Archive for October, 2015

Shanghai – further thoughts

October 24, 2015 2 comments

On Friday night I looked on my phone to discover a massive amount of twitter notifications. While I had been watching a rugby match my newsfeed had been lit up by people attacking and defending a post I’d written which most of them perceived as a negative response to an impending visit to our shores by a number of teachers from Shanghai (not to be confused with China, as I keep being told by many people.)

In actual fact I hadn’t written a blog post on the subject at all. What I had done was write a blog post posing some questions that occurred to me while watching an ambassador from China (I think, he could have been from Shanghai I guess) face a grilling from Andrew Marr on his Sunday morning show.

I had tried to outline my thinking around questions that occurred to me while watching the show, namely: “why is there outrage at working with China on these energy projects because of their human rights breaches but no one expresses these worries about working with them in education?”, and, “is it a superior pedagogy that allows them to excel or the culture/lack of behaviour issues?” These questions were simplified to “Can, or should,  we learn from China?” And I’m extremely interested in whether we can or should.

In general the reponses I got were either “I’d not thought about it like that, you have posed some interesting questions.” Or “Yes we should engage, that’s how we can eliminate their breach if human rights,” or ” I worked in China,  it’s not a fear of the state that drives them to succeed and behave but pressure from home.” I had lengthy discussions with two friends who have taught English there and was intrigued to find out more about the education system. I was certainly starting to lean towards a yes in each column.

Then on Friday I saw a tweet from Bruno Reddy (@MrReddyMaths). Bruno is someone I both like and respect,  and his tweet stated that was angry and disappointed with my post, and implied it was bigoted and racist. This shocked me, bigotry and racism are two things I hate and will stand against at any opportunity and I couldn’t understand where he was coming from. I ask for further clarification and Bruno duly obliged, writing his grievances in this well thought out post. It’s a great post, it gave me some information I was unaware of and furthered my understanding of some of the issues involved so I’m thankful for him for writing it. I do, however, feel that he has taken some inference that were unintended and have explained this in a comment, recreated here:

Your first grievance is against a view I don’t hold. I never said teachers coming here was a bad thing. Although having read your thoughts I can see my choice of language could lead to this inference and I apologise for that.

I feel I should say, however, that it is current,  not historic, human rights abuses that worry me. And I wouldn’t support removal of Germany cars because of Hitler but I would definitely support stopping of imports if Germany policy were to return to that of his day.

I will admit the next grievance is also my fault, although not my intention. Again I worded badly my sentiment that the massive cultural differences may in fact be more important to success than the pedagogical approach. That said, having read your post and spoken to friend who have taught there I’m now fairly sure we can learn from them.

As far as the iraq/Grimsby China Shanghai comparison goes, I feel again I may have massive mislead my thoughts. I was watching a Chinese ambassador get a hard time about human rights and had just read a numerous of articles suggesting we shouldn’t engage with China on new energy generation and I wondered why this sentiment wasn’t held to education.

The post was intended to explain the reasons I had come to ponder these questions and then ask the questions, (can and should we learn form China on education?).

It has lead to many discussions which have me leaning firmly to the side of “yes” and “yes”.

The debate on my twitter feed included a lot of points that assumed I was attacking the exchange programme that is due to take place in November, I had actually forgotten it was due then. Had I been thinking of the exchange I would have said Shanghai rather than China. There were also people suggesting I go and see the teacher’s before commenting, I’m hoping to be able to do that anyway as I’m genuinely interested in what we can learn from them. Speaking to one teacher who has been observed by Chinese guests the main take away he got was that their pupils would have learned the year 8 curriculum by year 5.

The questions are ones I still ponder, I really don’t understand why the folk objecting to working with China on energy don’t object to working with them in education. I really don’t think we can implement a pedagogical model as it is from a culture as wholly different to ours, such as Shanghai is. However, that doesn’t mean we can’t learn anything. In the same way that I can’t implement another teachers style exactly, but I can certainly pick up tips and use parts of it to improve my own style.

A Marxist thought

October 23, 2015 Leave a comment

This post was originally published here on Labour Teachers on 29th October 2015.

Recently I read a book entitled “Socialist Mathematics Education”, you can read my thoughts on it here. The book looks at mathematics education in the socialist and communist states at the time. It was published in 1978.

In the last chapter the author comments on the Education system and how it deals with economic and political education. Stating that the schools in these regimes were geared up to propagate the ideology of the state. They then quoted Karl Marx, to show that these states were working in direct opposition to the ideals of Marx.

Marx said that religious, economic and political education should be kept away from children. Letting then grow into critical thinkers before allowing them, as adults, to learn about these things when they are in a better position to be able to make up their own minds. I can see why Marx proposed this, it would negate any propaganda and allow people to be fully informed before making a choice, rather than having this choice thrust upon them. However, I think it would be entirely impossible and impractical to even try to implement this in today’s society.

Firstly, on religion,  it would be impossible to keep this idea away from children. They are inquisitive, they ask questions. They wonder why some people have little statues of men nailed to crosses on their wall or as necklaces. They wonder why some people wear prayer caps, why some people wear Hijabs or Nicabs. The natural inquisitive nature of children means that you need to have these discussions. Even in mon-religous households like my own these discussions are commonplace, and some of the questions mentioned are in fact ones I have been asked.

Then there’s politics. That’s everywhere too, people talk about it on the television, people sing about it in their music, children listen to the conversations the adults gave around them. My daughter was approaching her third birthday when she asked my wife “Mum, what’s a Tory?”

If we shun away from these discussions we could build in an intolerance of everything that’s different, and we would no doubt be adding to the already too great feeling of apathy amongst voters.

It is my belief that schools should not be propagating a world view, a concept of “the right way” to run a country or the right religion to follow. But that they should be educating the next generation on the different views that are held by different people and creating the informed critical thinkers Marx hopes for who can make their own informed decision.

Socialist Mathematics Education

October 22, 2015 1 comment

Earlier this week I was in the Brotherton Library at the University of Leeds doing some reading for my dissertation. I saw this book and couldn’t help but pick it up:


Socialist Mathematics Education edited by Frank J Swetz.

This wasn’t particularly relevant to my dissertation focus, but being a socialist and mathematics educator I was intrigued..what makes mathematics education socialist?

I embarked on a a mission to find out, but it turns out it wasn’t actually the mathematics education itself that was socialist. It was a study into the mathematics education that was happening within “socialist” states. I use the inverted commas as it seems the authors have a blurred definition of Socialism that seems to encompass Socialism, Communism and those regimes that are set up I  their name that don’t hold true to the ideology at all.

The book was released in 1978 and the countries it looks at are: USSR, East Germany, China, Yugoslavia, Sweden, Hungary and Tanzania.

There are detailed chapters on each state and the mathematics education within it, and the final chapter looks at themes and differences. It’s a very interesting read, if you are into that sort of thing.

One commonality that occured within these states was the heavy government debate on Maths Education, to a level where they were discussing the benefits of different approaches to each topic. One example cited was a debate on whether the vector approach to geometry was the best method. The authors pick out the positive of this as increased buy in from Economists, Labour leaders and other areas as they have a say and it increases the profile and visibility of education reforms. I agree with them that this is a positive, and feel that Gove’s greatest feat, whether you love him or hate him, was bringing Education  back to the forefront of political debate.  He made it a topic discussed around breakfast tables across the country and that can only be a good thing. The flip side is that this could de-skill teachers and remove from them some of the independence that is require in their classrooms. So educational debate on this level is good, but we need to be wary of producing something over prescriptive.

Other benefits of this approach to a collaborative approach to maths education from all sectors suggested involved the curriculum itself. The schools were trying to produce people to work in the government factories and industries and as such there was a strong focus on maths and science for all. There was also good links built between the education sector and the employers.

These societys all showed a heavy focus on mathematics, believing that mathematical advancement is paramount to the advancement of society. This lead to a hollistic approach to maths education with the aim of ensuring all young people had a strong foundation in the subject. This is an ideal I believe we should all be striving towards.


October 21, 2015 Leave a comment

Parallelograms, you know, the weird quadrilaterals that look like a sheared rectangle. These:


I’ve never rally thought that deeply about them, to be honest. They have some uses in angle reasoning lessons, and we need to be able to find their area in the GCSE, but I’ve not thought too deeply about them recently at all.

When teaching how to find the area I normally do this:


It’s a fine method, and easy to show that it works by showing that you can cut the end off, in the other end and get a rectangle which is clearly of the same area.

But last week I marked a mock exam in which one of my year 11s had done this:


I love this method, it’s much, much nicer than the other. I couldn’t wait to question him. When I did he said that he “couldn’t remember” how to do it, but knee how to find the area of a non right angled triangle so split it into two of them which were congruent using SAS.


I asked him what would happen if you split the parallelogram across the other diagonal. He thought about it for a while, and eventually told me it would be fine because of “how the sine curve is” and because, “the angles add up to 180”.

I was impressed by his reasoning. He has clearly understood this method and generalised the area of a parallelogram in a way I’d never considered. I would have phrased is slightly differently though:


The area of a parallelogram is equal to the product of two adjecent sides multiple by the sine of one of the angles. (Either will so as Sin x = Sin (180 – x) )

Learning Fluency within Rich tasks

October 19, 2015 3 comments

Today was the second edition of #mathsjournalclub. A bi-monthly twitter chat aimed at increasing engagement oaths teachers with the research on mathematical education. It was the first I’d managed to be involved with and I very such enjoyed it. As it happens, I’m working on the very early stages of my masters dissertation and have spent the day reading many articles about problem solving in maths and relational vs instrumental understanding, all of which links quite well to the featured article:

Mathematical ètudes: embedding opportunities for developing fluency within rich tasks Colin Foster (@colinfoster77) – article available here

I thoroughly enjoyed this article, it started by presenting the ideas of traditionalist teachers; those who feel repetition is the best route to fluency, if you don’t give opportunities to build fluency you are failing your students; and progressive teachers; those who feel mathematics should be all about exploration and never about drill and practice.

Colin’s discussion on these points was very insightful,  suggesting that drill and practice may lead to embedding misconceptions and that learning by practice doesn’t always lead to understanding. This is something I can agree with, I’ve seen these misconceptions become embedded through drill routines and seen people who can follow a procedure without knowing why. I even remember a friend at uni who left with a first but only had a surface understanding of the procedures rather than a deeper relational understanding of the maths.

Colin also mentions the need for fluency, which I can also agree with. When number facts are known, and skills are developed to a fluent level, then that frees up more working memory to take on the more taxing tasks that come with a higher cognitive load.

Colin’s paper sought to provide an answer, to find a common ground that could satisfy both the traditional and progressive methodologies. That could build understanding and develop fluency. He looked for his answer in music, borrowing the idea of an ètude. Something designed to practice a skill, but also to be pleasing to an audience. His mathematical ètudes are designed to practice a skill set within a richer context which can also build a better set of problem solving skills and a deeper relational understanding.

He puts forward some excellent examples of what he means, examples of rich tasks that still have the elements of practice required for fluency, yet have self checking mechanisms built in so students won’t bed misconceptions. There is also easy enriching extentions for those who master something and there can be self differentiation, as the tasks are accessible to all but can be taken to many levels.

One example was in the carte sian coordinate system,  instead of giving students tons of pairs of coordinates, give them a rule (ie the second is twice the first), this allows them to generate then plot their own pairs. The fact that the graph will show a pattern gives a great self checking mechanisms and also a prompt for the student to investigate further, the enrich and extend for the higher ability students could involve squaring or cubing. This simple task allows students of all levels to engage at the level best suited for them. I can’t wait to get back to school to trial some of these tasks.

Can, or should, we learn from China?

October 18, 2015 3 comments

This post was originally published here on Labour Teachers on 20th October 2015.

This morning the Chinese ambassador was on the Marr show, and he got a few questions on human rights and the alleged abuses of such by the regime in China. The main focus was around the deal to work with China on nuclear power. A decision that has come under cast criticism from almost everywhere.

This made me question a few things as this isn’t the only Chinese import the government seems keen on; almost every DoE document has some reference to Shanghai and it’s place in the PISA rankings. I’ve seen Vanessa Pittard speak a number of times over the last few years and Shanghai was a main feature of all those speeches.

We are shipping teachers in and sending ours over there to see what we can learn. So why is there no outrage over this? This is the same country we shouldn’t be working with in other sectors because of human rights abuses so why is it ok to embrace them in education? Isn’t that an area where we want to ensure human rights are protected?

I remember watching the opening ceremony of the Bejing Olympics with my friend Will. I mentioned it was spectacular and he said: “that’s the sort of thing you can do with a population who do whatever you say under the threat of death.” Now this is, of course, an over simplification but it is rooted in the truth.

This fear of the establishment is wide ranging and must be instilled from a young age. What sort of threats are issued within schools? I don’t know but I bet there are none of the behavioural issues that are prevalent within British school, so I’d guess that the issues facing teachers here and there are very different. No behaviour management problems, no need to try increase engagement and buy in, no need for teachers to be motivators.

It leaves me pondering two questions: “Can we learn anything from China on education?”  And “Should we even be engaging with them?”

A bizarre solution

October 9, 2015 5 comments

On twitter earlier I saw this picture:


It was tweeted by “Mathster”, an app which claims to be “a complete solution for UK and IB curricula”. The picture had me scratching my head. Why would you add the unnecessary step one into preceding?  Why would you refer to “moving terms”? Why? Why? Why?!

By saying “move terms” there is no explanation for changing sign, so learners may just move the term as is, which makes it perhaps even worse than the fabled “magic bridge”! There’s no mention of what’s actually going on! The final step is explained well, and I don’t know if that makes it better or worse!

A request for help

October 6, 2015 1 comment

So I’m working on some research, looking at motivation and effective teaching in A level maths. As part if my preliminary research has I’ve put together a short questionaire to help me shape the direction of that research.

If you have completed a maths A level in the last 5 years I’d be eternally grateful if you could fill in this short survey. It shouldn’t take more than 4 minutes.

I’d also be eternally grateful to anyone who knows anyone that has sat a level maths in the last 5 years if they’d share the survey with them.

The survey can be found here. (


Categories: A Level, Exams Tags:

Too young to decide?

October 5, 2015 3 comments

“Sir, I’m not even allowed to buy a bottle of wine to have with my dinner. How am I supposed to choose what I want to do for the rest of my life?”

A year 13 pupil in my home team (tutor group) asked me that today while discussing her UCAS choices and it stopped me in my tracks. The realisation of just how stressful year 13 can be and just how young year 13 students are really hit me. How many of us really know how we want to spend the rest of our lives when we are that age? I was still dreaming of “making it” in the music business, although I did thing teaching was the most likely back up plan. When it came to choosing a course for University I picked maths, not because I knew I wanted to be a maths teacher – I was considering it, but if I had fully committed to the idea then I would have done the 4 year maths with QTS. I chose it because I loved it and was good at it. The option of teaching was still there but so were careers in finance, accounting and plenty of other things, even research mathematics and lecturing. I had ideas, but no solid plan – I was lucky that maths opens so many doors.

I’ve written recently about Vocational Education. How we, as a country, have been getting it wrong for far too long and how we need to address this. I put forward a vision of a world where vocational qualifications were as rigorous and as respected as academic qualifications. This is still something I feel strongly about, but this students words made we wonder if I’d missed something. At what age would we be requiring young people to make the choice? What if a 13 year old choses a path and the 17 year old version of the person wishes he’d made the other choice? What if, like the student I was talking to, someone has no idea what they want to do?

It made me think, perhaps a general education, that covers a bit of everything, would be best. Allowing people to keep their options open until as late as possible. That would certainly be a good option for those who don’t know what they want to do. Perhaps along side these qualifications we need some rigorous conversion courses. A way for an 18 year old who chose the vocational route to convert back to the academic, or a way for an 18 year old who chose academic to switch to the vocational.

What’s clear to me is that the whole system needs a rethink. We are putting far too much pressure on 16/17/18/19 year olds who are often not emotionally strong enough to deal with it. Then we add to the pressure with talk of student loans and lifelong debt. Surely a graduate tax would be a more favourable approach? Surely education should be free, and be a right?

For now, I’ll continue to guide as best as I can. To try to help these young people to make the right choice for them, in a system that seems stacked against them, and certainly has its limitations.

Playing with jigsaws is the way forward

October 5, 2015 Leave a comment

This is a guest post written by my brother Andy (@andycav_25). Andy is a primary teacher in West Yorkshire and currently teachers Year 5.


Fractions Jigsaw from NRICH

In the 2014 Primary National Curriculum, there’s much more emphasis on problem solving in maths. Henceforth, we’ve had a few staff meetings and twilights on this recently. We’ve been encouraged to use ‘rich mathematical tasks’, and some colleagues (myself included) expressed sheer horror at some of the ideas. However, I did embrace it and took a bit of a risk with my Year 5 class last Friday. If an OFSTED inspector had walked into the first 30 minutes of that session, I would’ve been mortified. If they’d walked in at the end, I would’ve been ecstatic.


Definition from Simon Borget

We’d been doing fractions, decimals and percentages all week and, in my timetable, I have a 2 hour session every Friday morning. I normally do 2 lessons in this time unless it can be used for a science experiment, art or D&T depending on the long term plans. Last Friday, maths was the winner. The NRICH website is great for providing these rich mathematical tasks and I found this one, which I really liked the look of. Children had to complete a jigsaw on a 5×5 grid. Each square is cut into 4 triangles that were either blank (these would eventually form the outside of the jigsaw but there were a few extras thrown in) or they had a calculation using fractions. Obviously, the children had to match up the triangles to create a jigsaw.

I thought that it had to be a pair or small group activity, so do you group them as high/low ability or assign a high ability with a low ability? I kept the high achievers together this time, as an experiment in itself as much as anything.

What unfolded in front of me was just amazing. Every single kid in my class engaged. I don’t think I’ve ever achieved that before in 5 years as a teacher (and another few before that as a TA/HLTA).

One child in my class is ridiculously talented in maths (earlier in the term, it had taken him about 5 minutes, without a calculator, to find all of the factors of 256. He’s 9!). He absolutely loved this jigsaw task. He thrived on the challenge but was also made to reassess a few times when things didn’t appear to be working. It took his group about 45 minutes to complete the jigsaw, but when I spoke to them about how they did it, it was one of the lesser but still more able kids who had spotted the pattern in the jigsaw. They had taken on different roles in the group with child A quickly calculating in his head and child B spotting patterns to assist child A in finding the correct pieces.



That group also complained to me at one point that they had 6 ‘top’ pieces, which doesn’t work on a 25 square. They told me that it was wrong. ‘Look again,’ I said, numerous times. Eventually, they did realise that there were two blank areas inside the grid too.

The middle ability groups really struggled at first. As had been the plan at the offset, I shared a few answers and gave them a starting point after about 20 minutes. Bang. They started working through that grid as fast as I’ve ever seen them work in the 4 weeks they’ve been in my class. Not everybody finished (in fact probably only about half did, if that) but that didn’t matter either to me or them. They had all achieved something and we all knew it.

Once the HA group solved it, I gave them a template of the solution to make their own – they had fun testing each other. At that point, I also shared that template with the rest of the class as an extra piece of scaffolding. That made some of them look and immediately say ‘we need that shape here so which piece fits?’ Another great use of mathematical thinking. Key question: what’s the same and what’s different about the pieces and what does this tell us?

At the end of the session, I did two plenaries. First, what skills have we used this morning? Answers: ‘fraction skills’, ‘teamwork’, ‘spotting patterns’. It took a little bit of guidance but that’s fine.

I would’ve liked ‘problem solving’ to be an answer but alas…

Pic7 Pic6 Pic8

We’ll get there in the end!

The second plenary was simple: ‘who has been completely confused and felt like your head is about to explode at least once this morning?’ (62 thumbs up – there’s 31 children in the class).

Who thinks you’ve made progress with your maths this morning? (again, 62 thumbs up). I think this risk definitely paid off! I will be trying to do at least one of this type of task or investigation for every topic in maths from now on. The skills and achievement shown by every child at their own level was amazing and they really enjoyed it too! Plus, there’s no marking to do… Bonus!

I enjoyed reading this post. It’s nice to get a fuller view of what maths is taught at primary and how it is taught. I love the resources on nrich, I’ve not used this specific one, but I certainly would if I have a class that it fits too. Have you used anything similar? What are your views on this task/these tasks?

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