• Another interesting issue for us in our End of Year 12 assessments was a fake Casio calculator. We had a student who'd bought one from eBay to save money, but discovered in the assessment that it can't handle Binomial probabilities for large n. To me it was obviously fake when he showed me his calculator after the exam - it was shiny and felt lighter than it should - but he had gone the whole of Year 12 unaware of this. What a weird world we live in - who would have thought there'd be a market for fake calculators. 

• There was a lot of chat this year about 'teachers' (often not really teachers) claiming they know exactly what's going to be in exams, selling 'predicted' GCSE papers to students and making a lot of money from dodgy YouTube videos that are full of errors. This issue affects all subjects - it's worth reading this Schools Week article, and follow 1st Class Maths for more on this.

• I spoke to Dr Jen Shearman from the NCETM about the EEF's evaluation of the Specialist Knowledge for Teaching Mathematics (Secondary Non-specialist Teachers) Programme. This is done using a Randomised Controlled Trial which works by comparing the outcomes of a group of trial participants to the outcomes of a similar group which was not involved. So schools apply to the trial and evaluators randomly assign them to either an ‘intervention’ or ‘control’ group. At the end of the academic year, pupils in both groups are assessed: if the pupils in the intervention group achieve higher assessment scores than the control group, then the programme is said to have a positive impact. I find this really interesting - it's so important to assess the effectiveness of these programmes and schools need to be supportive of this. The NCETM are looking for more schools to be involved in this trial - there's more information here so please have a look.

• People keep asking me where all the maths teachers from Twitter have gone. My answer is that they are now on Bluesky. The chat on Bluesky is dominated by a small group of maths teachers, and can feel a bit intimidating at times. But it's early days. At the moment it's nothing like the glory days of Twitter (like when we ran #mathsTLP on Sunday nights) where there used to be hundreds of teachers discussing a wide variety of topics and sharing loads of resources, ideas and advice. So yes, we have lost something that I think was very powerful in maths education and I think it's going to take a while until we get back there again, but we just have to be patient. I think the best thing I can do is encourage my readers to not just join Bluesky but also start posting on there. If you have a question, or you're looking for a resource, feel free to tag me and I will help if I can.

With two weeks left until the summer holidays I’m very pleased we’re nearly there. I feel like I say this every year, but I think this was my busiest work year ever. I’m very much in need of a rest.

Enjoy the end of the school year! Thanks for reading.