The confessions of a maths teacher – how I slept my way to success


The confessions of a maths teacher – how I slept my way to success.

It may just be that all our work scrutiny, all that triple marking, all that group work and all those verbal feedback stamps have, at best, merely been tinkering around the edges, covering over the cracks, re-arranging deck chairs on the Titanic.

Perhaps we are ignoring the single biggest factor that could improve the learning and performance of the pupils in our care.

Sleep.

I’ve recently read “Why we sleep: The new science of sleep and dreams” by Matthew Walker and it has, forgive the pun, opened my eyes.

I like to call myself a “healthy sceptic” – I’ve seen fads come and go all too often in education, and I ain’t going to believe something just because someone tells me it is so. But the author of this book has the credibility of being an expert in his field, and the copy is littered with well referenced research and sources. He’s done enough to convince this old cynic.

Sleep has an enormous impact upon learning. Anyone who has ever been in a classroom will, I think, recognise that a tired student is less receptive to learning. What I didn’t appreciate was the importance of sleep after learning.

The author explains (and backs up with scientific evidence) far better than I could ever hope to do how we need sleep after learning to fix new ideas and knowledge in our minds. To be rested before a lesson is not enough – we must rest (sleep) afterwards as well, else the value of the lesson is lost. You could teach the best lesson ever, but its value and impact will be significantly diminished amongst those students who don’t sleep well (and for long enough) in the nights (note the plural, not the single) afterwards.

He explores the different types of sleep (nonREM and REM sleep) and their different impacts upon retention and problem solving. It is a fascinating book, I urge you to buy a copy and read it for yourself.

So what can we as teachers do?

In the book, the author conducts (an admittedly unscientific) poll of friends and colleagues across countries and continents and discovers that no one ever had any lessons on sleep, or the importance of sleep whilst at school. In school, we regularly teach our students of the importance of a good diet, exercise, the danger of drugs and many other vices – think of your PSHE programme and all the above will feature, but “sleep hygiene” never makes an appearance. Perhaps it is time to start educating our pupils on the perils of too little sleep.

We can also help ourselves to more sleep, which will make us more effective in the work place, or in other words, better teachers (and, as a by product, will also make us healthier, more attractive, slimmer, more creative)

Some readers may be in exulted positions and thus able to make systemic changes to the school day. In the book, Professor Walker presents clear evidence that a later start to the school day improves results.

Reading the book, I have come to realise that my schoolboy academic success may not have been down to my hard work (if I’m honest, did I really work that hard?!) or any innate natural talent, but more due to a fluke of geography that had me live a mere hundred yards from the school gate, allowing me to roll out of bed at 8 o’clock ready for a 9am start. I literally slept myself to exam success.

Sleep – has ever anything that feels so good been so good?

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What an ar$e

After yesterday’s blog post which highlighted the calm, statesman like brilliance of President Macron, today the pendulum swings fully the other way, allowing Piers Morgan to show himself to be a bullying buffoon, a despicable and pathetic man.

He tries to show that he is more intelligent than the guests on his show – guests invited in so that he can belittle them – by asking them about Pythagoras’ Theorem.

But he fails. He fails magnificently.

Clearly Piers himself doesn’t know what Pythagoras’ Theorem is, confusing it instead with Pi.  (And, you can just make out over the justified derision of his co-presenter, despite claiming to, he doesn’t know Pi to five decimal places.  When challenged he states that Pi is 3.147, which is not to five decimal places, and is wrong anyway.  Pi to five decimal places is 3.14159)

I know Pythagoras’ Theorem, and I know Pi to five decimal places, but that doesn’t make me any cleverer or better than Piers or any of his guests – I just know something that they don’t.

Piers: please don’t bully and belittle, take a leaf out of President Macron’s book and educate and inspire, it’ll make you a bigger, and better, man.

 

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Fantastic, Mr President

President Macron of France took a teenager to task for failing to show him – or more correctly, the Office of his Presidency – due respect.

It is a fantastic clip, in which the French leader displays gravitas whilst taking the opportunity to educate.

The day you want to start a revolution you study first in order to obtain a degree and feed yourself, OK?

Wise words.

It would have been so easy for him to have ignored the low level “cheek” from the garcon – and how often have we, as teachers let things slide, or seen colleagues do so?

As @Marcus Haddon said on Twitter:

I’ve seen some headteachers in the UK have less interaction with their students than this.

Watch the clip for a 30 second masterclass in how to set a positive role model.

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Most Competitive League in Europe

One in eight thousand

Saturday saw Aston Villa face Fulham FC in what is widely regarded as the most valuable game in world football – the winners of the Championship play off can look forward to the next season in the Premier League, a season worth circa £170 million, a sum far eclipsing the prize money of any other competition.

The above is easy to quantify, less so is the assertion that the English Championship is the hardest to gain promotion from, the most competitive league in Europe, although many will make this claim.

So which is the most competitive league in Europe?

Before we can answer that question, we have to determine how we can answer that question.

My solution (of course!) is to employ some maths – let the numbers do the talking.

Standard Deviation is a measure spread, a measure of how close to the mean (average) the data is spread.  A low standard deviation tells us that the data is closely clustered around the mean, whilst a high standard deviation tells us that the data is spread out around a wide range of values.

I calculated the standard deviation for fifteen different European leagues, and compared the standard deviations of the points each team gained in the season. The leagues with a lower standard deviation, I concluded, were more competitive than those with a higher standard deviation.  A lower standard deviation means that the points for each team were closer to the mean, suggesting that the clubs in that league were more matched, and therefore the league more competitive than those leagues with a high standard deviation.

68 95 99

68, 95, 99 – no, not the years that Spurs won the cup, but a handy rule of thumb, sometimes known as the 68-95-99.7 rule (or three sigma rule if you want to sound clever).  What it tells us is that for a normal distribution (or bell curve, and we can expect points scored in a league to be of this form) 68% of data points (points gained in our example) lie within one standard deviation (in either direction, above or below) the mean, 95% lie within two standard deviations and 99.7% (or nearly all) results lie within three standard deviations of the mean.

And the winner is …

So after all this maths, which league is the most competitive? Is it the English Championship as so many pundits would have you believe?

No, the most competitive league in Europe is the Russian Premier League, with a standard deviation of 13.3, closely followed by the Bundesliga with a standard deviation of 14.0.

The English Championship is not as competitive as the two divisions below it, although it is more competitive that the English Premier League it feeds into.

And it seems that the Bundesliga is bucking the trend – the other “big” European leagues have the higher standard deviations, suggesting that they are less competitive, with Italy’s Serie A coming bottom with a standard deviation of 20.6.

League of leagues

So here is my league of leagues, based on standard deviation, the most competitive at the top, least at the bottom:

League Standard Deviation
Russian Premier League 13.3
Bundesliga (Germany) 14.0
League 2 (England) 15.1
League 1 (England) 15.3
Greek Super League 15.8
Scottish Divison 1 16.8
Championship (England) 17.1
Dutch Eridivise 17.4
Ligue 1 (France) 17.6
Scottish Premier 17.6
Scottish Divison 2 17.7
La Liga (Spain) 18.2
Premier League (England) 19.2
Portugues Liga 19.3
Serie A (Italy) 20.6

 

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Financial Times – could do better

The above tweet [link] popped up in my twitter feed this morning, and it got me thinking.

Not about whether or not Dominic Raab’s claims* were valid.

No, I spent quite some time trying to figure out what that “graph” (info-graphic is probably a better term) was trying to say.

I just couldn’t figure it out.

Now, I’ll be the first to admit, I’m no economist and I’ve never formally studied the subject. But I would describe myself as reasonably numerate and (as I have written before) as a mathematician I am far more interested in the applied side of the subject to the pure; I am used to taking equations, data, charts and graphs and interpreting them. But on seeing the above, I just couldn’t understand it.

First schoolboy error was no axis labels (and no numbers on the y axis at all.)

The headline in bold mentioned house price increase from 1991 to 2016, suggesting a time series graph, where we are accustomed to seeing time flow from left to right.  The title did imply that we were looking at a change over time, yet this makes no sense in the context of the graphic (I’ve given up callling it a graph because, although presented to try and look like a graph for (I presume) gravitas, it ain’t a graph).

I was now becoming increasingly confused.

Having twigged it was not a time series graph, my mind then picked up on a couple of key features of the graphic.  The title said “average house price” and the top number on the x-axis was 275.  I knew that the average UK house price is around £275K (I’ve since checked – its a little lower, but in that ball park) so perhaps the graphic was meant to represent the average house price in the UK? But that made the chart even more nonsensical.

By this stage I was genuinely perplexed. I genuinely had no idea what this tweet and graphic was trying to say.

I could have (and perhaps should have) left it there and got on with my day. But I couldn’t. It was bugging me, so I did a bit of digging to see if I could fathom what the Economics Editor of the FT was trying to convey. It seems I wasn’t alone in my confusion, finding this thread on Reddit

[–]AlcoholicAxolotl1 point

I have no idea what this is trying to show.

[–]easy_pie1 point

I’m struggling to follow what his point is

[–]daveime#Puglife 1 point

Is it big or small?

Who the f$$k knows? Graph with no labels, one axis without values and the other without values or units. What is the Y axis exactly, Hedgehogs per Furlong?

FT Economics Editor, seriously? He must have been absent when they did graphs.

Fortunately, on the same thread, another user, DavidChild, was able to simply and succinctly explain what the Tweeter was trying to say:

Dominic Raab claimed immigration caused a 20% increase in house prices. The bar along the bottom shows percentages, the red and green showing the proportion of the change attributed, and not-attributed, to immigration.

The role of teachers and journalists alike is to educate and illuminate.

This graphic failed to do either – I would have expected more. *Dominic Raab was guilty himself of mangling statistics to suit his own ends and it is right that his (mis)use of data is called into question, but if one of my A level, or even GCSE, students had presented this to me, they wouldn’t have been getting many marks.

In conclusion, Chris Giles, Economics Editor at the FT: could do better.

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