## The maths of exam marks

At the moment, the Department for Education is considering changes to the league tables and the exam system. This seems an opportune moment to make a simple point about qualification-awarding and accountability: English school examinations are subject to measurement error in a really big way.

Here is a simple thought experiment to flesh it out. Imagine a class of 100 students. Let us specify that each one has a “true” ability that means that one pupil should get one point, one pupil should get two, one should get three and so on – up to 100 marks. Now, let’s award this class one of 10 grades: 90+ gets you an A, 80+ a B and so on.

Let us assume that the tests are perfect. If that were the case, you would get ten individuals in each grade. Easy enough. But what happens if we start introducing errors into the test? We can do that with a set of exotically named (but very simple) “Monte Carlo” estimates, which I calculated using this simple spreadsheetRead more

## Getting around the official statistics

Last week, I went to Wolverhampton where I spoke at a local debate, organised by the university and Pat McFadden, the local MP, about the local authority’s school. I was the warm-up act for Lord Adonis, former schools minister, setting the scene about the city’s education system before his talk on lessons on school improvement.

It was interesting event – and the city is clearly considering its future and the role of education within it. There is – judging by my inbox – serious and deep interest in improving schools in the city. One of the things I sought to do was set out Wolvo’s position in relation to the rest of the country – and what statistics about the city tell us.

Here is my presentation: Read more

## Competition in schools

Fraser Nelson, editor of the Spectator, has written up a paper on Swedish school reforms, which you can download here. I thought it was worth using to quickly flag up two important statistical public policy points.

The context to this is that Sweden has, since the early 1990s, allowed private (including for-profit) institutions to enter the school system – and parallels are often drawn between it and the ongoing reforms of England’s school system. This paper, as Fraser rightly says, comes to the view that increasing the volume of private schools in an area is associated with improved results. Mikael Lindahl and Anders Böhlmark say:

If we transform our estimates to standard deviation (S.D.) units (using the variation across all individuals) we find that a 10 percentage point increase in the share of independent-school students has resulted in 0.07 S.D. higher average educational achievement at the end of compulsory school.

## A grammar school confusion

Last week, the excellent Paul Francis, political editor of the Kent Messenger, reported that Kent, the most significant selective county left in England had come up with a clever plan: to make the entry test for grammar schools “tutor-proof”.

This idea comes up a lot, largely from people promoting selection. You can see why: it is often presented as a means of squaring a problem. They can argue that grammar schools help bright poor children while dealing with the fact that very few get into them.

But, in truth, a properly administered test, which accurately captures the education enjoyed by people at the age of 11, should exclude large numbers of poor children. Not because they are intrinsically less able. But, at 11, the poor-rich divide is already a chasm. Read more

## Benchmarking school systems

One question I get asked a lot is: “You say that Frewmanackshire is a terrible local authority. How do you know? Do you know what we are working with?” etc etc. It is true that schools with radically different intakes cannot be usefully compared. So I thought I would let you in on how I benchmark schools, and supply you with two jolly new maps.

What I do for secondary schools, is run a simple regression – that is to say, I fit a simple line through all the pupils’ school results in the country after asking it to account for the children’s ethnicity, poverty and prior test results. Unlike other models, the regression contains precisely zero information about the schools – only data about the children. Read more

## English GCSE and Ofqual

On Thursday afternoon, journalists were taken into the basement of a Westminster building, fed chicken satay and walked through Ofqual’s report on the recent English GCSE. During the summer, a late shift in grade boundaries shocked schools, leaving many high-flying schools with significantly worse results than they had been expecting.

The most striking outcome of the Ofqual research is that it seems to find evidence of cheating. It is incidental to the main purpose of the review, which was to ask whether the shift in the grade boundaries was correct. But it’s a stunning – and quite clear – finding.

Here is the issue: English GCSE can be taken in such a way that the pupil has done everything except for teacher-marked “controlled assessments” in the final months. If they do that, the teachers know what marks each pupil needs. And teachers give those marks.

In the graph below, Ofqual have worked out how many marks candidates needed from their teachers to get a C. If they got a mark to the right of the red vertical line, the teacher gave them a high enough grade to get the C. The shape of that distribution is, frankly, a sign of something horribly wrong. Teachers are massaging marks.

## Shibboleths and social mobility

John Goldthorpe, a pioneer and leader in sociology, is always worth reading. This week, he has written a piece that delivers a kicking to assumptions in Whitehall, Westminster and Fleet Street. But it also poses a significant challenge to organisations like TeachFirst.

The piece centres on the misreadings of the academic literature of social mobility. But, from there, it moves on to the limitations of an education policy on its own. His work suggests school reform is not going to improve mobility. This should be taken seriously.

He has been pointing this out for some time. But, this time, he’s done two things that ought to make this easier for journalists to follow. First, he uses smaller words than usual. Second, he talks about the media, and we are obsessed by that.

He posits why the media have not followed the argument. I rather like the idea of “media hysteresis”:

the tendency within the media, once a particular ‘line’ on any issue has become widely accepted, for this line to be maintained as the standard output, regardless of any further inputs.

Read it here. Or at least cast your eyes over the conclusion, which I have pasted below. Agree or not, they are fantastically interesting and his voice carries a level of authority usually only accorded to those of burning bushes. Read more

## A missing link in the exam system

The argument about GCSE English grades continues to boil away. Legal actions are commencing. The attention has uncovered clues that exam reforms over the past few years have, by accident, been more substantial than ministers or officials had intended. The marking system used for the old O-level might have been reintroduced by stealth – and accident.

Here’s why: English exams used to deploy a process called “norm referencing” (or “marking on a curve”). That means that, in effect, you hand out grades depending on their position. In 1963, it was decided that roughly the top 10 per cent of A-level entrants would get an A, the next 15 per cent a B and so on.

Since the 1980s, exams have used “criterion referencing”. That is to say, they say “if you know the date of the Battle of Hastings, that is worth an C. If you know about William the Conqueror’s claim on the throne, you get a B. If you know about Hardrada, get an A…” Under this model, you can have changing numbers of pupils getting each grade.

This graph, from Alan Smithers at Buckingham, shows what happened when England switched from one to the other in the late 1980s.

## The politics of Richard III

After rooting around in a Leicester car park, a group of academics have found a scoliosis-racked body with battle wounds. They think it might be Richard III: DNA tests await. If it is him, what do you do with him? On the one hand, he was a king. A long time ago, yes. But a king’s a king, right? And he has something of a following.

On the other hand, he is rather implicated in child-murder – and he was killed by his successor. If we think the suspected murder victims were legitimate kings and his successor, Henry VII, was as well, how do we treat Richard III? These are not straightforward problems. Perhaps we should ask the family. Read more

## Free schools and bad schools

So, we now know where free schools are going, I thought that I would quickly illustrate a curiosity about them. This map of local authorities is coloured by the performance of FSM-eligible children (a marker of poverty). Red is poor performance and blue good. Free schools are green.

I have chosen this measure because it’s a simple like-for-like metric. Differences are not scores simply accounted for by the fact that some areas have more poor children: I am looking only at deprived pupils’ attainment. This is a quick and dirty way to gauge LAs. Red areas, broadly speaking, are underperforming. Read more

## On hitting a moving target

The Ofqual decision that is all is well on the English GCSE has not been received well by schools. I thought, further to my last post, that it would help understand school leaders’ feelings about this if we took a case study of an excellent school.

I have asked Sally Coates, head of Burlington Danes Church of England Academy – one of the Ark Schools – to explain what she went through last week.  Before you read her account, I thought I would explain why this particular school matters.

Like other Ark Schools, BDA uses “progression” to gauge its success. It benchmarks itself on improving and stretching each child, regardless of the level of their education when they enter. It does not simply attempt to hit the government’s targets.

As a result, BDA expends effort on people who already know enough to get Cs in English, maths and three other subjects – the basket of achievement used by the government to measure school success. This school does not – unlike others – fixate on the C/D line.

This is easy to spot: Ark’s performance rises dramatically when you use a measure that gives schools credit for getting children to higher grades than C. BDA stacked up 24 children last year who managed straight As in English, maths and three other subjects.

Let me be clear,  the school does keep an eye on that grade boundary. Here, indeed, is a photo of the Venn diagram Ms Coates describes below, enhanced with some light photoshopping to make sure it is entirely anonymous.

Children are in a circle showing where they are weak. Each child in each circle gets appropriate tutoring to help drive them up to the line.

But this intervention is only one of a chain of monitoring lines. Children in the “safehouse” are being monitored against higher grades elsewhere. I will return to this, but BDA’s results show a great deal more As and Bs than is normal.

That is why Ms Coates’s anger is so important: despite being focused on progression, not the narrow “C will do” measures used by the government, the school was caught out by the shift in the C/D boundary. Now, over to Ms Coates: Read more

Over the weekend, Ofqual announced it will examine the English modules that have caused so much concern lately, where many children who expected Cs were given Ds. This will focus on chunks of the new AQA English GCSE and, one assumes, take in the equivalent OCR and Edexcel* qualifications.

This is a very brief blogpost to briefly explain why this matters so much to schools (beyond the fact that they want their pupils to do well). First, we start off with a very simple chart using 2011 data: for each school, I have worked out the share of children passing English, maths and three other GCSEs with a C grade or above.

This measure (the “PACEM” metric) matters: it is the figure that is used to rank schools, and to decide whether they get shut down or not. A school where below 40 per cent of students are below the line is at risk of a forced change of management.

So I have ranked schools on this measure, bundled them into percentiles, and lined them up with the lowest league table position populations are at the left and the best are at the right.

For each percentile of schools, I have published two numbers:

• The red section shows the share of pupils who passed on the PACEM measure, but only got a C in English. That is to say, pupils for whom a one-grade drop in results means falling below the PACEM waterline.
• The blue section indicates children who passed with a higher grade in English. The two areas are stacked one on top of the other, so the line marking out the top of the blue section indicates the total pass rate.

## The UK universities Olympic medal table

When Usain Bolt, not a naturally modest man, thanks you for your help after clinching his umpteenth gold medal, you have probably done something right. Brunel and Birmingham universities won his praise for their help in preparing and hosting the Jamaican team.

Other universities can claim to have done rather well. I quite liked this exchange on Twitter between William Hague, foreign secretary, and Patrick McGhee, vice-chancellor of the University of East London (which is hosting the US Olympic team).

But on to the medals! Here, courtesy of Podium, the body representing universities and colleges at the London Olympics, is the roster showing which institutions have done best at the sports. If you look on their site, you can see the full list.

For institutions, this table does actually matter: as I wrote last week, universities are an increasingly important spine of Team GB’s infrastructure.

UPDATE – 22:30, 14 August: The Podium list is correct, but it only includes conventional universities and colleges. However, the Open University won two golds and three bronzes. I’ve not included it in the table – some OU athletes are already booked as the undergraduate alumni of other universities, and this could get messy. But, bear in mind, if the OU were entered in it and credited with all of them, it would be in sixth place.

Institution Gold Silver Bronze Total
University of Edinburgh 3 0 0 3
University of Nottingham 2 2 1 5
University of Oxford 2 2 1 5
University of Cambridge 2 1 2 5
University of Reading 2 1 1 4
St Mary’s University College 2 0 1 3
University of St Andrews 2 0 0 2
University of Bristol 1 2 2 5
University of Bath 1 2 0 3
Peter Symonds College 1 1 1 3
Hopwood Hall College 1 1 0 2
Northumbria University 1 1 0 2
Staffordshire University 1 1 0 2
University of the West of England 1 1 0 2
University of Leeds 1 0 2 3
King’s College London 1 0 1 2
Barton Peveril Sixth Form College 1 0 0 1
Bournemouth University 1 0 0 1
Bradford College 1 0 0 1
Cardiff Metropolitan University 1 0 0
Durham University 1 0 0 1
Kingston University 1 0 0 1
Leeds Metropolitan University 1 0 0 1
University of Sheffield 1 0 0 1
University College London 0 3 0 3

What to make of this table? Here are also some important things to note – and I hope they’ll help illuminate some of the nonsense about sport and education in England that has been swirling around lately: Read more

## Neighbourhoods and schools

One of my grand theories is that public policy types are generally bad at geography. Or, at the least, they underestimate the importance of where you live. Here, below the fold, are two zoomable maps, coloured by the school performance of local state-educated children. The map is based on where the children live, not where they go to school. To explain:

• The colouring is red for weaker results and blue for better ones. Darker colours mean more extreme results. If you want detail on an area, click on any one of the blobs and it should give you a run down of local statistics, where possible.
• Both maps are coloured according to FT score results: that is the sum of state-educated pupils’ scores in English, maths and their top three other subjects.    Other data, including official measures, are in the boxes that pop up.
• On the first map, the geographical blobs are smaller than on previous maps: the lowest super output area in high density places, and the middle-layer output area in zones of low density (this way, we can show maximum detail).
• That map can be quite frazzling. The second might be more to some people’s tastes. This is exactly the same sort data, just arranged by parliamentary constituency. Since they are bigger lumps, we can include more detailed data.
• For the constituencies, I have given a barrage of results for all local children in state schools. But also the same just for FSM-eligible children, and for children dubbed “middle attainers” – kids who score in the middle tenth of results aged 11.
• (NB – Where statistics are missing, it is prevent people combining data sources to work out something about individual children.)

If you want a tour, I’d recommend scrolling along the coasts. Check out some of the coastal towns, and look at the belt of towns and cities between Hull and Liverpool. Also, take a peek at how few dark red areas there are in London. In-borough variation is interesting, too: look at the massive variation within, say, Kent. Read more

## Race to the top

Something I touched on in today’s coverage of the London school system is ethnicity: in short, everyone does better than white children, with poor white children particularly far behind. Here are 2010-11′s GCSE results, split by ethnicity, using the FT measure:

Some of the lines cut out suddenly: that is because there were fewer than 100 kids in those vingtiles, and the lines go absolutely nuts on such low sample sizes. For reference, when I say “white”, I mean pupils who have self-identified as “White British”.

That obviously has a regional effect: London has a lot of ethnic minority kids. But there is a chicken-and-egg question. Is the capital so good because it has these children, or do they do so well because they are in London? Well, the answer is “both”. Read more

## London’s big lead and social mobility

A big story we have published records the stunning improvement in London’s schools that has taken place over the past decade (also: analysis on the topic).

As part of the number-crunching I did for to that story, I can also provide an update from our measure on social mobility in schools – how much does poverty damage your school results? It’s not good news, alas.

Last year, we reported that our educational mobility index had been rising for five consecutive years – from 2006-10. Unfortunately, this year, things deteriorated a little. That blip upwards in 2010-11 means poverty exerted a bigger influence on the school results of children in 2010-11 than it had in 2009-10.

As a reminder, for those of you who have not committed these things to memory: we measure this through quite a simple metric. First, we draw our old friend, the Graph of Doom, which shows how exam results interact with poverty:

To come up with this graph, we divide the country into hundredths, by their neighbourhood deprivation. Then we plot each grouping’s average score on the line, according to a simple performance measure (which I’ve tweaked since we last did this). Read more

## MPs stress need for better open data

The coalition’s drive to open access to official data was welcome, but  more needed to be done to make information comprehensible, according to a report by the House of Commons’ public accounts committee, which monitors the effectiveness of public spending.

Official willingness to publish data was not enough, the committee said, since the information provided could be rather impenetrable. Some of the data are published as very large files that cannot be opened using a conventional home computer. Other files are difficult to interpret or can be only understood with the aid of large glossaries.

“It is simply not good enough to dump large quantities of raw data into the public domain, “ said Margaret Hodge, who chairs the committee. “[Data] must be accessible, relevant and easy for us all to understand. Otherwise the public cannot use them.”

## English university fees: the complete list

The new higher education fee structure, beginning in 2012, will allow universities in England to levy fees up to £9,000 a year.

This table shows each institution’s minimum,  maximum, and average fees, according to figures released on Thursday by the Office for Fair Access, along with the expected number of undergraduates it will have in 2012-2013. Read more

## Sir Michael Wilshaw, uncut

Last week, the FT published an interview with Sir Michael Wilshaw. Lots of interviewees, especially in public policy, are very guarded. Sir Michael is not. This may give his press handlers nightmares, but everyone should welcome it. This is for educationally minded people more than data nerds, but I thought I’d put up some more of his thoughts.

I’ll not publish the whole thing yet (there are a few things we discussed that I intend to return to). So this is still a highlights package. First, a few shorter snippets. It’s very striking how often London Challenge, a policy to improve schools in the capital, came up. Sir Michael, who rose to prominence as a London head teacher, kept praising that policy. For example, speaking about the north, he said:

What is it about those areas like Hull and Grimsby and North Lincolnshire that prevents those youngsters doing well? Some of it is quite honestly a political failure where we’ve known that these areas were failing for a number of years and if local politicians really want to address this, they can put pressure on both schools, local authorities, the department for education to do something about this. We’ve shown through London Challenge what can be done in London. London is certainly… and I’ve been a London teacher all my life. It wasn’t a good place to be in the 70s and 80s and 90s; now it’s one of the top performing parts of the country through London Challenge. Same happened in Manchester. So, why can’t we do that in these areas?

## Nylon slip-cleaning 101

Last week, courtesy of the brilliant Institute of Education librarians, I had a quick leaf through some old CSE papers – until 1988, many children not entered for the O-level were entered for this exam.

A few things of profound educational significance jump out from these exam papers. One day, I’ll probably write about that. Mostly, however, I just gawped at some of the odd things in them.  Exam papers are pretty revealing about the societies underpinning them. Read more