MEI Conference 2015

Last week was an incredibly busy week for me. On top of a number of family events and personal commitments, I did the following:

• Attended #mathsconf4 in London and helped run the TweetUp
• Hosted #mathsTLP on Sunday night and #mathscpdchat (on behalf of the NCETM) on Tuesday night
• Had my first SLT lesson observation at my new school
• Did my first ever TeachMeet presentation at #TMEpsom
• Wrote three blog posts and processed a dozen new Pret Homeworks
• Travelled to Bath to attend and present at the MEI Conference.

It was a great week but I'm so pleased it's over! I've already written about #mathsconf4, the #mathscpdchat about Problem Solving and #TMEpsom about Pret Homeworks, so this is my final post about the events of my busy week - this post is about my experience of the MEI Conference.

Maths CPD

I've already written about the importance of subject specific CPD. Although I do pick up some ideas from generic T&L events, my teaching benefits the most from conversations about maths - both the pedagogy and the subject. Unfortunately, aside from on Twitter, opportunities for such conversations are few and far between. My previous school's budget for external courses was zero (I'm not exaggerating! No external CPD allowed at all). So at the MEI Conference it was refreshing to see that some schools do still allow their teachers to attend conferences. I quickly discovered that the opportunity to learn about maths and develop as a teacher was immense.

Because I was presenting on the Saturday I got to attend that day for free, and I was staggered by both how much I learnt and by how much I enjoyed learning. The choice of sessions was huge - over the three days there were 12 sessions and in each session delegates could choose from 8 options. Many, but not all, sessions were focussed on A level teaching and/or the use of technology.

Ideas for A Level

The first session I attended was "The aspirational grade E student" by David Philip and Claire Phillips. The session was about how to support AS maths students who have an E as their baseline/target grade. We started by discussing the reasons that so many students fail AS level maths and then found out what David and Claire have done at their school to improve results. I've thought about this issue before (see my post Bridging the Gap to A level) so it was great to hear what they've been doing, including:

• They run an algebra bootcamp in the three days before term starts for grade B GCSE students.
• They issue students with a self-assessment workbook containing the MEI exercise for each chapter (and links to solutions).
• They use a flipped learning approach for the basics (ie students watch videos at home in advance of some lessons). Feedback from students has been good.
• They have a department Twitter account (@mathsnewvic) which is the only way they communicate certain pieces of vital information (eg when the next test is).
• They give students information about what questions will be in assessments in advance (eg 'the next test will consist questions from 2011 past papers') - students then do all those questions to prepare for the assessment, which is better than doing nothing at all.
• They have whiteboard paint on the walls. I wrote about Vertical Whiteboards in Gems 7 and again I've been convinced of their effectiveness. There are lots of alternatives (eg magic whiteboards or writing on windows) if you can't use whiteboard paint. David and Claire said that often their students arrive in lessons and start solving problems on the walls straight away - sometimes they don't even put their bags down! If they get stuck they are much more likely to ask another student for help than if they were sitting down. Another delegate said that this approach had transformed her teaching.

There's also a few things that David and Claire plan to implement next year. They intend to make assessment results (broken down by question) public so students know who the expert is in each topic, and they can then go to their peers for help. They are also going to make use of the MathsWatch App which is free for students when the school subscribes to MathsWatch (the A level video collection is growing).

Problem Solving
I also attended a session on Problem Solving at Key Stage 3 and 4 with Phil Chaffé. During this session I had fun trying out a range of maths problems.

My favourite problem, which I think would be particularly suitable for Year 8 or 9, was 'Zag Area 1', which is shown below and available to download (with solution) from Integral (login required).

The session notes also featured these business card problems from the FMSP - these will be available online from September.

All the problems featured in this session were drawn from Integral, the FMSP and Nrich. If you're looking for problem solving resources then do also check out my recent post Favourite Problems.

Mathematical Methods
The slides for my session 'Tricks and Tips' are available here. This session was very similar to a workshop I presented at the National Mathematics Teacher Conference in March. It was about alternative mathematical approaches (eg all the different methods we can use to find the highest common factor of two numbers). If you look my 'Methods' page then you'll see the posts I wrote after the last conference explaining the content of my workshop.

This time I added an extra section to my presentation - I spoke about how to factorise harder quadratics. I demonstrated three methods. The first was the 'guess and test' method (commonly used by anyone over the age of 20), the second was the 'grouping' method (used by many UK teachers) and the third was the 'slide and divide' method (sometimes used in the US, but considered a 'trick' by many). We talked about advantages, disadvantages and alternatives. If you're interested in finding out more then see my post Factorising Harder Quadratics, which I've just updated. An interesting alternative approach that many delegates had not seen before was 'the monic method', which is demonstrated in these two examples:

I hope that delegates found my session useful. I did get some nice encouraging feedback afterwards so I think it went well.

Summary

The plenary 'Bouncing Bombs and Boomerangs' by Dr Hugh Hunt, Senior Lecturer in the Department of Engineering at Cambridge University, was entertaining and fascinating. Overall my whole day at the MEI Conference was fantastic and I regret not being able to attend more sessions.

So there ends my busy week. I've fallen way behind with my to-do list so now it's time to get back on track. First up, I'll continue to work on my page of resources for the new GCSE specification.

Thanks to MEI for organising such a high quality conference - I really hope I'm able to attend again next year.

Pret Homework

At #TMEpsom today - which was hosted by my lovely new school, Glyn - I did a short presentation about Pret Homeworks. This post tells the story of Pret Homeworks - where they came from, how they work, why they're great and what's coming next.

Background
Last summer Kathryn Forster, Head of Maths at the TES 'Creative School of the Year' 2015 Seaham School of Technology, tweeted some pictures of a new homework template she'd devised. It was lucky I spotted this tweet in my busy Twitter feed because it turned out to be the start of something big.

The homework pictured below is one of Kathryn's original designs. The Skill Practice element is what most standard maths homeworks involve, and remains essential, but we also have an additional four elements:

• The Literacy element requires students to learn the spellings and definitions of key words. 
• The Memory element requires students to memorise facts or formulae. 
• The Research element is a short independent research task. 
• The Stretch element provides some more challenging questions.

So the design covers knowledge, skills and enrichment all in one place.

Kathryn's homeworks are used in conjunction with peer-assessed Homework Checks in class, like the Literacy and Memory Check pictured below.

When I first saw Kathryn's idea I absolutely loved it so I featured her homeworks in my blog post 5 Maths Gems #3 back in August 2014. Kathryn and I then made a few more homeworks, and I created a page on my blog containing links to our small collection. 

I decided we needed a name for this homework format. Takeaway Homeworks were popular at the time so I put a spin on the name and went for Pret Homeworks - creating an acronym for the words 'practise, recall, extend, think'.

I asked for Pret Homework contributions through Twitter and the collection quickly started to grow. Initially I stored all the homeworks on Google Drive and linked them through resourceaholic.com, but then something went wrong - they were being downloaded so often that Google Drive stopped letting people access them. The popularity of these homeworks was quickly growing - they needed their own website. 

The Website
So prethomework.weebly.com was born. I transferred all the homeworks from my blog to a new purpose-built website. It's been incredibly popular.

I've created a number of Pret Homeworks myself, but my primary role is collator. Anyone who creates a Pret Homework for maths is asked to email it to me at resourceaholic@gmail.com and I upload it to the website. I don't edit any of the homeworks submitted, but I do encourage submissions in an editable format so teachers can tweak them if required.

We currently have around 140 homeworks from 50 maths teachers - the full list of contributors is here. If Pret Homework were a business then Kathryn would be Head of R&D, I'd be Head of Marketing, and the contributors would be our brilliantly creative workforce. My sincere thanks goes to every one of them.

Variations 

Although all the homeworks on prethomework.weebly.com are for maths, this homework format works well in other subjects. I've seen adaptations for both Science and English. I also think the homework format would work well in primary school. Our collection currently ranges from Key Stage 2 to A level including Further Maths.

The design works well for classwork too. Danielle Bartram has made a number of worksheets which were inspired by the Pret Homework format.

Perimeter worksheet from missbsresources.com

Feedback 

I recently asked on Twitter for feedback from teachers who use Pret Homeworks. I received loads of enthusiastic replies. Some schools are now using these as standard homeworks across the maths department, in other schools one or two teachers are using them every now and then. Either way, the feedback is excellent. Teachers report that the quality of work submitted is often high and that students enjoy completing Pret Homeworks.

Thanks to all the teachers who shared examples of students' work. It's amazing to see Pret Homeworks in action! 

Pret Homeworks also featured as Craig Barton's Resource of the Week in November 2014.

What's next for Prets?
The collection of Pret Homeworks continues to grow. Eventually I may need to upgrade the website to make it easier to search by topic and Key Stage.

During the next school year I hope to see more Pret Homeworks for Key Stage 1 and 2, and for other secondary subjects.

I'm excited by the work being done at Burford School where they are making Pret Homeworks to fit into their new GCSE Schemes of Work. Their homeworks are very cleverly differentiated - these will be uploaded to prethomework.weebly.com soon.

There's still lots of buzz around Pret Homeworks. Have you tried them yet? Do let me know what you think.

Huge thanks to Kathryn Forster for the idea - she's been an inspiration to many.

My short presentation from #TMEpsom is available here.

#mathsconf4

I had a great day at La Salle Education's #mathsconf4 in the magnificent Grand Connaught Rooms in London yesterday. La Salle always do an amazing job of running fantastic events for maths teachers. I love these conferences - I always come away feeling inspired and excited to be a maths teacher. I also really enjoy meeting up with all the lovely people who I interact with on Twitter.

At the previous two conferences we heard from Vanessa Pittard of the Department for Education. The first time I heard her speak I was very interested in all she had to say - I learnt a lot about the politics and policies of maths education, but like others I was slightly aggrieved by her constant references to Shanghai and Singapore and the implication that maths teachers in the UK were 'substandard'. She did the exact same presentation at the next conference so it was a relief that we didn't have to hear it a third time yesterday. Instead we heard the very sensible views of Mark McCourt, who spoke about the dangers of assuming that pedagogical approaches that work well in one jurisdiction will work well in another.

A blurry photo of my table - @letsgetmathing, @El_Timbre, @WorkEdgeChaos, @DocendoTim, @tessmaths, @dwatson802, @mathszest, @MrMattock, @OxfordEdMaths

I also enjoyed the speed dating (ie resource sharing) session - I was given some lovely ideas by @mathszest and @Zfak102 - I'll feature these in future gems posts.

The first workshop I attended was 'From Euclid... to You' with the lovely @El_Timbre. In this session Emma talked us through her vast collection of fascinating maths books. I enjoyed seeing extracts from each book, such as the 'multiple ways to word a division question' pictured below (thanks to @danicquinn for the photo). It was also interesting to learn that issues in maths education in the UK (for example the lack of qualified maths teachers) have existed for decades.

The next session I attended was about Core Maths. My new school is offering Core Maths from September so it was important for me to find out what it's all about. It was a very informative session and I'm pleased to see that there's an excellent Core Maths Support Programme website for resources and case studies.

I was disappointed to miss Craig Jeavons' (@Craigos87) 'Best of the US' session. I often read US blogs and I've featured a number of ideas and resources from these blogs in my Maths Gems (such as Estimation 180, Visual Patterns, Open Middle and Graphing Stories) but there's lots I've not yet discovered. It sounds like the session was brilliant and everyone came away with lots of ideas to explore. I hope someone blogs about it!

After a nice hot lunch (thanks La Salle!) it was time for my highlight of the day - the Tweet Up! This was an opportunity to network and do some maths. Our Tweet Up team (led by the lovely Julia Smith) set up lots of fun activities for people to take part in.

The #mathsconf4 Tweet Up Team - Dawn, Nicke, Julia, Emma, Danielle, me, Tom and Martin

Thanks to Dawn (@mrsdenyer) for the fabulous 'you are following' t shirts

I ran a 'lowest positive integer competition' - I've previously written about this competition in my post about Open Evening. It was interesting to see the difference between maths teachers and children in their approach to choosing a number - when I do this activity on Open Evening the winning number is normally in the late teens and hundreds of children choose the number one. This time only two people chose one and the winning number was two! Lots of people chose prime numbers, especially 17 and 23. Well done to J Thomas for winning the prize.

I enjoyed meeting lots of new people and catching up with some familiar faces at the Tweet Up.

After lunch I attended a workshop about the new GCSE. I've already looked at the new GCSE specification and sample assessment materials in order to write my page 'New GCSE Support' (which is still work in progress) but there's some elements (eg area under a curve and rates of change) that I hadn't looked at in detail before this workshop. I was interested to learn how students are expected to work out the area under the curve pictured below - the Trapezium Rule is allowed but not essential. We were told that students would be required to use at least five shapes to estimate the total area. I found this session very helpful and would encourage any maths teacher who's not yet looked in detail at the new specification and sample questions to do so before September.

Find the total distance travelled and the acceleration at a certain time

The final session I attended was Martin Noon's (@letsgetmathing) 'Marking for the Reluctant Marker'. He shared lots of interesting assessment ideas that his department has tried. It was a very helpful talk and gave me lots to think about.

The maths cakes were amazing. I was pleased to see Dawn (@mrsdenyer) win the competition with her wonderful Pi cake.

I must say a big thank you to Tim Stirrup (@timstirrup) for delivering my awesome QAMA calculator at the conference. If you're not familiar with QAMA calculators, this extract from a Forbes article explains it nicely, "... QAMA stands for “Quick Approximate Mental Arithmetic” (and in Hebrew, it means “How much?”). As with most calculators, to solve a problem with a QAMA, you first do what you’d do with a regular calculator: type in the problem. But rather than just give you the answer right away, QAMA asks you for one more step: you have to estimate the answer. If your estimation demonstrates that you understand the math, the calculator will give you the precise answer. If your estimation isn’t close, then you have to try again before you get the precise answer.".

I ended the day with drinks and 'mathschat' in the bar with @MrBenWard, @MissWhiteMaths, @amaxmaths, @dwatson802 and my awesome former colleague Sharon.

Thanks to everyone for a great day, see you at the next one!

My favourite badge from @OxfordEdMaths

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Posts about previous maths conferences:

• Gems 8 (September 2014)
• #mathsconf2015 (March 2015)

Favourite Problems

On Tuesday 23rd June I'm hosting a #mathscpdchat entitled "Problem solving: what are 'good' problems? Where can you find them?".

What's a Problem?
A problem, in the mathematical sense, can be defined as "an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law". The word originated in the late 14th century,'a difficult question proposed for solution', from Old French problème, and directly from Latin problema, from Greek problema 'a task, that which is proposed, a question' (source: etymonline).

A problem from solvemymaths.com

I like this quote from Jennifer Piggot, "A problem is something that you probably will not immediately see how to tackle or which once started will challenge your thinking. This means that at some point you are likely to get stuck and this is OK. In fact it is important that you get stuck so that we can talk about possible ways of getting unstuck" (source: nrich).

My Favourite Problems
During next week's Twitter chat I'd like to see examples of your favourite problems. These might be interesting questions that you use when teaching specific topics - for example do you have a great question on standard form? Straight line graphs? Sequences? Remember that we're focussing on problems as opposed to resources, activities or worksheets.

Here's one of my favourite problems:

Source: Chris Smith's Newsletter, Issue 51

This is the sort of problem that could take minutes or hours to solve. It's certainly suitable for bright GCSE and A level students to have a go at. At first look it's one of those 'where on earth do I start?' questions. Draw in a few lines and a 'Eureka!' moment may come. We end up with a fairly straightforward problem involving Pythagoras and a quadratic equation (I say straightforward, but I'm assuming that the problem-solver knows Pythagoras' Theorem and knows how to solve quadratic equations... Prerequisite knowledge is a feature of many geometrical problems).

Eventually I aim to pull together a set of good problems for each topic on the curriculum - I've made a start with this Pythagoras Problem Set.

Problems don't have to be highly complex. Any question that makes students stop and think is valuable. For example this week I was looking for a starter on coordinates for my Year 7 class. I could have gone for a standard plotting activity - I believe that ongoing procedural practice is very important - but instead I've gone for the question below:

From Squares and Coordinates (Don Steward)

It's an accessible problem (the shape is a square) but I think my students will find it challenging. In fact I'm worried that I'll be met with a chorus of "can't do it, Miss" and then I'll lose their attention. I think this is a common fear of maths teachers - we want to give our students problems that will teach them to be independent and resilient mathematicians, but we worry that they'll lose focus if they can't work out how to get started. This is something we can discuss in the Twitter chat on Tuesday.

Finally, here's a problem that I've used a number of times when teaching surds - I love this one:

I really look forward to seeing your favourite problems in #mathscpdchat at 7pm on Tuesday - see you there.


Problem Solving Resources

• GCSE Problem Solving Materials - FMSP
• Support for Problem Solving - OCR
• GCSE Mathematics - 90 Problem Solving Questions - AQA (and PowerPoint collated by @EJMaths)
• Additional Mathematics Problem Solving Questions (& Teacher Guide) - AQA
• GCSE Problem Solving Questions (zip file) - Edexcel
• 55 Problems - MathsBox
• GCSE Foundation Problem Solving - Sheffield Maths
• Badger Maths Problem Solving Samples (Years 1 - 6) - via National Stem Centre
• Mathematical challenges for able pupils in Key Stages 1 and 2 - DfE
• Problem solving with EYFS, Key Stage 1 and Key Stage 2 children - DfE

Problem Solving Links

• Median Don Steward
• Solve My Maths
• Maths Problem Solving
• MathsChallenge.net
• Brilliant.org
• Nrich
• Openmiddle.com
• United Kingdom Mathematics Trust
• 1001 Math Problems
• Suffolk Maths - more problem solving links

Further Reading

• Taking Back The F-Word - solvemymaths.com
• What makes a rich task? - ATM
• What's in a task? Generating mathematically rich activity - QCDA
• Using Low Threshold High Ceiling Tasks in Ordinary Classrooms - nrich

5 Maths Gems #32

Hello and welcome to my 32^nd gems post. This is where I share teaching ideas and resources I've seen on Twitter.

1. Expression of the Day

You might already be familiar with Jeremy Denton's (@Jeremy_Denton) lovely starter activity Number of the Day. He's now created Expression of the Day too. These activities can be used to ensure that students frequently practise their number and algebra skills. Do check out Jeremy's blog post Starter Activity - Expression of the Day for the PowerPoint file and an example of how to use this fantastic resource.

2. Maths Documentaries

In the last lesson or two of the school year some teachers show videos during maths lessons, which I think is fine as long as students are learning about maths from those videos. Not sure what to show? Thanks to @AlgebraFact for sharing this page of Mathematics Documentaries from CosmoLearning - plenty to choose from here.

For more ideas for end of term lessons, see my post 'End of term!'.

3. Angles in a Polygon
Thanks to @sporteredu for sharing these pictures showing a practical demonstration of the exterior angles of a polygon summing to 360^o.  

@ProfSmudge shared a similar set of pictures of an irregular pentagon.

I've always used an animation to demonstrate this and have never thought of doing this lovely paper-based alternative.

For more animations see my post Animations and Simulations.

4. Reasoning Statements

Thanks to Mel (@Just_Maths) for sharing this awesome circle theorems activity 'Great angle chase'. I love activities like this - it's my favourite kind of maths problem.

I was very pleased that Mel shared this link because it led me to a resources website I'd never seen before. I've now added lots of resources from Top Drawer Teachers to my resources libraries. 

I particularly liked these reasoning statements -  a great list of propositions for class discussion. The teacher presents a proposition and asks questions such as "Is it true?", "Is it just sometimes true, or is it or always true?", "When is it true? How do you know?",  "How could we demonstrate/show/prove that it is true?".  Examples include:

• The mean of three consecutive numbers is the middle number.
• Triangles tessellate. 
• Volume = area of the end × length 
• If the water in our dams increases by 10% this month, and then decreases by 10% next month, it will be back to where it started.

5. Zoolander

Mary Pardoe (@PardoeMary) shared a lovely blog post by Simon Gregg (@Simon_Gregg) about teaching Year 4 about scaling. It features a Zoolander question from Robert Kaplinsky (@robertkaplinksy). Fans of Zoolander will like this!

Students need to think about how many times would you need to scale a model up to make a real school. Questions to ask and possible approaches are detailed on robertkaplinksy.com.

Update

This week I discovered that changing schools is a bit like looking after a newborn baby - I knew it was going to be really hard but it turned out to be even harder than I'd imagined. I'd read Mel's post about changing school which helped me mentally prepare for the challenge, but it's still been a huge culture shock. My previous school was a girls' grammar school and my new school is a boys' comprehensive. It's going to be a steep learning curve. I'm lucky to have started with a light timetable to give me a chance to find my feet, plus the maths department is very supportive and friendly, so I'll survive!

This has been such a busy week, what with starting my new job and celebrating my youngest daughter's 1^st birthday. On top of that there was the very funny #EdexcelMaths Twitterstorm that made maths a national talking point.

June will be a particularly busy month for me - there's lots going on including the Maths Conference in London, the MEI Conference in Bath and my new school's TeachMeet.

In other news:

• Colin Hegarty, who I did PGCE with at Kings, showed me his amazing new website. It's yet to be launched but I can assure you it is going to be awesome - maths teachers will find it incredibly useful. I can imagine every school in the country eventually using it for homework and assessment. Do remember to vote for it here if you haven't already.
• I'm enjoying the Summer Math Photo Challenge 2015. It's easy to join in - just check the weekly challenge (listed below), take a photo and tweet it with the hashtag #mathphoto15.
  
• I love the updates to solvemymaths.com, including the fantastic work Ed has done organising the #mathsTLP collection. If you've not yet participated in #mathsTLP then do join us at 7pm on Sundays to share lesson ideas and resources (more details here).
• Did you see my page 'New GCSE Support' which links to resources for the new GCSE topics? I'll be adding a lot more resources over the next couple of months. You can access this page from the 'Extras' menu on my blog (top right - unless you're viewing the mobile site in which case you'll need to click on 'view web version' to see this menu).
• The London Maths Hubs are joining forces to run a conference on Thursday 9th July. It looks like a good selection of speakers and workshops so if you're based in or near London it would be worth asking for a day out of school so you can attend.
• There's some lovely new resources coming from my favourite websites lately - do check out the recent offerings from MathsPad, Teachit Maths and Median Don Steward. 
• This article about the relative difficulty of maths exams around the world is interesting. I like these box plots:

• Finally, Billy Adamson asked people to describe maths in one word and here's the fantastic results:

Have a great week everyone!