23 May 2016

GCSE reform - will it work?

Nine months into delivering the new GCSE and I'm starting to wonder if these reforms are going to work. The Government wants to raise standards in maths education so that England can 'win the global PISA race'. But global league table dominance is not our country's only aim. The Government is also trying to increase the quality and quantity of students taking maths at A level. This, apparently, will make the country 'more productive' and increase our students' earning potential. These aims do not sit well with teachers, but we all agree that there is room for improvement in maths education. We want what's best for our students, and for future generations.

The Government's mechanisms for raising standards in mathematics education are:
1. Supporting teachers to improve the quality of teaching.
2. Increasing the amount of time spent teaching maths.
3. Increasing the amount of content on the GCSE specification.
4. Increasing the level of challenge in GCSE exams.

So is it working?

Quality of teaching
The best way to raise standards in mathematics education is to improve the teaching in classrooms across the country. Although there's lots of brilliant teaching, if you look at the bigger picture we're actually seeing a lowering of teaching standards as schools become more and more desperate to recruit. Vast numbers of students are being taught by teachers who lack the subject knowledge to teach maths effectively. There's also many classrooms where behaviour management comes before maths. Sad but true. The current landscape is not conducive to good teaching.

Many of us find that our busy teaching timetable often gets in the way of preparing high quality lessons. The only initiative that would actually make any significant difference to the quality of teaching across the country would be a reduction in contact time, giving teachers more opportunity to develop their subject knowledge and pedagogy. Of course, a reduction in contact time will never happen because of the costs involved.

The Government has made some investment in the Maths Hubs initiative, and a number of hubs are doing fantastic work, but it's definitely not enough. Not by a long way.

As Anne Watson says, reported in today's Schools' Week article, there has been “little support provided for this very radical shift of focus in teaching".

Timetable allocation
I welcomed the Government's drive to increase the amount of time spent teaching maths, which was incentivised by double weighting maths on Progress 8. But some schools have not adjusted their timetables. This has resulted in a huge mismatch in teaching time across the country, with students in some schools getting 5 hours a week compared to 3 hours a week in others. This disparity really adds up across the course of a school year. It's a maths education lottery for children.

New content
I taught Linked Pair GCSE this year, as part of a pilot in which students take four exams, leading to two GCSEs in maths. My students were taught a lot more content than students in most other schools. So did learning more topics in Linked Pair produce better mathematicians? I don't think so. Just because my class can calculate AER and (on a good day) estimate the area under a curve, it doesn't mean that they are better prepared for A level maths than your class.

If we want our students to be better prepared to embark on A level maths, we want them to be fluent with algebra, indices, fractions and surds. Strong reasoning and problem solving skills are important too. Adding new GCSE content like frequency trees and iteration doesn't achieve this.

The worst thing about the GCSE reforms, in my opinion, is the increase in breadth when in fact all we needed was more depth. We already had too many topics on the GCSE syllabus and now we have even more.

Harder exams
Making GCSE exams harder is only an effective mechanism for improving the quality of maths education if it is accompanied by a corresponding shift in teaching quality.

Vanessa Pittard of the Department for Education says, “As a country and culture we do need to reform our whole approach to mathematics, our expectations, our teaching, our attitudes to maths”.

This huge cultural shift won't happen overnight. It certainly won't happen by next summer. It's going to need investment, strong leadership and patience.

22 May 2016

#mathscpdchat - Celebrating Don Steward

Please join me for #mathscpdchat at 7pm on Tuesday 24th May to explore Don Steward's fantastic resources.

Don's blog Median has recently passed its millionth view so this seems like a good time to share our favourites from his vast collection of rich tasks. Join the chat to discuss which resources you've tried and which have worked well.

To start us off, here are three of my favourites.

1. 'One incorrect simplification'

I love this set of tasks. When I took over my current Year 11 class in October, I gave them this activity in the first lesson. At the time they were working at GCSE grade B or C and it was important for me to know how fluent they were with algebra. This activity is really engaging - as my students got stuck in, I had the opportunity to circulate, assess their understanding and discuss common misconceptions. They found the task accessible but quite challenging, which set the tone for what their maths lessons with me would be like.

This expression caught most of them out:
I'm sure you can see what the common mistake is here - most students incorrectly simplified this to 3 + 5n. This raises a useful discussion about grouping and brackets, or lack of brackets.

This activity also works brilliantly as a warm-up on A level induction day.

2. Difference of Two Squares
Recognising and being able to factorise a difference of two squares is a useful skill throughout GCSE and A level.

Give a student an algebraic fraction to simplify and you'll often find that they have no idea what to do with a 4x2 - 9 in the numerator, even though they seemed to understand how to factorise a difference of two squares when you previously taught it.

Don Steward has some great activities for teaching this topic, culminating in this awesome set of challenging questions. I love these.
This reminds me of another Don Steward task - 'Mega hard powers questions' which offers stretch and challenge for students learning fractional and negative indices. This task works well at A level too.

I like it that both of these tasks help students realise how much easier it is to use improper fractions rather than mixed numbers or decimals.

3. Form and Solve a Quadratic
Forming equations comes up a lot in GCSE exams (particularly in Linked Pair GCSE, which is what I've been teaching this year). I'm not sure our students get enough practice of this - which is partly why so many were stumped by Hannah's Sweets last year. Don Steward has a lovely set of tasks for forming and solving quadratics.

Students often find it really hard to know where to start on problems like this so careful questioning and scaffolding may be needed.

In this post I've only shared algebra resources, but bear in mind that Don's resources are awesome for shape, measure, number, proportional reasoning, data and probability too. I will share many more resources during the chat on Tuesday. See you then.

20 May 2016

C2 Revision Resources

This is a quick post to share some resources for Edexcel C2 revision.

  • Revision Lesson Activities
Your students might enjoy my C2 Revision Relay.
I've made a C2 Revision Clock and Andy Winterbottom has made one too. See my previous post for more on revision clocks.
I've also made a Quick Facts Quiz which would work well as a revision lesson warm-up. The questions are taken from my C1 and 2 Revision Cards

  • Topic Focus
If your students need to practise a specific topic then try the topic papers on Maths Genie. Solutions are provided.
The topic assessments from Oxford University Press are also helpful for topic-focused practice. 

  • Papers
There are loads of C2 practice exam papers online, including past papers, Solomon papers and tiered papers.
Challenging papers are available from madasmaths.com. I have used loads of these this year!
Additional C2-style questions can be found on m4ths.comStudyWell and mathshelper.co.uk. m4ths.com also provides an Extension Practice Paper

I hope this is helpful.

I'll try my best not to get annoyed at the inevitable social media overreaction on Wednesday! Some of it is actually quite funny... #edexcelmaths

13 May 2016

Revision Clocks Galore

In my last post I wrote about revision clocks - an idea from @teachgeogblog that was shared by @Just_Maths back in October. Check out the hashtag #revisionclock to see these in action in numerous subjects. They are now all the rage in maths. No wonder, given that they are easy to prepare and do a great job of keeping students focused during revision lessons.

The idea is that you set 12 five minute questions that students answer on an A3 clockface. I haven't yet used a revision clock with Year 11 (though lots of people have done so with great success) but I've used revision clocks in a number of A level lessons and have found them to be really effective. In these lessons I set a buzzer to go off every five minutes and at that point I write an answer on the board.

I've received so many tweets about revision clock activities that I thought it would be a good idea to share them here so that everyone can access the resources. This post contains revision clocks for both GCSE and A level


The resource for this tweet is here.

The resource for this tweet is here.

A level

And finally...
Here are template clockfaces for various combinations of timings - for example you might want to do 15 two minute questions followed by 6 five minute questions.

If you make a new maths revision clock resource then please upload it to TES or an online drive and tweet me a link so I can add it to this post. This should save teachers a lot of time in planning revision lessons. Thanks to all who have contributed! The final exam countdown is on...

8 May 2016

C1 Revision Activity

The revision clock idea has become incredibly popular now that it's revision season. It originated from @teachgeogblog back in October and was introduced to the maths world by Mel (@Just_Maths) in her post 'Keeping Time'. I shared the idea at my school's weekly staff briefing on Tuesday and it's now being used in a number of subjects across the school.

If you teach Year 12 then you might like to borrow my C1 revision clock which I have uploaded to TES. I've made two versions. The easier version took some of my students 30 - 40 minutes to complete. Others were working on it for the full 60 minutes.

I felt that I probably hadn't made it challenging enough for students aiming for a top grade, so I've now made a harder version which draws questions from MadAsMaths.com's IYGB papers. This one should take the full hour.

Question from MadAsMaths.com IYGB C1 Practice Paper X

(By the way, thanks to @icecolbeveridge, I now know what IYGB stands for. I wonder if you can guess. It's a reference to the difficulty of the papers...).

Both versions of my C1 Revision Clock are editable so you can tweak the questions if they're not suitable.

The revision clock activity allows students to practise working under timed conditions and keeps them on task and engaged throughout the revision lesson. It's worth trying if you haven't already - it works for any age group.

All my other resources can be viewed through my TES 'shop' - they are all free, of course. If you're looking for other revision ideas for A level and GCSE then check out my blog posts:

Not long to go! Less than two weeks until C1... eek.

7 May 2016

See you there...?

I'm looking forward to speaking at four maths education events in the coming months.

Warwick 2016
Edexcel's conference 'Excellence in Mathematics: Into the Future' is in Warwick on Saturday 2nd July. I'm incredibly excited about this event because Hannah Fry is the keynote speaker. You may have seen Hannah on TV recently (on Horizon and Gogglebox!) - she is a lecturer at University College London and author of 'The Mathematics of Love'. I saw Hannah speak at a Mathematics in Action event a couple of years ago and it was outstanding - she's a brilliant speaker and I can't wait to see her again.

The rest of the conference promises to be excellent, including the pre-conference dinner which looks like fun (there's a pass the parcel!). Delegates will be able to choose three workshops, including sessions from my Twitter pals Mel (@Just_Maths) and Emma Bell (@El_Timbre). I'll be presenting on 'The Wonderful World of Maths Resources' - I've enjoyed planning this presentation, it's a bit different to anything I've done before.

The cost of this conference is £185 (or £220 if you want to stay the night before). It's worth asking your school to fund this, it's a good price for a whole day of quality CPD and because the conference is on a Saturday you won't miss a day of school.
Two events for A level teachers
On Friday 8th July I'll be speaking at the FMSP's annual London KS5 Network Day. This is a popular event for A level maths teachers in London. For FMSP registered schools it's only £50 for two teachers. In my session I'll be focusing on resources and ideas for teaching the core A level modules. There will also be sessions on statistics and mechanics and an update on the new A level (by then we will have seen specifications and sample material).
Tom Bennison, Tom Wicks and Ria Symonds are hosting the East Midlands Key Stage 5 Mathematics Conference in Nottingham in the summer holidays. It's on Tuesday 9th August and costs a mere £25. I'll be speaking about A level resources and I'm looking forward to attending the other sessions too.
LIME Oldham
I'm very impressed by Lindsey Bennett's brilliant work supporting maths teachers. Her free LIME (Leaders Improving Mathematics Education) events are held after school in Oldham - recent speakers include Don Steward, Colin Hegarty and Craig Barton. I'll be making my way to Manchester on Monday 20th June to speak about mathematical methods. I did a workshop on methods at #mathsconf2015 - my session at LIME will be similar but I'll be focusing on new GCSE topics, including alternative methods to find the nth term of a quadratic sequence and solve a quadratic inequality. Come along to explore and evaluate which methods and explanations work best.
There are a number of other events happening over the coming months, including researchED Maths and Science on 11th June (which has now sold out), the MEI Conference (I went last year and loved it - read about that here) and La Salle's Complete Mathematics Conference in Leeds on 25th June (I'm disappointed that I won't be able to attend - these conferences are always good).

All upcoming conferences for UK maths teachers are listed here. Have I missed anything?

See you at an event soon!

1 May 2016

Animations for A level

Last week I presented on A level resources at Stuart Price's 'Maths in the Sticks' event. I spoke briefly about how we can use animations to support our explanations of mathematical concepts. Many teachers already make use of programmes such as Geogebra, Autograph and Desmos, but here I'm talking specifically about animated gifs that teachers can simply paste into a PowerPoint. Gifs run on a loop so students can watch them for a while, providing 'thinking time' in the lesson and allowing new ideas to click into place.

I use gifs alongside physical demonstrations where possible, for example when I teach Volume of Revolution I show animations and use paper props too (see Gems 45).

So where can you get animated maths gifs? A Google Images search is normally sufficient but there are a few websites you might like to check out:
Here are some examples of gifs suitable for A level. You can copy them directly into PowerPoint. Some are more helpful than others - watch each animation for a minute and decide whether you think it adds any value.

Definite Integration. Source: 0a explains
The Trapezium Rule. Source: Vivaxsolutions.com
Radians. Source: LucasVB

Tangent to a curve. Source: Calculus in Motion

Completing the Square. Source: LucasVB

Product Rule. Source: mathwarehouse.com

Quotient Rule. Source: mathwarehouse.com

Logs. Source: Purplemath.com

Normal Distribution by Robert Ghrist. Source: Gizmodo

If you're looking for animations for Key Stage 3 and GCSE have a look through my blog posts tagged 'animations'.

30 April 2016

Talking Points

I've been talking about three things on Twitter this week: study leave, calculators and contact time. I need more than 140 characters! All opinions are welcome, either through Twitter or in the comments below.

Study Leave
At my previous school all Year 11 and Year 13 students would disappear in early May, returning to school only to sit their exams. It was a girls' grammar school - the students were hard working, driven and independent. They made good use of their study leave, and the teachers made good use of gained time for projects such scheme of work development. I now work at a boys' comprehensive where students are expected to attend school throughout the whole exam period. This 'no study leave' approach is fairly common. I think it raises really interesting questions about how schools can best support students preparing for public exams. What do you think? What's best for students - studying at home or at school?

My school does Linked Pair GCSE and my Year 11s have one of their four maths GCSE exams in the afternoon, which is unusual. Three hours of maths revision at school has been scheduled for the morning of that exam. I'm worried that this will exhaust my students, perhaps to the detriment of their exam performance. Five hours of maths in one day doesn't sound like a smart idea.
I'd rather they stay at home, but it's not up to me. I will do my best to create a relaxing and encouraging environment at school. We'll do a little bit of maths, but certainly not three hours of intense last minute revision. What would you do?

Thanks to all who offered ideas on Twitter - let's hope it's a nice day so I can take them outside in the sunshine!

Last Sunday I attended the absolutely brilliant 'Maths in the Sticks' CPD event for A level teachers, organised by Stuart Price. I've already shared my initial views on the changes to A level, but in that post I deliberately didn't mention calculators because I haven't made up my mind about them yet.

I'm not a luddite, I'm not anti-technology, but I'm afraid I don't get excited about calculators like some people do. I still use the same calculator that I used at school and university.

I like the fact that C1 is currently non-calculator and I will miss this element of A level. I'm also quite fond of statistical tables. I accept that statistical tables will eventually go the way of log tables and slide rules, but I do feel a bit sad about it.
I used to tutor a private school girl who was struggling with A level maths. One day she showed me a snazzy new calculator that she'd been sold at school. Although she didn't understand the maths involved, she was very good at using the calculator. Clearly her teacher had spent a lot of time in lessons going through the instructions. I was surprised that this calculator was allowed in exams because it seemed to give her an unfair advantage over students who couldn't afford an expensive calculator.

You could argue that learning how to use this kind of technology is a useful skill, but I'm not convinced it's as important as people make out. I suspect that these skills will be forgotten within weeks of the end Year 13. Plus technology quickly becomes outdated anyway.
So forgive me for not welcoming the 'use of technology' aspects of the new A level with open arms. I'm already bored by it. There are also practicalities to consider. And don't even get me started on 'large data sets'...

Contact Time
Finally, thanks to everyone who replied to this tweet:
It was fascinating to see how much variation there is between schools.

As expected, it seems that larger schools are more likely to have a number of TLRs in the maths department. But this is not always the case - in some large schools the Head of Maths has to do (or delegate) everything (which is a lot!).

Answers regarding contact time were inconsistent, ranging from no extra time allocated to four hours per week. It seems that most Key Stage Coordinators are allocated between 1 and 3 extra non-contact periods a fortnight.

The job description of a Key Stage Coordinator also varies a lot - roles may involve running help clubs and interventions, preparing assessments, undertaking lesson observations and performance management, analysing data, processing exam entries, developing schemes of work, organising competitions plus a plethora of other duties.

Key Stage Coordinator roles are a good stepping stone to Head of Maths, so certainly worth having a go at. I used to be a Key Stage 5 Coordinator and really enjoyed it. I'm not sure I'd do it if I wasn't allocated any extra time though.

Opinions are most welcome!

Please do let me know your thoughts.

23 April 2016

Gem Awards 2016

On 27th April it's resourceaholic.com's second birthday!

Last year, on the first anniversary of my blog, I wrote Gem Awards 2015. Since then I've published an additional 28 updates from the world of Maths EduTwitter. Today I bring you some highlights from those posts. So raise a glass of champagne with me, and toast the winners of the second annual Gem Awards!

1. Best Game
The maths teachers at my school love Is this prime?. We get students from Year 7 through to Year 13 playing it in the classroom. We compete against each other in the Maths Office too. It's fun, addictive, accessible and surprisingly challenging. Top marks to Christian Lawson-Perfect for a wonderful game.
2. Best Teacher's Website
My favourite new find this year is drfrostmaths.com. James Frost teaches maths at Tiffin, which is a London grammar school shortlisted for the TES Maths Teacher or Team of the Year Award. His website, which I featured in Gems 41 last October, includes worksheets and presentations suitable for high attainers, enrichment resources, A level resources and more.
3. Best Gif
I love gifs! I particularly like these tessellation gifs which show polygons that do and don't tessellate. If you'd like to see how I used these animations in a lesson, read my post 'The Joy of Planning'.
Special mention to this Order or Operations gif that I featured in Gems 46 - it still makes me laugh!
4. Best Demonstration
Speaking of gifs, I've always used an animation to demonstrate to my students that the exterior angles of a polygon sum to 360o. I've never thought of doing this lovely paper demonstration instead. This was shared by Sharon Porter and featured in Gems 32.
This is exactly the kind of thing that Twitter is good for - sharing pictures of things you've done in the classroom that other teachers may not have thought of.

5. Best Prompt
Anything that prompts interesting class discussion is worth a look. I really like these lovely statistics graphics which get students thinking about the reliability of statistics. I used them in my first S1 lesson of the year. 
6. Best New GCSE Support
The most useful set of resources for the new GCSE is the collection of Exam Questions by Topic on justmaths.co.uk. Mel has collated exam questions from the sample, specimen and practice papers of all four awarding bodies. I find these resources incredibly helpful when planning Year 10 lessons.
The best department meeting we've had at my school this year was one in which we looked through some of these resources- see my post about this here.

Special mention also to AQA for their new GCSE support and resources - their Teaching Guidance is fantastic and I love their topic tests, which I often use as homeworks.

7. Best Resources
Don Steward has always been my favourite resource provider - in fact I gave him a Lifetime Achievement Award in last year's Gem Awards. His blog is approaching its millionth view and I look forward to hosting a #mathscpdchat next month in which I will be asking people to share their favourite Don Steward resources.

Given that I already gave Don the Lifetime Achievement Award last year, this year I have decided that the 'Best Resources' award goes to MathsPad

MathsPad is packed full of brilliant resources. Some are free and some require subscription. The writers, James and Nicola, are constantly adding new resources which are always well designed and high quality. I often feature their resources in my gems posts.

I also want to mention a couple more resources that I discovered in the last year.
  • I love angle chases! They're lots of fun. I was delighted when Mo from MathedUp! shared a great set of angle chases which I featured in Gems 35
  • In Gems 48 I shared a resource from Dan Walker on TES. He has taken problems from Junior and Intermediate Maths Challenges and organised them by topic in a PowerPoint, with solutions. This, along with Leanne Shaw's new website Maths Problem Solving, means that it's now much easier to find problem solving activities for specific topics.

8. Best Revision Idea
I love Mel's Keeping Time idea in which students are given twelve 4 - 6 mark questions to complete in an hour on A3 paper which has been split into twelve sections, like a clock face. This is a great way of practising working under timed conditions ahead of the exam and it helps keep students focused throughout the lesson.

Maths teacher Miss Suganthakumaran read about this idea in Gems 42 and found it worked really well in fast paced revision lessons with her Year 11s. She has uploaded her adaptation of this resource to TES. I look forward to using it with my Year 11s.
Special mention to John Corbett for sharing his revision idea which involves sending packs of goodies to students at Christmas. Read his post to see how it worked. I've seen lots of lovely adaptations of this idea, including this example from @mathsbrowning.
9. Best Puzzle
There are loads of awesome maths puzzle makers who share their creations on Twitter. Do check out the puzzles of Ed Southall and Emma Bell if you're not familiar with them.

My prize for the best puzzle this year goes to a different type of puzzle. The winner is Lisa's Puzzle from The Simpsons, because I really enjoyed my students' reactions when I took it into school. I put it on posters in the maths corridor to advertise an enrichment talk, and I later saw students crowded round it trying to work it out. Some people solved it instantly, but others (including maths teachers and Year 13 Further Maths students) couldn't work it out at all. I tried it with some Year 4 children and once they'd solved it they were really excited to take it home to try on their parents! It's great that a puzzle can appeal to all age groups.   
10. Bright Idea
My final award category is 'Bright Idea' where I look at some of the best original ideas that I've featured in my gems posts over the last year.

The award goes to Nikki's presentation guide, which I featured in Gems 35. I think it's really important to set clear exceptions for students at the beginning of the year.
John Corbett had a lovely idea, featured in Gems 39 - he put stationery baskets and photo frames on desks. The frames display Nikki's presentation standards. The picture can be changed regularly, for example to display information about revision sessions, star students and so on.
Other 'Bright Ideas' that deserve a special mention include Videoscribe, which I used to make expectations videos for each of my classes back in September; Famous Five, a lovely idea from Emma Mccrea that you can read about in my post 'Some Things I've Tried'; and Hannah's resources noticeboard for the Maths Office on which teachers pin their recommendations for upcoming topics - see Gems 39 for more on this.

That's it for the 2016 Gem Awards! What a fantastic collection of ideas and resources. If you want to read more Maths Gems, there's an index here.

Thank you to everyone who tweets about what they've tried in their classroom. Please keep doing so! I've been on Twitter for two years now and I still can't get enough of all the resources, inspiration and support. Long may it continue.

16 April 2016

5 Maths Gems #55

This is my 55th update from the world of Maths EduTwitter. If you're not a tweeter, or if you're wondering whether you've missed anything, here's a summary of some of the latest resources for teaching maths.

1. Daily Problems
White Rose Maths Hub (@WRMathsHub) will be publishing daily GCSE problems on Twitter in the run up to this year's exams. The files are available through TES.
White Rose Maths Hub has also made a fantastic collection of Reasoning and Problem Solving Questions designed for Key Stage 1 and 2.
2. GCSE Revision Cards
Thanks to Maria Howard ‏(@MrsHsNumeracy) for creating this nice set of GCSE revision cards so students can quiz each other.
3. Problem Solving PowerPoint
Thanks to Emma Bell (@EJmaths) for her work on AQA's Problem Solving PowerPoint. She has organised the questions by topic and tier so now it's much easier to find problems that are relevant to the topic you're teaching. She has also added the answers to make this a really user-friendly document.
4. Quibans 
If you teach Core Maths then you might be interested in these Quibans tasks from Mark Dawes (@mdawesmdawes). Quibans are 'questions inspired by a news story'. Mark's posts include suggestions of the sort of questions you could explore.
5. New Websites
I've seen a couple of new (free!) maths websites this week.

Darren Carter (@MrCarterMaths) has launched MrCarterMaths.com. This website displays sets of questions by topic. It is well formatted and easy to use.
Thanks to ‏@SaintAidansMath for making me aware of pentaed.com which is a revision website for students working towards a C. Again, I really like the uncluttered, user-friendly format of this website. Each page displays five GCSE questions - click on each question to reveal the answer. Follow @pentaeducation for updates.
I've had a busy first week of the summer term what with mock exam marking, reports, a Parents Evening and lesson observations. It seems like ages since the Easter holidays!

Did you catch my recent post about A level revision resources?

If you're looking for ideas for GCSE revision lessons then my post Higher GCSE Revision will help, as will Craig Barton's 2016 TES Maths GCSE Revision Collection.

Finally, I'll leave you with two puzzles that you might enjoy. The first was Alex Bellos' (@alexbellos#MondayPuzzle in The Guardian. Can you fill in this grid with the numbers 1 to 16?
The second puzzle is a Yohaku. The example below might work well as a lesson starter. Here you have to fill in the cells to get the products in each row and column and the sum of the four cells must be 31. Check the Twitter account @YohakuPuzzle for more challenging puzzles.