13 September 2017

The New GCSE Debate

On Saturday I participated in an Institute of Ideas panel discussion on the new maths GCSE. Here is the description of the session from the researchED programme:

At the start of the session each panel member was asked to speak for five minutes. Here is the transcript of what I said:
"There is so much to say on whether the new GCSE is fit for purpose. We can approach this discussion from the perspective of a number of different types of student, and I sincerely hope that we will cover all of those perspectives over the course of the debate today. But the one aspect that I want to focus on initially is whether the new GCSE is going to give us a stronger future generation of mathematicians. This includes the engineers, the physicists, the computer scientists, the statisticians, the maths teachers... - all the professions that are apparently so important to the 'success' of our country. Are we on track to create higher quality candidates for these professions?

Improving the 'top end' was one of Gove's key drivers. In his 2013 statement to Parliament, Gove said "[The new maths GCSE] will provide greater challenge for the most able students by thoroughly testing their understanding of the mathematical knowledge needed for higher level study and careers in mathematics, the sciences and computing".

So did it work?
I'm afraid that I'm not convinced that the new GCSE has had - or will have - a significant impact on the mathematical fluency and conceptual understanding of students coming through to A level maths. One week into teaching my new Year 12 classes, it seems to me that the gap is exactly as it's always been. It may even have worsened at some schools, because they are no longer able to offer AQA's Certificate of Further Maths in Year 11 (nationally, figures for this qualification have fallen by 34%).
Even though our new Year 12s have had more maths lessons over the last two years than previous cohorts, we still have students who got a grade 7 - equivalent to an A - who can't do the basics. The grade boundaries were such that these students may well have got all the algebra wrong in their GCSE. 
I have blogged previously about using an entrance test to assess algebra skills at the start of Year 12 - this wouldn't be necessary if the GCSE was doing its job correctly. I know of a student who got zero out of fifteen on his entrance assessment - which consisted of pretty basic algebra questions - even though he got a Grade 6 at GCSE. This begs the question, what does a Grade 6 in maths really mean? 
I'm not convinced that standards have improved. I'd argue that mistakes were made in designing the content of the new GCSE specification. 
Over the last two years, maths has gained extra teaching time in most schools. This has often come at a cost to other subjects. Many schools have gone from three maths lessons a week to four, or even more. But the extra time in the classroom has not been spent improving fluency in algebra and tackling fundamental misconceptions - which would have been the best way to spend the extra time. Instead we have had to spend the extra time teaching all the new, random, bitty topics that were added to GCSE - quadratic sequences, functions, iteration, frequency trees and so on. The breadth of the GCSE is vast - there are 97 topics listed in the government's specification. Why exactly were all the new topics added? 
It isn't a head start on A level at all - if our students spend a few lessons rushing through functions in Year 11, we will still have to teach them functions from scratch in Year 13. Due to time constraints, most students will only gain a superficial understanding of the A level topics that were added to GCSE.
What would have been better - what would have actually made a difference to our A level mathematicians - would have been fewer topics on GCSE. I am pleased that Higher GCSE got harder, it used to be too easy for many students, but in my opinion it got harder in the wrong way. I would have liked to have seen the questions on the important stuff - algebra, number, trigonometry - made harder. I'd have liked it if it was impossible to get a high GCSE grade without true algebraic fluency and understanding.
This increased level of difficulty - but on fewer topics - would have better equipped our students for the challenges of A level. Depth was the answer. And depth is the answer in many high performing jurisdictions. But our government went for breadth.

It all comes down to curriculum. It will be a few years until we are able to start measuring the impact of GCSE reform in any meaningful way - perhaps even longer, as we wait for the changes at Key Stages 1 and 2 to filter through to Key Stage 4. But at the moment, whilst the specification remains so broad, it's hard for me to see there being any significant impact on our future generation of mathematicians". 

There were some really interesting points raised during the debate, and I was frustrated that I couldn't address every point in as much detail as I'd have liked (particularly points relating to the suitability of the Foundation specification and the experience of students who struggle with maths). Apologies if you were at the session and raised something that we didn't have time to properly explore - it would be great if we (ie the maths teaching community) could continue the conversation on Twitter or at a future conference. It's really important that teachers make their voice heard in discussions about qualifications and curriculum.

Many thanks to the Institute of Ideas Education Forum for organising the debate, and to Tom Bennett and all those involved in researchED for hosting an excellent conference.

10 September 2017

Cover Work

No one likes being put on cover. We have precious few free periods and we're always ridiculously busy, so last minute cover is an absolute day-ruiner. I lost count of the number of times I had to do cover for other subjects last year. It prompted me to think about what makes a decent cover lesson.

Unlike long term supply, a cover lesson for an unplanned absence is normally delivered by a randomly chosen teacher from another subject who happens to have some non-contact time. These lessons are planned in a hurry, either by an unwell teacher who has logged in from home, or by a busy Head of Department. I think we have to accept that a student may not learn anything new when their teacher is off sick. As long as it's rare, that's not the end of the world. There are plenty of useful things that a student can do independently when their teacher is absent - in fact, it can be a really good opportunity to do some focused practice. To me, the worst kind of cover lessons are those where:
  • The lesson requires expert knowledge on the part of the teacher delivering it. No one should be expected to stand up and teach a full lesson on something that they know nothing about. Cover lessons should be written with non specialists in mind. 
  • The lesson is hard work for the cover teacher. From a staff welfare perspective, we must be nice to our colleagues and not give them anything complicated to deliver or challenging to oversee. Activities should minimise opportunities for disruptive behaviour. No one wants a cover lesson from hell.
  • There isn't enough work for students to do, or the instructions are unclear, or the required technology doesn't work, or there aren't enough resources to go round. Four students huddled around a single textbook isn't ideal. 

Ideally we should always set an assessment in a cover lesson. That works perfectly. The cover teacher simply has to invigilate, and may even be able to get on with their marking or lesson planning. Instructions are clear and the risk of behaviour problems is minimised. However, sometimes the timing isn't right for an assessment.

From a maths perspective, the next best option is a whole lesson's worth of independent work - starting with a reminder of a method (in a textbook, on a worksheet or in a video), then a good set of practice questions and some extension problems. Ideally this lesson will be a continuation of the topic covered in the previous lesson. If your school has textbooks then this is easily done, but for schools without textbooks, I think that Corbett Maths is a very useful source of material.

Below is an example of a standard set of instructions for this kind of cover lesson - this can easily be copied and adapted for any topic.

Cover Lesson: Solving Quadratic Equations by Factorising
  1. Students write down the date and title in their exercise book.
  2. Show this seven minute video: https://corbettmaths.com/2013/05/03/solving-quadratics-by-factorising
  3. Display this slide on the board for the remainder of the lesson: https://drive.google.com/file/d/0B9L2lYGRiK2bRkhHM19WeGVPT1E/view?usp=sharing 
  4. Hand out these worksheets: https://corbettmaths.files.wordpress.com/2013/02/solving-quadratics-by-factorising-1-pdf.pdf. Students must work independently in their exercise book. They must write down the questions and show all workings.
  5. If a student finishes the entire sheet, hand them these extension problems: http://donsteward.blogspot.co.uk/2011/09/two-root.html
  6. Five to ten minutes before the end of the lesson, display or read out the answers and ask students to mark their own work: https://corbettmaths.com/2016/10/15/solving-quadratics-by-factorising-1

This lesson is easy for a non-specialist to deliver. The video ensures that all students are reminded of the method and therefore able to get started. Students then work independently throughout the lesson, getting lots of worthwhile practice done. Perhaps the cover teacher will allow them to quietly ask their partner for help if they get stuck. Meanwhile, depending on the class, the cover teacher (assuming they're not a maths teacher) may even be able to get on with their work.

Mathsbox provides helpful cover lesson resources (with subscription), but I don't know of any other resources available that are specifically designed for cover. Corbett Maths videos and textbook exercises seem to work very well though. I'd love to hear if you've come up with another approach to cover lessons that makes them easy to plan, easy to run and worthwhile for students. Please share!

2 September 2017

5 Maths Gems #76

Welcome to my 76th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. 'For Interest'
Dr Frost has made a set of 'Just For Your Interest' posters for A level mathematicians. These provide great subject knowledge development for maths teachers too.

I met Jamie Frost for drinks over summer - he has loads of exciting plans for his website so it's worth following him on Twitter (@DrFrostMaths) for updates. Lately he has been publishing PowerPoints for the new A level so do check them out if you're teaching Year 12 this year.
Drinks with Jamie Frost (@DrFrostMaths)
and Megan Guinan (@MeganGuinan1)
2. thaMographe
I was very pleased to receive a free thaMographe in the post! This is a wonderful invention that combines an entire maths set into a single piece of equipment.
I admit that I'm not great with accuracy at the best of times - constructions are my least favourite part of maths. I hate to see students struggling to use a pair of compasses and I very much hope that the thaMographe will one day be widely used by school children. It is certainly easy to use and accurate enough for school level mathematics - as demonstrated by my quick perpendicular bisector:

Ed Southall has written a thorough review of the thaMographe here.

You can order a thaMographe from www.thamtham.fr - shipping is free! Hopefully it will be available to buy in the UK soon.

3. Subtraction Methods
I love this graphic showing alternative methods for subtraction. It was shared by James Tanton (@jamestanton) who tweeted "Math is for each of us to own and do in whatever good way suits us best".
4. Graspable Maths
In Gems 75 I shared an algebra maze from MEI that was very popular. Through a comment left on that blog post, I discovered graspablemath.com, which is an exciting new interface for working with algebra. It's lovely to use - if you're on a computer and have some time to spare, have a play with the online algebra maze.
5. A Level Problem Book
Stuart Price (@sxpmaths) has been hard at work pulling together a large set of problems for A level maths. He has collated questions on a topic-by-topic basis, in four sections: Techniques; Problem Solving; Puzzles & Challenges, and Exam Review. The idea is that students can use these sets of questions for independent study throughout the course.

It's work in progress, but if you want Stuart to email you a link to his work so far (it's great!) please contact him via Twitter.

Here are my recent posts, in case you missed them:

I also launched my new 'Topics in Depth' page.

I was very grateful to a kind Summaths attendee for lending me copies of these 'Developing Thinking...' books which will help me in my research for my Topics in Depth project. These books come highly recommended.
If you're going to researchED next Saturday then do come along to the debate about maths GCSE - I'm on the panel of speakers.

Have you booked your ticket for #mathsconf13 on 30th September in Sheffield? I hope to see you there.

TES Maths Panel
On Tuesday I spent the day at TES with the lovely members of the Maths Panel which is led by Craig Barton. The TES Maths Panel reviews all free maths resources that are uploaded to TES. We do them in batches every now and then - it's a great way to discover hidden gems. We also do project work, for example we created a page of recommended resources for every single GCSE topic. TES are considering setting up panels for other subjects, and are changing the way that the review interface works, so we spent the day discussing this and other things related to maths education. It was a really good day and I was very pleased to finally meet Chris Smith (@aap03102), writer of the awesome maths newsletter that I blogged about in my 'Newsletter Gems' posts here and here.
With one of my favourite Scottish mathematicians - Chris Smith

Pizza with the panel

I had Inset yesterday and I start teaching on Monday - exciting!

Don't forget that my resource libraries might help with your lesson planning.

I'll leave you with this thought from Underwood Dudley, taken from his excellent piece "What Is Mathematics For?". I think this is quite inspirational at the start of a new school year.

"...when I am before a bar of judgement, heavenly or otherwise, and asked to justify my life, I will draw myself up proudly and say, “I was one of the stewards of mathematics, and it came to no harm in my care.”"

28 August 2017

Summaths 2017

My Summaths event took place yesterday in the glorious sunshine at Bletchley Park. In this post I just want to share a few highlights and say a few thank yous. This was the fourth maths teacher event that I've organised (my previous events being Christmaths 2015, Maths Meet Glyn and Christmaths 2016). I think that our online maths teaching community is wonderful so I really enjoy getting everyone together in person.

I fell in love with Bletchley Park when I visited it last summer. I knew that it would be a great venue for a maths teacher event.

75 teachers arrived bright and early on Sunday morning and spent the day exploring the beautiful Bletchley Park. Thomas Briggs ran a series of workshops on codebreaking which were very well received by all. In another room, there were maths activities and excellent Enigma demonstrations.

After a lovely lunch and glass on Pimms on the lawn by the lake, we wandered round to the National Museum of Computing. This place is awesome. They have loads of cool stuff for mathematicians, including collections of slide rules and calculators. I loved playing Mario Kart on an old N64, and one of the highlights of my day was a virtual reality dinosaur.
We returned to Bletchley Park for a super hard quiz which was won by Angus, Em, Jan, Brian, Em, Chris and Rob who only dropped one mark! Very impressive. The quiz is here if you'd like to have a go (with answers, and previous quizzes). Thank you to Ed Southall (@solvemymaths) for contributing the cryptarithm and anagrams.

Each attendee got a goody bag which contained freebies from @TTRockStars, @JaneAppleton24, @AQAMaths, @OCR_Maths, @thinkmaths, @FlipTheSystemUK, @Cipher_Master and @BuzzardPublish. Thank you very much to each of these generous contributors.

A large group of us went to the pub for dinner afterwards, and had a really nice evening.

Huge thanks to Thomas Briggs (@TeaKayB) from Bletchley Park and Jacqui Garrad (@JacquiGarrad) from The National Museum of Computing for helping me to organise the event. Thank you to everyone who enthusiastically participated, and special thanks to those who helped me fill and distribute goody bags. Finally, a huge thank you to my lovely colleague Lizzie Stokes (@MissStokesMaths) for giving me a lift to Bletchley and back.

It was a hot and tiring day, but I loved every minute. All of my photos are in a Facebook album here, and check out the hashtag #summaths to see more photos and tweets from the day.

I'm back to school on Friday, feeling inspired and raring to go.

15 August 2017

Planning for September: Year 12

I'm looking forward to teaching the new linear A level to two Year 12 classes this year. I've been preparing some materials for these classes and thought it might be helpful to share them here, in case they are of use to anyone.

1. Scheme of work and resources
When preparing schemes of work, schools have had to look very carefully at timings to make sure they can fit all of the A level content into the two year time frame (I blogged about this here). At my school we took the estimated hours from Edexcel's scheme of work as a starting point and cut everything by around a third - it just about works, though our teaching will be rather rushed.

My school's new A level scheme of work looks very similar to our GCSE scheme of work, with a front page showing an approximate timeline and then a more detailed page for each topic showing the specification and resources. We won't have any student textbooks so links to resources are vital. I've blogged about A level resources before and many of these are still useful for the new A level. There are a few gaps for new topics but we'll have to cross that bridge when we come to it.
Although the content of the maths specification hasn't changed dramatically, there are a few minor tweaks that we need to look out for. For example the AS specification now includes fractional inequalities like those shown below (these were previously on FP2 for Edexcel). It's a subtle change and straightforward to teach, but could easily be missed.
From Pearson Textbook Pure AS (spot the typo!)

Many schools are planning to teach the pure content first and leave the applied content until later in the year. When we come to the applied content, it will be useful to refer to Edexcel's Teaching Guide for Mechanics and Teaching Guide for Statistics.

2. First lesson
I've created a PowerPoint for my first lesson with Year 12 which you're very welcome to borrow and adapt. It includes course information, some introductory algebra activities (from Don Steward, Susan Whitehouse and Underground Maths), and the entry assessment I blogged about here.
First lesson activity from Susan Whitehouse
3. Student blog
At my previous school I was a Key Stage 5 Coordinator and really enjoyed running a simple blog for Sixth Form students. I hope to do this again this year. I've set one up at glynmaths.blogspot.co.uk and will use it to share information and exercises with students. As they won't have textbooks, it's important that I make sure they have access to plenty of independent study material throughout the course.

4. Student handbook and checklist
Our Sixth Form students are required to keep a course handbook or specification in their folder for every subject. This year I have updated our handbook for the new A level, including the topic checklist at the back. If you'd like to borrow and adapt this, there's a Word version here.
Delivering the new A level will be hard work for all involved, particularly for those teaching Further Maths. Initially we will have all the same challenges that we had for the new GCSE - a lack of past papers, relatively few resources, no grade boundaries and uncertainty around timings. But nevertheless, I think we're all really looking forward to getting stuck into teaching it next month.
Teaching support from Tarquin A level

4 August 2017

5 Maths Gems #75

Welcome to my 75th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. New Displays
I recently updated my displays page with some lovely new resources. This might be useful for teachers preparing their classrooms or corridors for September. One of my favourites is the new Maths Word of the Week display from @missradders.
2. Algebra Maze
Last month I joined the MA and received an exciting parcel full of publications. This included an edition of Mathematics in School in which I spotted this algebraic expressions maze from MEI.
The MEI wrote eleven consecutive articles for Mathematics in School and are soon to start up again. You can access all eleven of these MEI Insights here - thanks to @MEImaths for sharing these.

3. New A level Resources
I now have a page of resources for new A level topics. It's much like my new GCSE support page, but I'm still hunting for resources.

Thankfully a few new A level resources have been published recently:

4. Sector Area
In my post 'Polygraph Rocks' I wrote about the wonderful Desmos classroom activities. There's now a huge collection of activities on Desmos - they're definitely worth exploring. These lessons are really easy to run and work well if you have access to a decent IT room or if your students have tablets or laptops in the classroom. I spotted 'Sector Area' on Twitter recently and really like the way it's designed. It's a proportional reasoning activity in which students explore the relationship between circle area, sector area, and sector angle.
5. xaktly
I found the website xaktly.com by Dr Jeff Cruzan (@DrCruzan) which is like an online textbook for maths, physics, chemistry and biology. The maths section contains very clear explanations and some helpful graphics on misconceptions, definitions and methods.
The page on the metric system is a good example - Dr Cruzan's method for unit conversions is interesting and worth a look.

There's lots of A level content, including a page on optimisation with very useful example problems. 

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

I also published a list of maths education conferences for 2017/18 and my case study was featured on mtpt.org.uk.

My Summaths event is in three weeks and now I've seen the programme of workshops I'm even more excited. I'm also really pleased that I've had some generous donations of freebies to hand out on the day. There are still a few tickets left and booking closes on 14th August.

Do check out Craig Barton's latest podcasts and Adam Creen's list showing where to buy the cheapest calculators this summer.

In case you missed it, I'll leave you with this wonderful news about the success of the UK team at this year's International Maths Olympiad in Rio. The UK finished in ninth place, out of 111 participating countries, and top of all European nations for the first time ever.
The UK is hosting the International Maths Olympiad in 2019. Incidentally, Dr Geoff Smith's 'Advice to Young Mathematicians' is worth reading.

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.

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!