From Here to Infinity, Ian Stewart – A Book Review

September 16, 2014 Leave a comment

I finished this book a while ago, but haven’t got round to reviewing it yet, so thought I would jot down my thoughts belatedly.

Ian Stewart is an author whom I first discovered through Terry Pratchett. Together (and with Jack Cohen) they penned the “Science of the Discworld” series of books which use stories based on the Discworld to explain the science of our own world an universe, if you haven’t read them, I would certainly advise you do! I enjoyed them, and so I thought I would enjoy this one too.

From here to eternity had me hooked from the opening salvo, a paragraph so powerful it made me stop and write this blog post. Here is an abridged version:

“One of the biggest problems of mathematics is to explain to everyone what it is all about. The technical trappings of the subject, it’s symbolism and formality, it’s baffling terminology, it’s apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were summed up as ‘a lot of tadpoles drawn on a row of lines.’….. The symbolism of maths is merely its coded form, not its substance…. Mathematics is not about symbols and calculations, these are tools of the trade….  Mathematics is about ideas…. It is about how ideas relate to each other….understanding why an answer is possible…. good mathematics has an air of economy and an element of surprise. But above all, it had significance.” (Ian Stewart)

I was nodding along from the get go and my mind was entirely hooked from the get go. Stewart uses humour and anecdotes to weave an engaging tale around some really heavy mathematics, and all the elements add up to a thoroughly enjoyable book.

While reading it I found my love of group theory, graph theory and knot theory rekindled. The booked took a surface view of the topics and I found these tasters made me yearn for more. There were also area’s I knew little about, such as non-euclidean geometry, which I now have the desire to research further.

The book is exciting, and informative and I would urge anyone with an interest in maths to give it a read. Especially those embarking on a degree in maths who don’t yet know the area’s they want to investigate, it will give them a great taster.

Categories: Maths Tags: , ,

Damaging short cuts

September 10, 2014 5 comments

Yesterday, my year ten class were doing Standard Form (Why did we drop the word index? Standard Index Form is much better!) During the lesson it became very apparent that they were nowhere near fluent in the use of negative numbers, so today I taught a lesson on directed number to fill in the gaps.

The first few examples were of the form – a + b, or a- b, and were easily dealt with, but then I gave them an example which blew their minds. The example in question was:

-7 – 4

I talked through it to nods of agreement but then I got this:

“It can’t be -11, there are two negatives and Miss so and so said that two negatives always make a positive”

AAAAAAAAARRRRRRRRGGGGGGGHHHHHHHHHHH!!!!!  went my internal monologue. Others in the class murmured agreement. A long discussion ensued, about where this fallacy comes from and why it’s entirely wrong. We got there, and now the class have a deeper understanding of negative numbers and how to deal with them, however,  I think this could have been entirely avoided if this short cut just wasn’t taught. If they had just been taught how to handle negatives in the first place.

This isn’t the only topic that falls foul of this. I’ve written before about “BIDMAS“, Tina Cardone (@crstn85) has put together a superb book on a variety of similar things and just yesterday Michael Tidd (@michaelt1979) tweeted “Can we all just agree to stop using the crocodile inequalities analogy”.

This is one that infuriates me. Every year I have to unteach this because a number of pupils have quite understandably changed the story in the head to “the big number eats the little number”. This seems sensible, as a big crocodile would certainly be more likely to eat a smaller crocodile than the other way round.

Why can’t we just teach the concepts and forget about the shortcuts? They are more of a hindrance than a help!

Happy New Year (2014/15)

September 8, 2014 1 comment

It’s funny that in most of the world the year starts in January, but in Education we start in.September. (Not to forget those finance types who start in April) But that’s how it is. My mind has always been set to a September new year. Probably because I’ve been around education for most of my life. I still work out people’s ages based on school years!

This time of year, for me, is one of new beginnings. I came across this post this evening. It’s last year’s happy new year post, and in it i set out some hopes and ideas for the year ahead.

This year is different, it’s not just a new year, but a new school. I do, however, have a similar feeling of excitement, perhaps more so.

Last year I wrote of wanting to ensure my lessons were as good as they could be, and I think I managed that on the most part. That’s not to say they were perfect, just as good as I could have made them. This year I want them to be better. I think that all teachers should be striving for those constant improvement. The way I plan to do this is to observe as many others as I can, to trail different things in my lessons, to use ideas I’ve seen and read about, continue to attend teachmeet and conferences (and any other CPD I can get) when given the chance and continue working towards my masters.

Last year I also spoke about wanting to read more. I have managed that, and the education books, journals and blogs I’ve read, and the Maths ones, have indeed helped my teaching. I even managed, fiction book! (Terry Pratchett’s collection of shorter writing entitled “A blink of the screen”, for those who are interested.) My “to read” list, however, is constantly growing, so I hope this year to be able to read even more from all categories, and hopefully these will improve my teaching too.

The new school brings with it a new role, and a move from TLR responsibility to leadership responsibility. This is exciting and I want to make sure that this side of my practice is as good as it can be too. My school have put me forward for a course which will help here and I have a lot of great people around to learn from.

Another exciting thing this year is purchased involvement with the core maths qualification. We are lucky enough to be a pilot school for the scheme and I’m excited by the prospect. We have a decent group of pupils who have signed up, and we are motoring along, even though there is, as yet, little information on the course. This new qualification is something that will be shaped over the next few years, and I look forward to being part if that.

All in all, I am excited about 2014-15, excited by its prospects and hopeful that I can improve myself, and the outcomes of the pupils in my charge.

Changing Schools

September 5, 2014 7 comments

I’d never done it before, changing schools. I had been to two schools as an ITT trainee, then moved onto employment at a third school, but that was that. I had been there since. When I left at the end of last term I had very mixed feelings. I was excited to test myself in a new classroom setting, I was excited to sink my teeth into the new role I had been appointed to, but I was sad to leave the place I had enjoyed working at so much. I was sad to be leaving my friends and colleagues, and I was sad to be leaving my classes. As summer drew on both these feelings remained. Had I made the right choice? Would I like it at the new school? Would I fit in to the department?

Now we’ve been back two weeks. That first week, when all the other teachers I know we’re still on holiday, was tough. But the thought of 2 weeks at October was certainly enough to keep me going! The first day was a training day, which was focused around the good results achieved last year and the challenges we face to keep them heading in an upward trend. I felt it was an exciting school to be at, and am exciting time to be here.

I get on with the others in the department, and there is a good team spirit which I already feel part of, so the worries I had there were unfounded. I’m still getting to grips with parts of my role, but I’m thoroughly enjoying the process and the challenges.

That leaves the lessons. The new school has promethean boards, not smartboards, so I had to get use to the new equipment and the software. The room layout is different too, so I’ve had to get used to that, but I feel I have made the switch well. I have met all my classes and I really like them. There have been one or two settling in behaviour issues, a by-product of being new to the school, but I feel that I’m on top of them.

All in all, I am enjoying my new role and the new chapter in my career. I feel I have made the right choice, and I look forward to the journey ahead.

Why do sky bet not simplify?

August 26, 2014 1 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.


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