June 2019 A level Grade Boundaries

Image by Andrew Martin from Pixabay

Offered without comment, below are the grade boundaries for the new spec. Maths A level, June 2019: Grade – Percentage (Raw Score)

Note, all boards the maximum raw score is 300

AQA

A* – 77% (231)

A  – 62% (185)

B  – 50% (151)

C  – 39% (118)

D  – 28% (85)

E –  17% (52)

EdExcel

A* – 72% (217)

A  – 55% (165)

B  – 45% (134)

C  – 34% (103)

D  – 24% (73)

E  – 14% (43)

OCR

A* – 72% (216)

A  – 54% (161)

B  – 43% (130)

C  – 33% (100)

D  – 23% (70)

E  – 13% (40)

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Hola!

I think it was only a few years into my teaching career that it dawned on me. A realisation of which I am not proud, a moment of self-awareness that still leaves me cringing.

I must have been one of those pupils that drive teachers to despair.

Not all my teachers, mind. No, my maths, science, and history teachers were more than happy with me, my English teacher comfortably ambivalent towards me. No, it is to the various French teachers I had through the years that I owe unbridled apologies.

In most of my subjects I was a model student, working hard and securing good grades. Except in French. I was lazy, I was unmotivated and I was probably a nuisance in lessons. I would have skewed the French department’s data (had “data” existed back then. In happier times, it didn’t) – despite getting “A’s” in my other  O’ Levels (no A* back then), I managed to fail French, (although I did secure a Grade 1 CSE in the subject. That dates me!)

But now I am making amends.

I have just returned from a wonderful week in Mallorca and, before I went, I determined to learn the most basic rudiments of Spanish. I downloaded the Duolingo app and began a few minutes study each day. I quickly picked up a few phrases and, whilst on holiday, tried to tune into to the local conversations and pleasantly surprised myself by being able to pick out the odd spoken word in a hundred.

Since I’ve returned, I’ve continued with my studies, in part (in main) to try and learn more Spanish, but its also been instructive to think about how and why we learn.

It is a well designed app and it makes some impressive claims (such 300 million users) that I have no reason to doubt.

It seems that, at its heart, it heavily uses the concept of spaced repetition (as discussed on my post about the Ebbinghaus curve) – having met a word or phrase in a lesson, you meet it again in the same lesson and will then probably encounter it again in your next series of lessons. If you make a mistake on a question, the question will be repeated before the end of the lesson to give you the chance to correct your error (looks a bit like Assesment for Learning to me!)

Each lesson takes circa 5 minutes to complete so your learning is done in small, discrete, bite sized chunks that you control. There are rewards – such as gems to collect, leader boards etc., which may appeal to some, but to this old cynic are peripheral to the learning.

In addition to helping me learn the language, it has got me thinking about two crucial questions – why we learn, and how, and thinking about those will also help me  develop as a maths teacher.

I now have the motivation (to learn a language) that I didn’t have as a schoolboy, and I’m enjoying some success – I think this may have been lacking before: the 14 year old me thrived on the success I achieved in maths, science etc, but having never quite “got” French I wasn’t successful in it, so didn’t bother with it – a viscous, downwards spiral.

And it has re-enforced my strength of belief in spaced learning – I can successfully learn a phrase one day, but need to see or hear it the next day, week, month etc to fix it into my mind. I spend two weeks teaching my Year 10s trigonometry in January, they “get it” at the time and can do some difficult problems, but if they don’t meet it again until the summer of Y11 in a GCSE exam they’ll be in trouble.

So the real take away from my Spanish adventure is not the vocabulary and phrases I’ve learned, but the knowledge that, to be effective, learning needs to be “spaced.”

Adios!

 

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Genius!

Genius!

In my 20+ years of teaching I’ve encountered trends, gimmicks, fads and theories, but I think I have just found the best bit of teaching advice, ever.

Thank you Jonathan Whellan, that is pure genius!

And for your convinence, here is a ten minute timer on YouTube (click on the cog icon/settings to change the playback speed)

 

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My favourite curve

So what is your favourite curve (do you even have a favourite curve? You should!)

A contender would be the Normal Distribution curve, above, which encompasses so much of the natural and statistical world.

Or perhaps the more humble straight line: y = mx + c gets your vote

To simple? Well the quadratic curve crops up a lot and has the right level of difficulty to make it non-trivial, but is within the scope of all.

And then there is the sine curve, an understanding of which opens up a huge area of mathematics, not just a curve, but a wave.

Sine Curve

But none of the above are my favourites, although they all stake a good claim.

No, my favourite curve was first plotted by a somewhat obscure 19th Century German Physcologist, Hermann Ebbinghaus, his “Forgetting Curve”

Ebbinghaus Forgetting Curve

I first came across his curve a few years ago, and it made instant sense to me. In essence, we quickly forget what we have learned, no matter how well we may have been taught. However, if we revisit the work we soon remember but once again, we soon forget, although the “speed” of our forgetting is diminished, and we don’t forget quite as much as we did before.

If we continue this process, each time we forget less and retain more.

It confirms what experience has taught me – that we need to constantly revisit and revise work, it is not enough to master a topic in a week, because in a month we’ll have forgotten most of it.

The idea is being given a modern spin (retrieval practice and spaced learning being a few new buzz words that use Ebbinghaus’ work) and, whilst I think I’ve always done this in my teaching, since discovering Ebbinghaus I’ve made a more conscious effort to resit the relentless pressure to plough on with the syllabus and revisit work covered earlier in the term and year.

For example, every few weeks we have unit tests – so we revise a few weeks work for the test (the first revisit), but then after the test I also devote a lesson or two to revisit unit tests from earlier in the year, thereby revisiting topics again and again as the year unfolds.

To find out more about the Ebbinghaus Forgetting curve, this Wikipedia page is a good starting point.

And, as an aside, I’ve often thought tha investigating the Ebbinghaus Curve could make for a good EPQ project – plenty to research, plus the opportunity to devise one’s own test to try and replicate the curve, thereby creating primary data of their own.

(Now having read this blog post, make sure you came back next week, next month, next year … to ensure you don’t forget it!!)

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Searching for the Solskjaer bounce

I’ve spent much of the last week helping students with “Hypothesis Testing” as they prepare for their A level exams in the next few months.

Fed up of wading through connived examples, and upon stumbling across perhaps the best headline I’ve read in sometime (“Man United regress to the mean after Solskjaer bounce“) I thought I’d use a bit of A level maths to see if the Solskjaer bounce was real or just another Norse myth.

(I’m about to walk through how this may be presented as an A level question, followed by my worked solution, so my less mathematically minded readers may want to skip the next few lines.)

Since taking over as manager of Manchester United in December 2018, Ole Gunnar Solskjaer (OGS) has transformed the club, returning it to winning ways.

In the season to date, in all competitions, Man Utd have won 24 out of 43 games.

Since OGS was appointed manager, Man Utd have won 15 of their 21 games.

Does the data support the theory that OGS has transformed the club at the 5% significance level?

Let p be the probability that Man Utd win a match. They have won 24 out of 43, so the probability of winning is 24/43 = 0.558

Ho:p=0.558
H1:p>0.558

The null hypothesis is that the probability is 0.558, the alternative hypothesis is that the probability of a win (under OGS) is greater

Let X be the number of wins in a sample of 21 games (the games that OGS was manager)

If Ho is correct then X~B(21,0.558)

We’re modelling the data as a Binomial distribution as there are two outcomes: win, don’t win.

Test statistic: X = 15 (the number of games OGS won)

P(X>=15) = 1 – P(X<=14)

= 1 – 0.8905 = 0.1095

We use our calculator in Binomial CD mode to find the cumulative probability of up to, and including 14, then take that away from 1 to get the probability that Man Utd would win 15 or more of their games under the null hypothesis (i.e OGS has made no difference), which works out to be 0.1095 or 10.95%)

0.1095 is not less than 0.05

Sometimes easier to think in percentages, even if we give answers as decimals. 10.95% is not less than 5% (our significance level)

So there is insufficient evidence to reject Ho, our null hypothesis

(Non-mathematicians, start reading from here)

At the 5% significance level, there is no evidence to support the theory that OGS has transformed the club.

Or, in other words, the Solskjaer bounce is probably just a myth.

We have shown that even if there had been no change of manager there was a 10.95% chance Man Utd would have won 15 out of the next 21 games.

In fact, even if we widened the significance level to 10%, the data still wouldn’t have supported a Solskjaer bounce. Winning 15 out of the 21 games since taking charge whilst unlikely was not so unlikely that it couldn’t have been due to chance rather than the genius that is OGS.

My theory: if we’d looked for the bounce a little earlier, we may have found evidence for it – perhaps the bounce peaked at around 15 games and Man Utd are, indeed, now regressing to the mean.

As ever, statistics raises as many questions as they answer, but it is good to be able to apply some A level mathematics to answer a “real” question.

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