Category Archives: mathsconf

Notes from #mathsconf6 – 10 things to take away

We like lists because we don’t want to die.

Umberto Eco

Hello all. Instead of writing a comprehensive report on the goings on at the latest #mathsconf in Peterborough this weekend, I’ve decided for reasons of efficiency, saving time and my sanity, to boil my findings down to the 10 things that had most of an impact on my thoughts. Hopefully you’ll find this just as useful, if not more so!

As Wikipedia showed, people are willing to share their knowledge and insight for the greater good, in their own time, without being paid.

I do not have any grudge against people who charge for sharing their time. Our profession has ever increasing demands on our time, and so whatever we can offer, and yet hundreds of people showed up on Saturday to learn about, share ideas on and celebrate the teaching of our subject. You cannot argue against this idea, and I want to personally thank everyone involved for all of their contributions – particularly the speakers and La Salle for putting everything together, but also people like Rob Smith (aka @rjs2122) who ran the tuck shop and the raffle without any expectation.

What can be seen as ‘traditional’ should carry no less weight for being so.

Andrew Taylor’s opening speech had much of what could be seen as ‘old school’ thought that unsurprisingly still holds consideration presently:

  • The Cockcroft report stating that we should not believe that it is fair for students to be entered for an assessment where they can only attempt a third of the Mathematics covered in the paper (he was talking about the CSE then, never mind the new GCSE).
  • The influence of SMP – developing and nuturing coherent approaches and pedagogy, not just resources and CPD; bringing users together; creating a curriculum model that drove assessment, not the other way round.
  • The example of leadership in Mathematics as a way to create opportunities for staff, understanding that good Maths teachers are rare and valuable, and that they should exercise that potential power.
  • The adage “whatever management tells you to do, don’t do it unless it helps students” – can this be argued with?
  • Nobody gets clever by sitting an exam: we have to understand the purpose, timing and assessment framework when putting together tests so that they are right and proper for the stage of a student’s learning – interestingly, Taylor stated that “teaching to the test is the right thing to do if the assessment is purposeful in it’s aims”. We can argue either way if the new GCSE is purposeful or not – but that is not a troubling thought taken out of present context.

There is still a place for intellectual approaches in the leadership and management of departments.

Ben Ward (aka @MrBenWard) and I took the stage in the first group of sessions to talk about data. Whilst I looked more at the practical opportunities to record, monitor and analyse data, Ben made connections to the wider running of a department and links to school leadership. One point that was made in our talk is that data in itself is not the end – it is the means to help make decisions, and widely, part of a set of tools in the case for forming arguments, i.e. the use of ethos, pathos and logos to form a rhetorical case.

  • Ethos in terms of appealing to authority – i.e. in the case of your teachers, using their professionalism to come to a conclusion of where to take a group of students forward to improve their understanding. In terms of management, demonstrating that you have a clear handle on the progress of students and what it is that needs to be focused on to make the greatest difference;
  • Pathos in terms of appealing to emotion – how do you get your staff to own and care about their data? By helping them see the bigger picture and how thought and planning on their part will not just impact on the life chances of those in their care, but also for them to see the contribution their efforts make on the greater performance of the department;
  • Logos in terms of appealing to the facts – gut feeling and hearsay is not enough. By providing objectivity to what are often subjective arguments, effort can be targeted more properly and in a more structure fashion.

Cynics may say that you should not have to persuade staff to take a course of action based on data – that staff should have the freedom to make their own decisions because they are professionals. I would retort with that idea that it is because they are professionals that they should use every scrap of evidence and support to help the make better judgements about their planning and interventions.

Some people think that the designing of questions and a marking policy is a complex process, but I can assure you it’s even more complex than that.

Ben Stafford gave a wonderful insight into how assessments are written and the level of detail that goes into getting a question right. I discovered some insights that I will take away when writing questions to test student understanding:

  • Ask questions that are unfamiliar – are you truly testing students if it’s completely obvious what they’re being asked to do?
  • Front load information, and ensure it’s laid out in a way that anything key doesn’t lack clarity.
  • Do give a clue to how students should answer.
  • Remember that in assessments parts of questions are independent of each other – if students can’t answer part a) of a question that should not prevent them from answering part b).
  • Avoid the need for students to assume a line of thinking. Set out the parameters of the question carefully, thinking about the language you use. Use as few words as possible, but enough for a student to understand what the question is asking.

There was also the argument regards reliability and validity. If you test enough students, you’ll get a statistically reliable result. But is it valid? Where you are giving marks for partially correct questions there has to be a level of structure in the mark scheme for validation to occur.

Even in an arena without politics, some people can still pursue an agenda.

I can appreciate why someone might ask about how one caters for EAL students in assessments. But Ben’s talk was not the right time, not was it the right stage or environment. There are lots of questions to be answered in that regard, but it was unfair to put Ben on the spot.

Don’t overthink things.

Well done to Megan Guinan for completing the Pringles Challenge! She passed on her know-how to her family – and look what happenedtwice!

Optimise the amount of questions you ask to get student to an objective, rather than bombarding them with practice.

I am a great fan of Craig Jeavons‘ work – practical, easy to follow ideas that can be implemented very quickly. As well as reiterating principles laid out by the likes of Bruno Reddy on working on the right foundations, building a culture for learning in your classroom, he also talked about how with whatever concepts you want to bring to your teaching – don’t go in all guns blazing. In relation to problem solving, ensure your students have good number sense, and an understanding of proportion. Incrementally develop problem solving as part of your day-to-day practice, and then don’t be afraid to start going ‘off piste’ or leaving things ‘open ended’.

I took one thing away from Craig’s talk that we are already looking at developing in our teaching practice in my department: the idea of “if I only had five questions to get students to the objective I want them to achieve, what would they be?”. I often worry with students that they can labour too long on the easier, rote elements of an exercise and not face challenge much earlier.

Through the use of minimally different examples, moving from one question to another with only one or two elements of procedural variation, you can actually get student from a low level of entry on an exercise to something quite complicated rather quickly. Tieing this in with proper review time that takes students through these five key questions, I do feel one can get students to be dealing with more contextual problems much quicker.

Some teachers and departmental leads are not responding to very public discussions and information sharing.

I was rubbing my hands at the thought of Eddie from OCR, Graham from Pearson and Andrew from AQA going toe-to-toe in front of a baying crowd. I’m only joking, but I was looking forward to some real insight cued up by some thoughtful questions. Unfortunately a large chunk of the talk was given up to answering the questions “what do the new grades look like” and “do you have an assessment package to support the grading of students”. I mean, COME ON. Have you been living under a rock? We’ve known the answers for a long time now. There are no, and have never been any ‘graded topics’. The grade descriptors given by the DfE are deliberately vague. As for assessment packages – the exam boards have been incredibly open around how they are as much in the dark as we are. They have sample assessment materials and supporting documentation to try and help guide us – but nobody truly has all the answers. All they can do is advise.

The decision to be made about GCSE tiers has been simplified somewhat.

I did baulk a little at the question “please can we have guidance on tiers?” – but gratefully we had something proper to take away from those who need to make such decisions. As I heard it – and I’m welcome to be corrected – the current fallout rate of students taking the higher tier, i.e. getting U – is 1% of entrants. Based on the standards of grading expected for the new GCSE, 10% of students currently getting a grade on higher spec would only get a U.

Also, bearing in mind that there will only be a sixth to a third of questions that students working at around grade 4 to 5 might confidently be able to answer, then asking these students to sit for 4 and a half hours (4 and a half hours!!!) with the confidence only to be able to accumulate at best about 25-30 marks per paper is perhaps placing undue stress on students. The system will still be gamed, don’t get me wrong, but the risks are even greater.

Even for an experienced dog like me, stay hungry.

It never fails to impress me how I can walk out of a conference absolutely buzzing with ideas. I am paying real attention to refreshing my teaching practice at present; all of the workshops that I attended helped my thinking about what I can do to get students a) retain concepts b) improve their problem solving skills and c) be prepared for exams.

I’d like to thank Ben Ward (aka @MrBenWard) for collaborating with me on our workshop on Getting The Most From Your Data – he’s a brilliant example of the modern, informed and proactive department leader, and I absolutely recommend that if you’re not already following him via Twitter then it’s about time you did.

Mark McCourt (aka @EmathsUK) has done a blinding job in launching and continuing the National Mathematics Conferences – I and a lot of people get a great deal out of each and every workshop and long may they continue. I’ll even let him off the fact that he doesn’t follow me on Twitter!

I hope the more concise approach to my notes from #mathsconf is just as enlightening and a little less demanding. Future posts will aim to be just as concise, but with more of a teaching and learning focus from now on. Watch this space!

Actual Maths: Thoughts on #mathsconf5, part 5

If history were taught in the form of stories, it would never be forgotten.

Rudyard Kipling

This is the fifth (fifth!) in a multi-part series on the 5th National Mathematics Conference. If you like your blog posts in linear order, then start here. I really recommend that you do.

Kris Boulton – The Stories of Mathematics

I have a lot of time for Kris Boulton. Kris’ ideas and work have long been an influence on mine own, and over the past year or so as I’ve got to know him better, his well considered and deeply-researched ideas continue to augur my own motivation to improve my own work.

The last workshop of Kris’ that I attended was on the assessment of mastery and it is still having reprecussions as I continue to develop the practice of my department. However like me Kris has an appreciation of the interweaving of strands that make up Mathematics teaching – not just the subject, or the pedagogy, but also the stories behind how our subject came to be.

An excellent point that Kris made at the beginning is that we often forget how much hard work goes into the development of Mathematics, the creation of new methods, the proof of theorems (and how they themselves came about. We often take for granted things like Pythagoras’ Theorem, the Fundamental Theorem of Arithmetic, the Cartesian coordinate system.

Kris himself had put a lot of work into this talk, about 40 hours of watching and reading, getting an understanding of not just the impact on our subject but on civilisations too. Major historical figures and their contributions were also considered. Kris produced a timeline of Mathematics – you can find it here. It’s an incredible piece of work in itself.

Kris wisely decided to choose a sample of the events along the line, placing the spotlight on paradigm shifts, rather than incremental developments. So we were taken to a time where we found out what people did before they could count, how the number of things we can remember is generally limited to four, and thus how counting, tallying and one-to-one pairings – ideas at the foundations of all Mathematics – came to be.

We were then taken through a journey of a combination of classic stories, scientific truths and debunking myths. I particularly liked the focus on linguistic development of terms like Trigonometry, and how an understanding of the etymology of the jargon we use is a great way of demystifying such terms.

I also think that there is something else to consider here. Mathematics, ultimately, is a branch of Philsophy. Early in human civilisations, when people asked why the sun rose, the rain fell, the wind blew, etc, those in power would retort that it was the will of Zeus, Gilgamesh, Ra, etc. Only when people began to realise that this was not good enough, and that a true understanding of the nature of the world would allow them to make it a better place, did true progress come to be, i.e. it was the beginning of Philosophy that started to answer such questions.

Thales of Miletus, of whom Kris spoke in his talk, was the first ‘name’ in Philosophy, the first individual recognised for his philosophical approach. He gains recognition because of being able to measure the height of the Great Pyramids, one of the first occasions where something considered only in the scope of the efforts of the Gods brought under the yoke of human thinking. Pythagoras, as a student of Thales, extended that idea by touring the known world and linking the knowledge of three of the great ancient civilisations (Greek, Babylonian and Egpytian) and began to codify the discipline of Mathematics as an answer to philosophy’s great questions – over 100 years before Socrates developed his methods and well over 200 years before Euclid created the Elements.

I believe there is a case that there should be a greater element of the history of Mathematics within the programmes of study at GCSE. Certainly the philosophical elements like Platonic ideals (which led to geometry as a formal discipline), the Vedic appreciation of the void that let to the concept of zero as a proper mathematical concept (alien to the likes of Aristotle), Leibniz’s understanding of binary numbers as the creation of something out of nothing.

Ultimately I feel that Mathematics is the language of nature, and that language was formed by the philosophical questions that have been asked from the days of Thales. What power there would be if we could answer the question ‘what’s the point?’ with a bit of historical/philosophical storytelling? Also, from a purely functional point of view, there is apparent evidence that teaching Philosophy has a positive impact on the progress students make in Mathematics – why not explore that at a deeper level?

Kris didn’t have time to go through his whole plan, which was a shame considering it was an engaging and lucid presentation of findings that weaved together into an appreciation of the breadth, scope and constant evolution of the subject we teach everyday. It was worthy of a longer, more encompassing keynote, a double-session at least. I hope Kris produces a sequel or series to follow up this start.

In the interim, I know Kris recommends the book Zero – The Biography of a Dangerous Idea by Charles Seife, and just finishing reading it I concur with this. If the history of Mathematics is something you’re interested in, particularly the development of ‘big’ ideas, I can happily recommend everyone reads Euclid’s Window by Leonard Mlodinow and Marcus Du Sautoy’s Music of the Primes. Sometimes we are too concerned with the process of teaching our subject, losing the reasoning of how Mathematics came about and what the ultimate opportunities of having mathematical skill mean. It’s a healthy process to stop, reflect on what we’re all here for, and thing about how we can translate this to our teaching. The stories of Mathematics are not a bad place to start.

Actual Maths: Thoughts on #mathsconf5, part 4

Design should not dominate things, should not dominate people. It should help people.
That’s its role.

Dieter Rams

This is the fourthin a multi-part series on the 5th National Mathematics Conference. If you like your blog posts in linear order, then start here. If not, then ENJOY!

Amir Arezoo – Design Cues for Great Resources

Firstly if you missed my talk but you want to have a look at the slides – click here. Feel free to use, adapt, etc.

I want to thank everyone who attended and gave me feedback. I’m glad my message got across and I’m flattered that so many people – some who I haven’t been able to get back to yet – wanted me to work with them on design principles.

It was interesting being able to talk about something that I’m interested in that extends beyond my job. I like well designed things. I appreciate when something does its job well. All too often in teaching I have come across what I can only describe as ‘tat’ wrapped up in hype and presented as a revolutionary idea. This workshop, really, was my rally cry for ‘proper’ design in Mathematics.

Field Notes – Principles of Design

Since a very early age I have had a love of visual and instructional design. Flags, football kits, maps, logos, and such like have held a fascination for me. Likewise something tangible and well executed excites me greatly. I remember a particular fondness for the original Super Nintendo joypad (despite the fact that we had a Sega Megadrive), the simplicity of the design matched with the splashes of colour appealed to a visual style that I’ve been in love with since.

My brother had an equal love of design – we are equally fascinated by great album covers, for example. However where I am purely a theorist when it comes to design principles, he took the practical elements and ran with them – here’s his own website. My theorist approach led me to engineering, and to quote my lecturer and inspiration, John Slater, I was “a crap Mathematician, but a bloody good designer”.

Design is not purely a visual process. Design is making function as simple as possible. Why have three steps to do something when you can execute it in two? It’s why people love contactless payment – no one likes parting with money, so why draw out the ordeal? Rory Sutherland, in his three TED talks so far, shows how well thought out design makes life easier.

As I’ve moved into education, I often found myself up against crap design. It might be a textbook, or a worksheet, an online resource, or how something is set up in a school. I am lucky to find myself part of an academy that recognises the importance of execution in plans, resources and teaching, but others are not. We need to recognise where design problems arise, and also how we can overcome them.


There were a number of sources that I pulled together for my presentation. I claim no sense of originality, I am a kleptomaniac when it comes to ideas and this was a kind of ‘greatest hits’ of these that knitted together to underpin my beliefs.

Humans in Design

The Humans in Design blog is not as frequent in updating as it used to be, but it’s an essential source for recognising the importance of design from an ergonomic point of view. The post Using My Car Keys To Make A Point About What Makes Great Design was the source of the two axes of design. I think I would have come to a similar idea anyway, but Humans in Design framed the idea so much better.

99% Invisible

The podcast 99% Invisible looks at how design prinicples influence a wide range of our daily experiences. The episode on Flags was recast as Roman Mars’ TED talk, and it’s essential viewing. You can listen to all of the 99% Invisible podcasts on their website, and I highly recommend you do.

Jan Tschichold

Tschichold’s De Neue Typographie might be too esoteric for some. But look at some of his work, and you’ll see why a minimum of colour combined with sharp typefaces is wonderful.

Bruno Reddy, Kris Boulton, David Thomas

When I decided I was going to look beyond the people around me to inform my instructional methods, I looked to people who had the intellect and patience to look deeper into the psychological ideas underlining good teaching and learning in Mathematics – these three gentlemen have been a massive influence.

Christine Norledge

The use of colour is quite often problematic in resource design. I chose Christine’s resources because she understands that whilst colour is important, it should only be used to emphasise, rather than swamp the element of a resource that needs attention.

Ed Southall

In Ed I see a like-minded individual when it comes to proper teaching and learning. He also recognises how simple design tweaks have huge leverage in terms of making the teaching of Mathematics better. Ed’s whole website is a cornucopia of resources, ideas and prompts on how to improve conceptual understanding. Read it, you’ll learn something.

Will Emeny

Will has constantly inspired my thinking, and is an excellent summariser of teaching and learning concepts. His presentation of ideas such as bar modelling and algebra tiles presents a range of prompts to use in trying to implement concrete/pictorial approaches in an easy to understand manner. He is also a great resource designer in his own right.

Don Steward

Ah, Don. Dieter Rams once said “Products have to be designed in a way that they are comprehensible.”. Don Steward seems to embody that principle to his resources. I’ve eulogised about his work so many times, I’m getting boring! Keep it up, Mr S.

Kayleigh Blackburn

About 5 or 6 years ago this force of nature joined my then department in Rotherham. Now she’s pulling up trees of her own. The whole Bronze, Silver, Gold, Platinum idea was an idea she kept hammering until I gave in (I am naturally skeptical). There’s a whole article on the impact of Semiotics and the interplay of signs and signifiers on our teaching that I could write, but if you could summarise it in one process, stop doing ‘RAG’ and start doing ‘BSGP’ with your differentiation.

There’s a job to be done.

I think there’s a role for individuals in schools to be responsible for design. Routines, procedures, curricula, lessons, resources – how all of these work and fit together for the benefit of staff and students alike. I know some schools – as I say, I’m in one of them – take this seriously and it really does show. We should strive, as much as humanly possible, to remove ambiguity in education.

What now?

Well, Mr Ben Ward and I are joining forces for the next #mathsconf – “Getting the most from your data”. I’m beginning to think of it as the final part of a series of my greatest passions in education: Leadership, Design, and Data. I’m not done with the conference scene – not at all, I love attending them – but I think it’s time for a new breed of teachers to come and contribute, and I feel that I’m in the way of that to a certain extent. People like Naveen Rizvi, Craig Jeavons  and Ben have a lot to offer, and it’ll give me more time to focus on this little darling of mine, my beautiful wife, and finally helping Dixons Trinity Academy students get brilliant Mathematics qualifications. I don’t think that can be argued with.

Actual Maths: Thoughts on #mathsconf5, part 3

If you don’t contradict yourself on a regular basis, then you’re not thinking.

Malcolm Gladwell

This is the third in a multi-part series on the 5th National Mathematics Conference. If you like your blog posts in linear order, then start here. If you like things a little more in Tarantino approach to narratives, then read on.

Peter Mattock – Concrete Approaches To Abstract Maths

Before this edition of #mathsconf, I’d made a conscious decision to look at refreshing my teaching and learning practice. If I’m honest – I’m built-in the classic mould of teaching – find out what students don’t know, teach them something, let them practice, check if they’ve mastered it… rinse and repeat. The activities were rarely concrete in the ‘kinesthetic’ sense; I’ve always liked using diagrammatic methods, but never really used counters, blocks, rods, etc. This is for two reasons:

1. Often the classes I taught quickly demonstrated that they couldn’t handle concrete, hands on work. I don’t mean that in the sense of “I tried it once, it didn’t work, never again”, but in the sense of I tried it with every class, and no matter how I planned these lessons, it wouldn’t click.

2. I have an aversion to constructivist, discovery mathematics. I was lured in by the constructivist movement about 4 years into my teaching career, but I felt the point I was trying to make was lost in the ‘guff’.

This is kind of ironic. I am notorious for being able to use 100 words where only 10 would do when explaining a point. Anyway.

So it was with this in mind that I ventured with trepidation into Peter Mattock’s workshop. I love Peter’s enthusiasm for teaching Mathematics; he’s not a nerd or overly geeky about things – he just exudes a passion for making concepts stick. The difference between him and me is how he does it – whereas I build my learning around pencil and paper – Peter gets creative.

From the use of string and hoops to demonstrate circle theorems, to using steps built from multilink cubes to move students from understanding linear sequences to geometric sequences (hello new GCSE programme of study), Peter’s workshop aimed to reframe the worry about concepts that are now being expected to be covered in our schemes of work as an opportunity to rethink how we teach them. Likewise where the learning of concepts has traditionally been riddled with misconceptions – directed number, for example – Peter demonstrated methods that are mathematically sound but more memorable because they’re an event. Take, for example, his vector-based negative number approach of ‘jumping numbers’. By getting students to physically move along a number line, and change direction when the ‘-‘ sign is combined with another, e.g. 4 – -2, the problem over ‘two negatives makes a positive’ is removed.

Like ‘jumping numbers’, lot of Peter’s approaches involve the physical movement of students. Concepts like cumulative frequency and bearings can be taught in places like the hall, getting students to line up or position themselves based on a mathematical concept and thus removing the need to provide a pseudo-context in a problem because their experience is the concept. I like this principle. I hate exercises that try and make the most tenuous links between mathematics and real life, so where students can actually visualise something in context themselves, it should make the impact (and therefore the ability to recall) much greater.

Due to time constraints – a recurring theme on the day, actually (I’ll come to this) – Peter didn’t get through everything he wanted to, and I felt that with a little more time delegates would have been able to work with some of the concrete methods more and really appreciate their possibilities. There was a genuine enthusiasm for many of the ideas Peter put forward and those who might have been more skeptical could have at least appreciated the thinking behind the strategies.

As for me? I’m in a strange position as I’m in a new post and I want to get my classes into good routines first. However I still would like to give things a try, particularly where in my experience students have struggled to get an idea to click in their mind. I will be honest, some of Peter’s ideas were a bit left-field for my teaching style, and I feel I have to be true to that.

However, I did have my preconceptions tested, and I am willing to see what such techniques can add to my skill set. Everyone should challenge their beliefs from time to time, and if Peter’s the one to do that, then that’s no bad thing.

Next up – me!

Actual Maths: Thoughts on #mathsconf5, part 2

I’m not the smartest fellow in the world, but I can sure pick smart colleagues.

Franklin D. Roosevelt

This is the second in a multi-part series on the 5th National Mathematics Conference. If you like your blog posts in linear order, then start here. If you like things a little more in the Pulp Fiction narrative mould, then read on.

Hannah Thornton, Tom Gray and Elliot Satur – Hooking Y7s Into Becoming Mathematicians…

I’ve known Hannah for a couple of years now (thanks to a mutual colleague recommending her ideas), and I knew that her and her team’s work at Penistone Grammar has been a beacon for quality Mathematics teaching, resulting in some of the best performing GCSE Mathematics students in the region.

The PGS three (makes them sound like a crime gang but you know what I mean) spent a great deal of time focusing on their work with Y7. Now, I am pretty much old school when it comes to how classes in Maths should be: in groups, learning through a mixture of practice, application and problem solving. PGS do it differently in Y7: mixed ability, project based learning.

The team openly admitted that – like I – they pick ideas from the best teaching and learning practice in Mathematics and put them together to form a curriculum that puts concepts in context. I was delighted to see that they make use of the Create Maths project materials, a severely under used and under appreciated resource that any teacher worth their salt should try. In what might seem a left field but completely principled move, Decision Maths is also a part of their Y7 curriculum. I think this is a bold decision (ahem) but one that will pay dividends long term.

The team admitted the traditional nature of their teaching between Y8 and Y11, but understood the need to develop a strong feedback system throughout, and have developed a system they call NTT – I didn’t actually catch what this stood for – which they use to monitor, support and intervene with student progress at the conceptual level. Ideas like ‘My Favourite Mistake’ (pre-empting misconceptions), getting students to verbalise what they were getting wrong and the use of multiple-choice testing to build a picture of student understand all combine to create a formidable package.

This three pronged methodology of project-based learning, traditional classroom practice and cutting-edge feedback struck me as something that hasn’t just been thrown together, this is a process that has grown organically from a few key principles that suit the needs of the students attending lessons at PGS.

What struck me was the honesty of what the PGS three (there’s that phrase again) presented and their enthusiasm – which was manifested in the student interviews that were shared on the big screen, there openness in terms of their description of the journey they’ve taken so far and the challenges that they face.

As someone who lives in Barnsley, and who has worked in a rural area similar to Penistone, I know the environment that Hannah, Tom, Elliot and the rest of the PGS team work in, and I have to admire their innovation, creativity and determination in creating a different experience for their students and making Mathematics accessible to all of the students in their care.

My honest opinion is that as long as the quality of instruction and monitoring of progress is top notch, it doesn’t really matter what approach to teaching and learning you want to take – we all know where we want our students to end up, and we want them to be engaged and enjoy lessons whilst they get there. The PGS approach is very different from what I and others employ, but it’s paying dividends and I’m delighted to say so.

What I personally benefitted from this workshop was the reminder that it’s always important to see a point of view that challenges your own. It removes hubris and keeps your feet on the ground.

I hope that the PGS Mathematics department go from strength to strength. If we were in the Penistone catchment I’d be happy to send my little girl there, going by the impact they’ve made so far.

Tweet Up!

So, I was strong armed into running a little part of Tweet Up, which has become an integral part of #mathsconf5; Julia Smith asked me to see if I could get people to make this ‘Pringles torus’…

So, I had a go on the Thursday night beforehand…

First time lucky! No glue, or fixings, nor paperclips as one delegate asked me (paperclips!).

So it was with great enthusiasm that I asked people to roll up and have a go themselves…

Yes that’s me in the background… and as you can see I had a few punters willing to try their luck, including Emma Bell and Grant Barker who succeeded!



I think this could make a great optimisation problem. The engineer in me would love to try and make this with the least possible number of Pringles. Perhaps the Pringles makers might want to get in touch with me and send a few free tubes to get started???

Anyway well done to everyone who gave it a go, and I’m sorry I couldn’t replicate the feat, but it was a great bit of hands-on Mathematics and not something I’d normally do. Thanks also for Jessica Bramwell for her sheer skepticism about my own effort, honest. Nothing like a mate to show confidence in your efforts…

Next up, the strange and frightening world of concrete approaches to Mathematics with Peter Mattock. Stay tuned…

Actual Maths: Thoughts on #mathsconf5, part 1

Daring ideas are like chessmen moved forward. They may be beaten, but they may start a winning game.

Johann Wolfgang von Goethe

It’s been a year since I went to my first National Maths Conference. A lot has happened in my career since then. My current role, status and network of colleagues pretty much exploded into life after the September event in Kettering (the 2nd of the conferences).

I’ve learned a lot, and also been reassured that my own mission and values chime with some of the most influential and successful teachers across the land.

My new role has taken a lot of my time and energy – hence the lack of new content on here for such a long time – but everything that I’ve shared on here and my continual search for improvement lives on, and it’s by continuing to attend #mathsconf and blog on here I’ll be able to feed that hunger.

Bringing It All Back Home

The fact that #mathsconf5 took place in Sheffield filled me with equal excitement and dread. Excitement because we were now on ‘my turf’ really; I was ‘forged’ in Sheffield and I believe it and the rest of South Yorkshire have a wealth of untapped teaching potential (from first hand experience) that can be unlocked by such events. Dread came from the fact that I had 8 current and former staff and trainees of mine, as well as a huge number of friends from local schools in the room and I was presenting – it’s always a harder task in front of people you know closely.

#mathsconf grows and grows in terms of its scope, and I’d made a conscious effort to go to workshops that were more focused on classroom practice and that piqued my interest rather than ones that looked at leadership and progress, as a good head of department should.

Danielle Bartram – Effective Differentiation: Support, Stretch and Challenge

Danielle is someone I’ve been meaning to go and see for a long time. Her drive and energy in finding ways to engage as many students as possible in Mathematics is remarkable, and it’s great to see her get recognition for her efforts (and a book deal!).

Danielle started by talking about Maths department’s place in a school, the importance of proper communication and connection between Maths and other departments, staff of varying responsibilities and students within school. A department should be comfortable enough to take criticism, force itself to make links and build for the future, rather than being short-termist.

We were told, correctly, that students all have their own starting points and needs, and teachers should strive to understand to that. By implementing a range of different strategies such as light touch topic marking, mini-tests, DIRT time and follow-up, teachers should be helping students plot out their learning journey and their progress on the way.

Danielle went into great detail about strategies she employs – highlights being the need to model success at every possibility by expecting your students to mirror the amount of rigour you as a teacher put into solving problems; spending time focused on command words such as ‘evaluate’ and ‘simplify’ and how they set out expected methods in solving a problem; regular time spent on retention of knowledge (or RoK); planning challenge at all levels through the use of ‘Ski Slope Learning’ and Sizzling Starters.

I liked that Danielle addressed the idea that challenge is multi-dimensional and as such teachers should employ a continuum of lessons to provide this, rather than trying to provide depth in just one.

As someone who has a deal of experience and uses a lot of methods that mirror Danielle’s work, understanding the impact of what she has done offered reassurance that my students are benefitting from similar strategies, but I will admit that in many respects Danielle’s strategies show much more finesse.

I learned much from Danielle’s workshop and I was struck by how many of her strategies were of the ‘why have I never thought of this before?’ mould. For example, the new GCSE Science specification requires students to memorise 20 different formulae: why spend time thinking of formulae to use in teaching substitution and transposition when you can help your local friendly Science department by using the very ones students need to know down pat?

Likewise, the use of ‘red herrings’ in covering concepts to ensure students recognise when a misconception has taken place is particularly relevant (in my mind) to when GCSE classes are preparing for exams and just need their conceptual understanding of topics polishing up.

I would have liked Danielle to maybe have gone into more detail about some of the strategies she employs, how they’re exemplified in her day-to-day practice and what that has resulted in with regards to students’ success. However time was a factor so it wasn’t feasible, but I had more than enough detail work with.

I definitely recommend people going to see future workshops by ‘Miss B’ if you get the chance. Also she has a book out. If her website and resources are anything to go by, it’ll be a worthwhile investment. Go buy it. Now.

I’m soooooo, sooooo, sorry…

Julia Smith. Jo Morgan. I missed you again. One day, I’ll be in attendance. One day. Soon. Hopefully.


Actual Maths: Thoughts on #mathsconf4, part 5 (at last!)



Reflection time

If there’s one thing that going to these conferences has taught me is that the game is never over. Outstanding practice is not an award, but a process of action. Growth mindset has it’s detractors but I believe if you simply have an approach of ‘I can, and will, always do better’ then success is only round the corner. It is important that all teachers get opportunity to experience the conference environment and learn from each other. The well will never dry, and the only way that the national Mathematics teaching body can improve is if everyone gets chance to drink from it.

So if you’ve not been a conference yet, get to one! It doesn’t have to be #mathsconf – although you will miss out on the chance of meeting yours truly (!) – just somewhere where you can chew the fat with fellow practitioners in the same boat as you. It’ll really move you forward in your practice.

Amir Arezoo, The Art of Leading a Department

So, first things first. I’m reviewing my own workshop not out of some level of self interest, but because a number of people asked me some follow-up questions, where they could get materials and so on.

Firstly, the follow up questions…

What did you mean when you said ‘BODMAS is a waste of oxygen?’

Well I’ll be honest – I lifted that straight from the previous talk by Robert Wilne. It succinctly underpinned my belief (and hence a point I made in the presentation) that we should prevent students seeing Mathematics as an accumulation of tips, tricks and magic. I didn’t train to be Paul Daniels. Instead we should ensure that the logic, rigour and rules that make up our discipline are understood by students. When students can appreciate the patterns and interconnectivity of what they study, they’ll have a toolbox of approaches to solving problems, rather than using the (analogy alert) proverbial hammer to fix every problem, or trying to pull rabbits out of hats. Sure, mix this principle up with a bit of wizardry from time to time, but don’t build your whole teaching career on tricks. You’ll fail the kids.

Where did you get your lovely slide templates from?

Ed Southall! He’s got a whole set of them. Much better than the standard ones from Microsoft. Cheers Ed!

Where can I get some ideas around a common calculation policy?

Pages 15-22 of this document are a good starting point. However you design it, I recommend strongly that a) you share this with, and train, your feeder schools and b) you differentiate to suit expectations at different Key Stages or Years.

Where can I get a copy of your presentation and suggested materials?

Click here!

The assessment tracker is very similar to what David Thomas has recommended in the past, it’s just my own version. It’s conditionally formatted to ‘RAG’ scores relative to 100% or out of 10. Feel free to play around and recommend changes to it.

I didn’t actually create the staff tracker, my colleague Victoria Westoby created the original. I just wanted to promote it because it’s a really good idea. Remember that this is for you and not to be used as a stick to beat people with!

Can I come and see you in school?

I would like to say yes, but as I am starting a new job myself in September I would like to get settled and into a good routine first before offering invites. As you can appreciate I have an important day-to-day job to do myself and I don’t want to let my staff and students down!

What books do you recommend?

What, apart from here? I’d prioritise

Leverage Leadership, Paul Bambrick-Santoyo
Teach Like a Champion 2.0, Doug Lemov
Why Don’t Students Like School?, Daniel Willingham
The Behaviour Guru, Tom Bennett
Thinking Mathematically, Jon Mason, et al.

How do you start building a professional network?

Read this. It’s a good primer.

Did you enjoy your workshop?

I was bloody nervous at first. Thanks to Dr Bennison for lending me his clicker – it meant I could pace around a bit and get rid of a bit of nervous energy. I mistook people listening intently for them thinking I was a little bit negative, but those I’ve spoken to since assure me the former was the case. I was a bit worried that my incredibly broad northern twang (Barnsley via Manchester and Sheffield) would require subtitles.

Ultimately though, I got incredible feedback, lots of positive responses and great follow up on Twitter. It was a genuine honour to present to a group that included so many people that have influenced my work over the last few years. I hope now that I’m starting to give back.
I have an idea for a workshop for #mathsconf5, this time looking at another interest of mine – the world of design. I know Ed promotes the importance of good design in teaching, as does the likes of Dan Meyer and Don Steward. It’s been chosen – so watch this space!

A final point

In my talk, right at the end in the ‘if I could boil it all down’ I talked about the importance of developing character in your staff and students, but didn’t go into great detail. My experience tells me that it doesn’t matter what your skillset is, what your experience is, or what level you are at, your character will determine success, not your personality. Personality is great. If you can get on with people and are effusive and generous then people will align with you and want to be part of your team. But once you’ve overcome that social barrier, then personality is not enough.

Personality makes promises. Character delivers on them. You can make that into a meaningful infographic if you like.

Leaders have all sorts of foibles and things that personally challenge their effectiveness, but great leaders manage them and deliver no matter what the circumstances. Great character is not necessarily working hard no matter what (a la Major in Animal Farm) but having a strong sense of what makes a difference and using that to steer one’s team.

I have met many successful leaders whose personality is somewhat lacking. But the fact was that they delivered on what they set out to achieve. For too long in educational circles we have let great personalities drive decisions and policy. It’s time to let character take over.

Likewise with students. Students often look to the great personalities in their classrooms – the ones with biggest voices, keenest eye and sharpest wits. Yet it is those very same students who are found lacking at the crunch, and are quick to dish out excuses for missing the mark. The characters – the ones who turn every day, follow your instructions and quietly get on with their studies, need to be put at the front of the celebration queue.

Over the next week, make a point of praising your characters. Give the ‘personalities’ short shrift and celebrate bloody hard graft. Please.

Thanks, as always, for reading!

Actual Maths: Thoughts on #mathsconf4, part 4

Children must be taught how to think, not what to think.

Margaret Mead

This part four of a five (!) part series of notes on the 4th National Maths Conference organised by La Salle Education. You can find part 1 here, part 2 here and part 3 here. Or you can just start reading from this point. But you’ll be missing out…

Regrets, I’ve had few (reprise)…

Julia (again, AGAIN!), Danielle, Martin, Mark – be it scheduling conflicts or a difficult choice, I was unable to make your workshops this time round. Hopefully in future conferences this can be rectified. Either that or I’ll do a primer in quantum electrodynamics and see if I can be in two places at once.

People are People

In a previous role, my line manager once said “the thing is Amir, you’re not a typical Maths teacher”… Maths teachers, in his eyes, were a little snooty, socially deficient and obtuse – or at least they were from his experience…

Well, if National Maths Conferences are anything to go by, then I think he couldn’t be further from the truth. I mean, don’t get me wrong, you have to be a little geeky to teach Maths (I mean come on, there’s Geek Club!) and yes, you might get into a deep conversation about non-Euclidean geometry or different ways to factorise a polynomial. But what has struck me, and continues to strike me, is how bloody down-to-earth everyone I meet at such events are. The ‘typical Maths teacher’ not longer exists!

I think I know why. The landscape of education has shifted somewhat since the middle of the 20th century and it is actually beneficial to have a worldview beyond your subject (shock). Being personable with your students (without trying to be their mates) and staff (whilst at all times knowing what the purpose of your job is) matters.

I think this is one of the reasons why – and I don’t have anything against people with amazing qualifications – it is not a given that a better degree means a better Maths teacher. As someone who had to work at their Mathematics at every level of study, I think it matters that you can frame your subject in others’ (less confident or assured) eyes. What I saw in the many people that I met at the conference last weekend and those previously is that there are 100s if not 1000s of us who share that view. Good on you.

Robert Wilne, “A Wise Man…”

My first encounter with Robert Wilne was at the previous National Maths Conference during ‘the Great Mastery Debate’ (which wasn’t really a debate, more of a consensus of opinion, but that’s a different story). Robert is engaging and witty and absolutely passionate about having high standards of Mathematics teaching in the UK. I missed out on seeing him last time so I was glad I could get chance to witness one of his talks this time round.

Robert – and I hope he doesn’t mind me saying so – has a distinctive way of presenting that needs to kind of ‘strap in’ and enjoy the ride. From the start of the session to the end you were hooked in – such that he only left me with about 5 minutes to prepare for mine but I didn’t mind one jot!

I saw an overarching theme to the workshop. Given a calculation such as

0.62 × 37.5 + 3.75 × 3.8

some students will just ‘do’ the calculation in brute force terms, whilst others will identify an underlying pattern and execute the calculation more swiftly. It is the latter methodology that we need to engender in our students, and there are many ways of doing so.

Now, Robert looked to Shanghai to show how reasoning skills can be developed through teaching and learning. It would be tempting to come out in hives at the term ‘Shanghai’ but actually a lot of what he referenced he acknowledged was already happening in schools over here.

Students tended to master a single step in a concept per lesson – a bold and controversial idea but one that ensures that the connections that are required in mathematical thinking are deeper and stronger than if students shuttled through topics at a blistering pace ‘to keep the challenge high’. Differentiation is less explicit in terms of resources, more so in the dialogue that takes place between the teacher and student. Students are taught to look for structure and exploit patterns in their study of Mathematics. If you look at many schools at the forefront of mathematics pedagogy you can see that happening.

Robert suggested reasoning could be developed from a three fold approach.

Procedural variation – identifying a single mathematical construct to be taught, and then adjusting variables in given problems only slightly so that the key ideas is embedded, rather than creating a situation where students worry about calculation as much as the process.

Conceptural variation – ‘what is and what isn’t’. Robert used the example of fractions, where students can be asked to demonstrate whether a diagram indicates a third or not, and why. Teachers should identify potential misconceptions before they’re raised, and pose problems that highlight such issues, or tackle them through their questioning and exemplification.

Intelligent practice – rather than setting an exercise that expects repeated practice of a concept, set one that requires creative thinking and reasoning on the part of the student, from relatively simple starting points. Robert went into great detail about this aspect of teaching and learning, particularly in using the interplay of numbers and operations to generate a variety of representations of the same connection. This was interesting considering the example from an incredibly old textbook of various methods of establishing mastery in division, shown in Emma Bell’s earlier talk.

From there Robert looked at more examples that meet the three criteria established above and I’m sure he won’t mind sharing these examples if you get in contact with him, as they really are worth exploring. As I say Robert would acknowledge that much of this is already taking place in UK schools, but his remit is to make sure that his message gets as far and wide as possible and through mediums such as #mathsconf it’s only right that he does so.

On reflection of Robert’s workshop, I have the following to say. For a number of years now the emphasis on Mathematics departments in schools has been to ‘finesse’ students ability in the subject in order to get them a high a grade as possible, because of the high level of accountability they find themselves in. However the recent reforms in both curriculum and assessment mean that this cannot – continue. Students should be instilled in reasoning and problem solving skills anyway, but now accountabilities demand it, there needs to be adaptation.

If there’s one thing I personally am going to take away it’s looking more into the concept of intelligent practice and making sure what I serve my students in terms of exercises and practice ensures mastery of the central concepts I want them to understand.

In the next post, I’ll be talking about my presentation. I’m not doing this in terms of a self-serving attitude, but because so many people have asked me to exemplify points and share some of the materials that I demonstrated!

Thanks again for reading, and I look forward to any feedback!

Actual Maths: Thoughts on #mathsconf4, part 3

Every man lives by exchanging.

Adam Smith

This is the third instalment of my notes on the 4th National Mathematics Conference in London. If you missed the first and second instalments, click here and here respectively – otherwise, let’s continue looking back over the workshops.

A slightly hypocritical point of note

As I alluded to before, social media is a big driver of the community that surrounds #mathsconf and obviously the general Mathematics Blogosphere. However I have noticed a trend – and it is one I have been guilty of.

I love my iPad and iPhone. I am an information and communication addict, and my technology is my mainline to feed that addiction (a hot topic of discussion between me and Mrs A). I’ve noticed at times that during presentations I’m often tweeting so frequently that I lose the thread of what’s being discussed and miss important points. Our tweets, photos and shares are so useful to non-delegates that it’s good that we’re all sharing and interacting on these multiple levels (not being able to attend the first #mathsconf didn’t matter as much because of the plethora of sharing going on via Twitter!) but…

… I think I need to be a little more ‘in the moment’. The first time I recognised this was not at #mathsconf but at the Tour de France’s Yorkshire stages last year – where people were so busy filming the race they didn’t properly first hand witness the spectacle of the peloton roaring up hill and down dale in God’s Own Country. The main problem was that people were trying to take ‘selfies’ with the peloton and nearly wiping out half of the competitors because they were leaning so far in.

As I say, I know why people do this – it’s a useful part of the experience – but in the case of the conferences we attend I think we need to find a balance between being part of the workshop and instantly feeding back to others on it, myself included!

Craig Jeavons, Best of the US

I thought I knew what the best stuff going on in the USA was. I’ve been following Dan Meyer, Vi Hart, Sal Khan and others for a very long time now, yet Craig Jeavons showed I was barely scratching the surface.

Craig didn’t just go through a trawl of his favourite websites from state-side but made it clear how work that’s going on over there can assist curriculum development in light of recent reforms.

For example, developing student sense of number through; students using and testing their problem solving and reasoning skills through Dan Meyer’s Three Act Math; ensuring students have mastered key concepts through the problems shared on These are all great examples and the best bit about them is that their depth and extensive reach of resources, allied with the familiar context that study in the US provides means that much of the content is easily transferable to our setting.

I particularly liked the Depth of Knowledge charts he presented – useful in supporting differentiation in lessons, and the website, which appears to be particularly focused on curriculum and lesson design – a hot topic at the moment over here. The materials on the website looks very similar to our own Kangaroo Maths – so useful to compare and contrast.

It was interesting learning through conversation during the workshop with Tim Stirrup and Craig himself that the Common Core Standards, a kind of National Curriculum for the US in Mathematics, are optional. I see that the American ideal of individual liberty manifests itself in some odd ways. A shame that the standard of curriculum offered by someone in say, Houston, might be quite different from someone in Sacramento.

Another chord that struck with me regards Craig’s talk goes back to the similar contexts we find the US and UK. Whilst I have no problem with learning from the successful East Asian nations in terms of their pedagogy, it would be nice to look in the other direction and see what is successful over the pond, considering how much we share culturally (despite our grammatical differences!).

In summary, if I had any advice for Mathematics teachers through their career it would be this:

Be outward facing – don’t just rely on your own steam
Be curious – constantly look for whatever can add to your practice
Be appreciative – show gratitude for whatever others have contributed to your success
Be a cheerleader – promote what has worked for you, pay it forward.

Craig, and his talk on what he’s learned from the work going on in the United States, meets all four criteria. I really enjoyed what Craig featured in his workshop, and like Emma Bell’s talk, it has set me off to make further investigations. I always like to see into what works in other contexts and how I can build that into my pedagogy.

Good workshops reassure delegates and give them an inkling of how to move forward. Great workshops challenge delegates, get them to reflect, and give them a different viewpoint on how success can be achieved. Craig Jeavons’ was definitely in the latter camp.

Next up, Robert Wilne’s talk on developing reasoning skills in Mathematics. Thanks as always for reading, and I’d love to hear your feedback on anything I’ve elaborated on so far.

Actual Maths: Thoughts on #mathsconf4, part 2

If you don’t know history, you don’t know anything. You are a leaf that doesn’t know it’s part of a tree.

Michael Crichton

This is the second part of my notes on the latest National Maths Conference in London on 20th June. The previous post is here – otherwise, read on.

And you are…?

There’s an interesting social dilemma that manifests itself during ‘#mathsconf’: when having a conversation with someone, you feel you should know them because you think you follow them on Twitter, but don’t recognise them (because their twitter ‘avatar’ is often not them or a very small image, they’re wearing sunglasses (me) or purposefully obscured). Therein lie the issue – do you risk offending them by asking who they are? Or do you go all Sherlock Holmes, ask questions that reveal clues and from there piece together their profile and therefore who they are?

Piece of advice everyone. ASK. I’m not offended. Let’s just cut through the social graces. We’re all here to work together, and if an hour is lost to worrying about getting introductions right, then it’s time you’ll not be able to use productively. I’m not saying do a Prince Phillip sort-of ‘and what do you do?’ sort of thing. Just say hello, I’m …. and share your alias. I’ll give it a go if you will.

Either that or La Salle need to provide big sandwich board size badges with a full biography for every delegate. Perhaps…

Emma Bell, ‘From Euclid to You’

Often as Maths teachers we get fixed in what is present and fresh in our practice that we often a) neglect what tools are available from the past, b) forget that Maths teachers have had the same problems for time immemorial and c) thus fail to recognise the power of what history has to show us to aid our teaching.

Enter Emma Bell. I too was at that very same talk by Johnny Ball that inspired Emma to look at historical texts for teaching Mathematics. Whilst we both appear to have a spark ignited by Mr Ball in our appreciation of history in our subject, Emma has taken it to another level, a point she hinted at when she contributed to this very site’s Behind the Mathematician series.

Emma showed, from teaching texts, reports, graduate theses and other scripts from the past that she has sought by scouring the internet and beyond, that there is much to translate from the past into our current frame of reference.

For example, as we are now tasked with developing problem solving and reasoning skill (not that we weren’t trying to do that already), why not look to I Giochi Numerici Fatti Arcani or the Liber Abaci? These are texts full of problems and puzzles accessible at via study of most secondary level students.

Emma showed us how Euclid’s postulates still influence the questions found in assessments from KS1 up to KS5 and beyond, and how an appreciation of these postulates (and for more able students, the concern over the ‘parallel postulate’) supports the study of such problems.

One of my particular highlights of Emma’s talk was this, from a early 20th century text.

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Wow. How many ways can you describe division? Absolutely brilliant mechanism for recognising if students have mastered a topic by checking their literacy skills.

Emma’s talks was one of those where a flood of ideas springs forth in one’s mind and you start to create a whole realm of possibilities right there. It was a classic example of how being in a conference environment, with the right people leading, help you make a move to the next level in your thinking or prompt you to improve the quality of your present practice by those fine margins.

An interesting point, and something that I’ve alluded to in previous ramblings of mine own  – Emma will have to remind me from which text because I neglected to make a proper note – was the separation of Arithmetic as a skill set and Mathematics as the application of it. I’m a big fan of this principle, and I don’t know why this line of thinking wasn’t pursued in the GCSE reforms. If the Mathematics GCSE is to be counted as being worth double in all accountability measures why not make it two proper GCSEs?

Time and again in Emma’s talk there were voices from history that rang true with our current situation. I think two points are raised there. The first is that the challenges we face as teachers of Mathematics have, are, and will be constant. They might have differing levels of impact over time, but there always will be those who fail to appreciate the merits and technical potential of being fluent mathematically, and we need to constantly challenge them. The second point – and I’ll come back to this at a later date – is that ideas might lose their novelty and thus appear to be cliches but that doesn’t mean they are not correct.

Ultimately Emma’s talk was informative, enlightening, funny and inspiring. I know she was nervous about making sure it went well – it did, and I had no doubt that it would.

Next up is Craig Jeavons’ look across the pond to see what we as Maths teacher can learn from the practice taking place in the United States. See you next time.