28 July 2017

Bridging the Gap... Revisited

Back in 2014 I wrote the post 'Bridging the Gap to A Level'. The concerns and ideas I shared in that post are very much on my mind this summer, as we approach the start of the new linear A level.

Experienced A level teachers know that every year there are many students who find the transition from GCSE to A level very challenging indeed. It's heartbreaking when a hardworking student struggles with A level maths because they have gaps in their underlying knowledge. I'm always wondering if there's anything we could do differently in the first few weeks of Year 12.

Will the new GCSE help?
I don't think that GCSE 9-1 has done much to lessen the gap between GCSE and A level. I previously thought that all the extra maths lessons would make a big difference. But the extra time in the classroom has not been spent improving fluency in algebra and tackling fundamental misconceptions - instead we have had to spend the extra time teaching all the new topics that were added to GCSE - quadratic sequences, functions, iteration, Venns, frequency trees and so on.

Perhaps I should wait until after GCSE results day to say this, but I have a feeling that a student will be able to get a Grade 6 with pretty poor algebra skills. At my school, the entry criteria for A level maths is a Grade 6.

If you're wondering how on earth it's possible to get a Grade 6 with poor algebra skills, I'll explain... There's a really wide range of topics in maths GCSE. A student might have memorised how to find a mean from grouped data. They might have memorised index laws. They might be good at Pythagoras, probability trees and scatter graphs. They might pick up a lot of marks on best buy questions...  But at the same time as picking up marks in all these random topics, they could write a load of algebraic nonsense in their exam. They might make fundamental algebraic errors when expanding brackets, or solving a simple equation, and it's still possible to get a decent mark - maybe a Grade 6.

These students might choose to do maths at A level, even though their algebra skills are such that they will get totally lost in the very first lessons of Year 12. We need to help these students catch up from day one.

Previous attempts
The Bridging The Gap Test that my school used in September 2016 was an hour long and tested a wide range of GCSE topics including algebraic fractions, linear graphs, surds and solving quadratic equations. The average test score was 79% for 95 students, with marks ranging from 50% to 100%.

The correlation between the September Bridging the Gap Test scores and February C1 Mock scores was positive, but it wasn't particularly strong. This either tells us that our early intervention was somewhat effective (there were students who did badly in the Bridging The Gap Test but did fairly well in the C1 Mock), or it tells us that the Bridging the Gap Test results were not a good predictor of future performance.
It's really hard to assess whether intervention is effective. In fact it's hard to assess whether anything in teaching is effective. One of my Year 12s still couldn't expand double brackets a week before his AS exams. I kid you not. It's crazy that I'd been teaching him calculus when he didn't have Year 8 algebra skills. I wonder what we could have done differently for him, and others like him.

A new entry assessment
I've written a new entry assessment that hopefully pinpoints exactly where the gaps lie, to allow for highly targeted intervention. You can download it from TES here. This test is:
  • short (because we are really pressed for time in Year 12 next year)
  • print-budget friendly (only one side of A4)
  • very quick and easy to mark 
  • highly specific 

This 15 minute test is intended to be issued in the first maths lessons of the year. Its purpose is to identify the students who need immediate intervention, and to identify which specific skills they need to be taught in order to access the basics of A level maths. 
This test is not intended to challenge the brightest students at all. To them it's just a quick and simple refresher. The content of the assessment is straightforward, in fact it's mostly Key Stage 3 stuff. This shouldn't be necessary, but it is. I don't want to patronise my new A level students so I will emphasise the expectation that every student should get full marks. Students with a Grade 6 or higher in their maths GCSE should easily be able to score 100% on this test, shouldn't they...? Hmm, we shall see.

If you're looking for a longer or more challenging baseline assessment for A level, Edexcel has a one hour assessment here. They have one for Further Maths classes too - this is a great way of assessing suitability for Further Maths.

A new approach to intervention
Testing and intervention needs to be immediate, allowing a student to change course if required. If a student decides to pick another subject instead of maths, they must do so in the first few days of Year 12 so they don't fall behind in their new subject. Some schools leave testing and intervention until the third week of term. I think that's too late.

Using the entry assessment to select students for compulsory attendance, I will run five separate intervention sessions within the first two weeks of Year 12. These will be on simplifying, expanding, factorising, solving and number (basic roots and indices, negatives, and the order of operations). The sessions will involve specific teaching, practice and a homework task on Hegarty Maths.

Once the initial two week intervention period is over, we'll run the usual after school help clinics all year round. The question is, how do we effectively support those students who really struggle throughout the two year course? How do we avoid the Us? How do we encourage the right work ethic? I'd love to hear what your school is planning to do.






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.

Resources
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.

CPD
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.

Update
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!