Why do sky bet not simplify?

August 26, 2014 Leave a comment

This evening I came across this while checking the headlines on the sky sports app.


Apparently, Celtic are 100/30 to reach the group stages of the champions league after going behind. My current footballing knowledge isn’t strong enough to know whether they’re good odd or not, but I do know how odds work.

For those who don’t, the first number is the pay out and the second the stake. In this instance of you place a £30 bet and then Celtic do reach said group stage then you would win £100 (and get your stake back). Any other bet would pay out in the same proportion, so a £15 stake gets £50 and a £60 stake pays £200 etc.

Normally odds are presented in their simplest form, if it can be expressed as a unit ratio (I use this term as I think it’s the closest to what we’re dealing with, I think they should use proper ratio notation in betting shops) and if not 7/2 9/4 etc. In this case the simplest form would be 10/3. Even people with a basic grasp of maths can see there is a common factor of 10 and would find it easy to perform the simplification.

So why have they not? I can only think it is to encourage people, perhaps a little worse for wear, to put £30 on, instead of £3. Or perhaps it’s just a typo. Either way, I find it irksome to see these things left unsimplified!

The Early Entry Question

August 21, 2014 6 comments

This evening I happened across this tweet from Tom Bennett (@tombennett71):


“Very sad for individual schools, pupils who lose out. But these reforms eg early/ multiple exam entry, are fairer in the long run” -Tom Bennett

The ensuing conversation intrigued me, and there were lots of things I wanted to interject, but I felt 140 characters was a tad too short, so decided to sum up my feelings here.

So, early entry? A bad thing?

In itself, I would say no. I sat my maths GCSE a year early, aced it, and moved on to a certificate in additional mathematics which I enjoyed and which set me in good sted for the a level. Used this way, early entry is fantastic, and I feel it should be. This year, my school sat 3 y10 girls for their maths GCSE and they all hit A*s, there is no way they should be made to go over stuff they are majorly fluent with already for the whole of year 11.

So you think the reform Gove put in place was bad?

No, I’m majorly in favour of it. The scenarios mentioned above are not stopped by the reforms. They are the reason early entry exists. They are not, however, what early entry was being used for by the majority of people.

In my NQT year I had a year 11 class once a week. They all had Cs from the end of year ten and they would very politely tell me they weren’t interested in enhancing their maths grades as the had the C and Cs all you need right? (Wrong, actually read more here!)

That link is to a post I wrote on the idea of a threshold pass being the be all and end all, and mentions my views on early entry. That y11 class should all have been aiming for As, but stuck with Cs. If they’d not been entered early, they would have had better maths grades.

Why did schools do it then?

I don’t know. I’m fairly certain that no one involved in the decision making process at any school did it to hold pupils down. I think they must have overlooked the possibility that students would act this way. I think the driving force behind doing it was to boost the headline 5 A*-C including English and Maths figures (there’s that headline figure again- let’s hope progress 8 gets rid of this idea!)

How does it help that?

Well, it highlights pupils who may need extra intervention in order to reach the C and allows that provision to be put into place. This, in itself, is not a bad thing. I’m all for putting extra sessions and interventions on for those who need it, but I know of some schools that have, in the past, put weak teachers, or even cover supervisors, on the pupils that have hit the C and moved all their resources to the borderline.

There are bright pupils who end up with Cs who should be getting higher, but the bottom gets hit too. Weak pupils who scrape Gs or hit Us would also, at some schools, be forgotten about. They can’t get the C so why bother? I think that these pupils are the ones who need intervention most. (Again, I hope progress 8 can curb this behaviour too.)

So you think the elimination of early entry is good for top and bottom as it favours the borderline?

Actually, no. The borderline get hit with the same topics over and over because they are “big mark” questions or “dead certs” to come up. The system which put them through 4 a year meant for many “borderline” pupils at many schools they would sit maths 5 times. Each would be preceeded by a mock and revision time, leaving little time for actual, new learning. Surely it would be better to let them learn at their own pace and achieve what they can. How many people capable if A/A* were pigeonholed as “borderline” in year ten and put through this limiting regime meaning they left with a C? I’d wager a fair few.

So, what’s all that mean?

In short, I’m in favour of early entry for pupils who are ready and need to love on to the next stage. But I’m against this early entry game that was prevalent. I think that the idea to limit league tables will definitely stop it, so that’s a good thing. I do worry though that some schools may be reticent to enter the pupils who should be entered.

As for the threshold pass, C is everything idea, the faster it goes the better. I have high hopes for progress 8, let’s hope they are met.

The Problem with Democracy

August 17, 2014 10 comments

Today Ross Morrison McGill (@TeacherToolkit) tweeted this:


The sooner politics is separated from education, the better for everyone. (Ross Morrison McGill)

The tweet was in response to this guardian article which claims that Rachel de Souza was given advance warning of inspections. If these claims are substantiated then this is a ridiculous situation, but I feel it is particularly worrying that people are arguing that we should remove Education Policy from politicians entirely. This is a claim I’ve heard often, and it scares me.

We live in a democracy, everyone over a certain age (bar some prisoners, but that’s a different debated for a different day) is entitled to turn out on election day and cast their vote, based on the manifestos put forward by each party. These votes are counted and the party who gains the most seats forms a government. In an ideal world everyone who is enfranchised to vote would read, at the very least a summary of, each manifesto. They would decided which manifesto agrees with their own views, and vote accordingly. In reality more people don’t vote than vote for any party and vast swathes of those who do vote on issues that are extorted by the press and don’t realise what they’re voting for! (I refuse to believe that THAT many people thought that the best way to improve the UKs deal from the EU was to vote for a party who refuse to vote in EU decisions as policy!)

I was (still am) a vocal opposer of both the Conservatives and the (not actually so) Liberal Democrats at the last election. But as a believer in democracy I had to accept their mandate to form a government. The other option would be to raise an army and revolt, and although I’m sure I could make the country a better place if I was in sole charge, I can guarantee others would disagree.

So what’s this got to do with Education?

Well everything really. When we choose a government those manifestos involve Education Policy. Education is a massive party of running the country. And I feel it should be.

What are the other choices?

We could hand control of Education to the private sector. This idea is abhorrent. Education would be reduced to a balance sheet.

We could hand it to the third sector. We could, at least then there wouldn’t be profit element involved. But who would be in charge? Someone I chose? Someone you chose? Someone the government appoints? Someone elected? All of these scenarios give rise to exactly the same problem that the government being in charge gives. So why create extra bureaucracy?

I do get annoyed by the fact that Education Policy seems to be used by politicians to score points, I’ve written about it before, but Education is important and people do hold different views on the best way to run it. It should be part of the remit of the government, it should be at the forefront of what they do and how people vote.

If you don’t like what’s happening, there are democratic channels to go down to affect change and I would urge everyone to do so. Write to your MP, campaign for the issues you believe in and campaign for the party that best represents your views.

There are 2 main problems with Democracy, the first is we don’t all always agree. This is an inevitable by product of the democratic system, a system that is, in my view, the best way to run a country. The second problem is apathy. At the recent local elections national voter turn our was less than 40% so around 2/3rds of those with the right to vote told us they just don’t care. This is a problem we need to address. I’m not sure how, perhaps compulsory voting as in Australia?

Addendum: Since writing this post I have spoken with Ross and he wasn’t advocating removing Education Policy from the government. He was expressing a wish to end the corruption and the way people politicians and press buy favours. This is certainly a sentiment I agree with and may write about more in future. I have, however heard others express the view that Education Policy be removed from government control.

Concentric Circles Puzzle

July 31, 2014 5 comments

This morning I happened across this tweet from David Marain (@dmarain)


As you may know, I have a penchant for puzzles, and find it hard to leave them unsolved, so I thought about it and came up with an answer. I thought I would jot down my thought process here.

For those who can’t see the picture, the puzzle is:

A point is chosen at random inside the larger of two concentric circles. The probability it lies outside the smaller one is 0.84. What is the ratio of the larger radius to the smaller radius?

It’s a lovely little puzzle that combines a bit of geometric thinking with probability theory, so do have a little go first.

You done? Good.

My thinking started as: “that 0.84 must be equal to the area of the big circle – the small circle all over the area of the big circle.”

I used a as the area of the big circle, b as the area of the small circle and formed the following equation:

(a-b)/a = 0.84

With a little rearranging I got:

0.16a = b

So a ratio of areas that is

1:0.16 (a:b)



Which is equivalent to


Which simplifies to


As we are looking for the ratio of radii, we need to square root each side, which gives a ratio of


A nice little solution to a lovely puzzle. Thanks for sharing David.

Nb: no photo of envelope workings as I did it mentally.

Stem and Leaf – is there a point?

July 25, 2014 1 comment

Stem and leaf diagrams, or “Those leafy stem things”, as one of my former pupils used to call them, have long been an annoyance of mine. I’d never heard of them until I was brushing up on the GCSE syllabus ahead of my PGCE and when I did come across them I couldn’t see anything that they brought to the party that couldn’t better be shown using alternative methods.

You can imagine my feelings then as the KS3,4 and now 5 curricula jettisoned them, meaning the end was in sight for the need to teach them. I let my feelings on this be known in my recent post around the new A level curriculum and this led to further discussion around them on twitter. Then Jo Morgan (@mathsjem) wrote this fantastic piece which supports their place in a classroom and gives some great activities to use in teaching them.

It got me thinking, are my feelings unfounded? Should I be writing off stem and leaf diagrams? I’ve long been an advocate of maths for maths sake, see this defence of circle theorems for one example, so why is this feeling bot the sane for stem and leaf?

Perhaps it’s that it falls under the banner of “stats”, a very applied area of maths. This suggests that there should be an application associated with it. The use mentioned in Jo’s blog for bus and train timetables is the best example I’ve seen, but I think a normal timetable will be easier to read for the majority if people, as the majority of folk aren’t familiar with stem and leaf. Hannah (@missradders) suggested that they were used a lot in baseball, but I can’t see any reason that they would be better than a bar chart or a boxplot.

Colin Wright (@ColinTheMathmo) suggested during the twitter discussion that they could be used to build understanding around data, even though they are no use for any real data sets which would be far too big. Jo also uses this idea in her defence, saying they could provide a good introduction to the ideas of skew, quartiles and outliers. I can see this argument, but I still think there are better, more visual and less convoluted ways to introduce these to pupils, such as the aforementioned bar charts and box plots along with scattergraphs and a host of other data presentation methods (but not pie charts, they’re just as bad, if not worse! But that’s a topic for another day!)

I really enjoyed Jo’s post, if you haven’t read it I would advise you do. It made me think and look hard at my views. In the end though, I still see no need in stem and leaf diagrams and will be glad to see the back of them. If you have opinions either way I would love to hear them, especially if you have further real life uses!

The draft maths A Level- initial thoughts

July 22, 2014 3 comments

So the drafts of the new Maths and Further Maths A-Level courses have been released and the Department of Education and Ofqual are in a consultation period. (You can download the drafts and find more details on the consultation on it here.)I am left pondering the rationale behind the summer holidays consultation periods that the department seem so fond of, you could say it is an attempt to reduce consultation as most involved with education are on holiday and not thinking about work. Or you could say it was to give those same people more time to consider it. I think it will probably reduce the amount of responses.

I have had a quick read over both drafts, and wanted to make a few initial remarks here. I will be spending some further time on these and putting together a fuller response to them as part if the consultation, which I will also publish here.

A Level Maths

The overview

The big change is, of course, the switch from a modular to a linear course. This has also been coupled with a,switch to a course that us 100% prescribed. I think that a linear model may be better than a modular model, but I did like the choice element offered previously. Students with no interest in physics who want to study psychology or biology etc don’t necessarily need mechanics, and would benefit from doing a course that is more stats heavy. Likewise, a student who wants to go into physics would benefit from a heavier mechanics load in their qualification.

Overarching Themes

These seem to be fairly similar. There is a bigger focus of set theory, which I feel us good. I was disappointed not to see more of this on the reformed GCSE. There appears to be a bigger emphasis on proof, it mentions contradiction, exhaustion, deduction, but no specific mention of induction. A stronger emphasis on this can only be good.

This section also alludes to a bigger emphasis on problem solving and modelling, which is one of the main applications of mathematics, so more focus here can’t hurt either.

The Content

This seems to be what you might expect. It covers the majority of the current core modules, a fair bit of mechanics 1 (and higher) and stats 1 (plus the binomial distribution, which appears on stats 2 for some boards.)

There is more mention to modelling throughout, and it looks as though they have brought linear programming into the algebra section, which also includes a bit around looking at transformations of the normal curve. The rest of the curriculum which pertains to the current core modules is very similar. Solids of revolution have gone, and been replaced by newton-raphson, but that seems to be it.

The stats has lost some if the nonsense involved currently (an end to stem and leaf! Hurrah!) and is more focused on the important bits, like probability theory and the two big distributions (Normal and Binomial).

The mechanics section looks exciting. It is based around forces and kinematics (of course) but is more advanced than the current m1, incorporating the calculus that doesn’t come into the current mechanics course til m2/3.

What should have been there?

There is no mention of graph theory, the best part of the current D1 module. I think that’s a real shame as it is newer than the majority of the syllabus and is vastly different to what students have learned before now. I know that universities were keen for this to be on there.

Something else the unis wanted to see on the a level was an intro to Matrices and Complex Numbers. These are two topics important in many courses (engineering, computing, etc) and they have to be taught at the start of such courses, so I was expecting to see these, and would have liked to see them too.

Further Maths

Unlike the Maths course, this one includes an element of choice, kept up to the exam boards. There is core content listed but this only accounts for 50% of the course. This gives the boards an opportunity to diverge. Surely we will see graph theory here, and hopefully game theory, knot theory, perhaps caos theory?! Will any be brave enough to include quaternions?! There could be massively different courses between boards, or they could all go with the same, safe choices.

Core Content

The core content is drawn from the current FP1-3 modules, (plus volumes of revolution from the current core.)

It looks to have a good basis, covering complex numbers, matrices, hyperbolic functions, polar coordinates (Grrr) and builds on the topics from the Maths Alevel such as calculus, vectors and differential equations.


I was expecting a massive change to the curriculum. When the review finished for the other subjects we were told maths would be released later as it needed the mist significant changes. But the changes to the curriculum are not massive. The majority of the core maths is still there and the major bits of stats and mechanics are there. The most significant change is the switch to a 100% prescribed curriculum, something I can see arguments for and against.

Similarly, the further maths core content is the same as it currently is. The 50% left to exam boards could be the same as we have now, or could be radically different, depending on the courage of the exam boards. We won’t have a solid answer until they release their materials.

If you are involved with teaching maths, or are a mathematical researcher, or based in any job or uni department that depends on maths, do have a read and respond to the consultation. It closes mid September. I’d also love to hear your views

Mid year review

July 19, 2014 Leave a comment

Right at the end of January I wrote this piece reflecting on 2013 and looking forward to 2014. There were a lot of others doing the same and it was nice to read all the reflection going on and to see people’s hopes for the year ahead.

A week or so ago Jill Berry (@jillberry102) tweeted to say shed enjoyed those pz
osts and would love to hear,some mid year progress updates. Again, many others have done this and I’ve enjoyed reading them so I thought I would jot a few things down here.

A review of those plans


I have continued to watch my daughter grow, my partner and I have both enjoyed the education we are receiving and I do feel it is positively impacting my classroom practice, so they’re all ticked. We have also finally set a date and my daughter is looking forward to being a flowergirl.

Educational Events

I have been to more teachers, I did attend northern rocks and I also went to the ResearchEd York conference. All of which have been great and have helped. As you can see, I have continued this blog and I feel that us helpful too.

Reading and Maths

I have managed more reading and to investigate more areas of maths, but not as much as I would have liked, I guess this is still a target!

Education Policy

I’m fairly pleased with the new Maths GCSE Curriculum, it’s more rigorous and challenging than the previous one. I’m also pretty stoked about the proposed Progress 8 measure which I hope will take us away from the threshold pass. Now that Gove has gone all bets are off! I’m worried about the new Education Secretary, but am prepared to wait before making a judgement. It’s too early to tell if the new ITT systems will help retention, but 2014 hasn’t yet seen the amount of teachers I know leave the profession as previous years, so that at least is positive.

What else?

When I wrote that blog in December I had no idea that I’d be sat here today having spent my last day at the school I was at. It’s a crazy feeling. It all happened so fast, and although I’m majorly excited about the new challenge that waits at my new school I’m also pretty say about leaving too.

I wrote briefly about leaving here, but even then I didn’t quite realise what it would feel like when it finally came.

Saying goodbye

Saying goodbye was hard. It was really hard to say goodbye to year 13, the yeargroup included some of the most amazing people I’ve ever known, but at least this was inevitable. I would still have had to make those goodbyes, with my other classes it felt like a premature goodbye.

My year 12 class have spent the time since I told them I was going guilt tripping me, to great effect I might add, and it was incredibly hard saying goodbye to them.

My year 11 class was another particularly hard goodbye. It’s a strange one this, it’s one that in one teaching years has felt a natural goodbye, but this year the vast majority of them are staying on at sixth form and around three quarters of the class have provisionally chosen maths Alevel, so it did feel premature. Two of them called into see me on Thursday and that was really nice.

All my other classes were hard too, but particularly my coaching group. I’ve been their coach since they started the school in year 7 and I’ve seen them all grow from timid little children into confident young adults. I feel really guilty that I’m leaving before they have finished year 11, and I know they were all upset, but I think they understand.

Then there is the staff, over the years I had been there I have build many great friendships, and I will miss seeing those friends on a daily basis. And I will miss the afterschool joint planning and chatting sessions that happened on an almost daily basis too.

The last day was emotional, especially the last coaching session and the speech my friend and (now former) colleague gave about my leaving that had me both in hysterics and on the verge of tears. I think I need the holidays to recover.

Looking ahead

Looking forward I see excitement. I’m starting a new role. The school seems like a good fit for me, the role us definitely a good fit and I think the team I’m working in will be too.

I’ve got more responsibility, and a brilliant timetable. I’m already excited about some potential conferences and I’m really looking forward to the second year of my masters course.

But that starts in autumn, the summer is about recharging the batteries, spending time with the family and making sure I’m ready (with a couple if trips into the old school for results days if course!)


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