A-levels and GCSEs: How did the exam algorithm work?

GCSE students in England, Northern Ireland and Wales are receiving results based on teacher assessments, after a last-minute change to the system.

They were originally due to receive marks worked out in a mathematical model, or algorithm, but this was abandoned following an uproar over last week's A-level results.

It follows a similar change in Scotland.

Students in the UK did not sit exams this year because schools were closed following the coronavirus lockdown.

In England, they were given grades by the official exam regulator, Ofqual.

Teachers were asked to supply for each pupil for every subject:

These were put through an algorithm, which also factored in the school's performances in each subject over the previous three years.

The idea was that the grades this year - even without exams - would be consistent with how schools had done in the past.

The teachers' rankings would decide which pupils received the top grades in their particular school.

Ofqual said this was a more accurate way of awarding grades than simply relying on teachers' assessments.

It argued that teachers were likely to be more generous in assigning an estimated mark, and this might lead to grade inflation - a much higher number of pupils getting the top grades.

Similar algorithms were applied for pupils in Wales and Northern Ireland. They were also used in Scotland for the Scottish Higher qualification, which is broadly comparable with A-levels.

When A-level grades were announced in England, Wales and Northern Ireland on 13 August, nearly 40% were lower than teachers' assessments.

There were similar issues in Scotland.

In England, 36% of entries had a lower grade than teachers recommended and 3% were down two grades.

What's more, the downgrading affected state schools much more than the private sector.

The prime minister defended the system as "robust", but there was widespread criticism from schools and colleges, as well as from the opposition and some Conservative MPs.

Ofqual said that its objective for A-level results was to ensure that national results were "broadly similar to previous years".

However, by basing it so much around previous school performance, a bright student from an underperforming school was likely to have their results downgraded through no fault of their own.

Likewise, a school which was in the process of rapid improvement would not have seen this progress reflected in results.

In Scotland, figures showed that the Scottish Higher pass rate for pupils from the most deprived backgrounds was reduced by 15.2 percentage points, compared with only 6.9 percentage points for the wealthiest pupils.

Private schools are usually selective - and better-funded - and in most years will perform well in terms of exam results. An algorithm based on past performance will put students from these schools at an advantage compared with their state-educated equivalents.

There was a further factor at work according to statisticians Philip Nye and Dave Thompson of FFT Education Datalab. They said class sizes in independent schools are usually significantly smaller than in state schools.

Where there were fewer than five pupils studying a subject at a school, their grades were decided only on the basis of teachers' estimates.

Where there were between five and 15 entrants for a subject, teachers' assessments would still be given more weight.

On 17 August, the government announced that A-level results would be changed to reflect the original teachers' estimates - the so-called centre assessed grade or CAG - rather than the result produced by the algorithm.

The only exception would be if a student had received a higher grade from the algorithm than the CAG.

Education Secretary Gavin Williamson acknowledged "significant inconsistencies" in the grading process and apologised for the "distress" caused.

He also announced that GCSE results would be decided according to teacher assessments.

This year has seen a considerable amount of grade inflation as a result of the last week's events.

Universities now have to deal with a rush for places by students who had previously been downgraded.

Alistair Jarvis, the head of the university body Universities UK, says there are "challenges" ahead, such as capacity, staffing and facilities.

Many universities will be able to accept extra students, particularly now the government has withdrawn its cap on the numbers each institution can admit.

Health Secretary Matt Hancock has said that the government is "absolutely looking at" also lifting the cap on the number of places to study medicine.

But there could be logistical problems for some oversubscribed universities or courses.

Durham University, for example, is offering financial incentives to students who defer entry until 2021.