How to get on the housing ladder:

For example, the homebuyer raises the cash to buy 50% of the property and then pays rent on the remaining 50%. The benefits of shared ownership schemes are:

• For many this is the only way to achieve home-ownership
• You can buy a share as low as 25% or as high as 75% at the outset

…

Help for the elderly in mortgage trap:

Under the deal customers were able to borrow around a quarter of the value of their property.

But when they sell they must also pay back 75% of the increase in value, leaving many unable to buy a new home.

…

Well, if you only buy 25% of your house, you will only get 25% of the value when you sell it. Sounds quite fair to me.

So, in conclusion, the BBC thinks banks are evil for offering shared ownership schemes, and at the same time thinks they are a good idea. So that's clear then.

Ever a person of habit, I decided to look at the numbers for maths A-level, as I have done in the previous 2 years.

There is a rise in numbers for 2006:

The government press release highlights this as the big success of the year, and declares that the trend has been reversed. Indeed this is true, as far as it goes: maths has risen as a percentage of A-levels back to the level of 2 years ago.

Of course, there is a lot of ground to cover before the damage of the previous trend is fully unwound:

The rise in the number of A grades has taken this to an almost absurd 43.5% of candidates. The number of A grades is up 20% in 5 years, against the decline in numbers taking the exam. One has to wonder if making the exam easier is doing more to encourage people to take the exam than any of the other measures taken.

Maths now has the highest percentage of A grades of any subject except for… further maths, and Irish (going by the available figures). Out of the major subjects (which I'm calling those with more than 10,000 entrants), the next highest A-rate is French at 36.2%. How long will they let maths continue to give such relatively high grades, I wonder.

(All figures for 2001 onwards taken from the JCQ press releases.)

(Previous discussion.)

From the BBC:

One in four maths teachers in England is not a specialist in the subject... Shortages of well-qualified maths and science teachers were worst in schools with low GCSE scores and those serving the poorest children

A total of 60% of the heads of maths departments said they had experienced either "a great deal" or "quite a lot" of difficulty in terms of staff shortages.

The difference between sensationalism and raising a serious issue is this: sensationalism is where you state your story using the worst case interpretation of the statistics, without explaining this to the reader — or just plain misinterpretation. Serious discussion of a real issue is where you quote statistics that show there is a problem even under conservative assumptions.

So it is disappointing to see the usually excellent Motley Fool veering into sensationalism with its articles on consumer credit. So what if consumer credit has quadrupled in 12 years? — that tells us nothing without allowing for inflation and economic growth.

Their starting figure for 1993, 53 billion pounds, is about 8.3% of 1993's GDP. Their estimated figure for 2005 is 193 billion pounds, about 16.2% of estimated current GDP. So it would be entirely sensible to say that consumer debt had doubled; and that is enough to say it's a growing problem. Saying that it has quadrupled, OTOH, is misleading, and is exactly the sort of thing that gives statistics a bad name.

Nothing more in the press, as far as I can see, about the maths A-Level story. In fact searching for that story on google gives my blog entry fairly high in the results. Anyway, I had a look to see what the figures are like for 2005.

There is a slight rise in numbers for 2005:

But nothing significant to the long-term trend:

Maths continues to drift down as a percentage of all A-levels:

But a sharp rise in the number of A grades takes these to almost 40% of candidates:

(All figures for 2001 onwards taken from the JCQ press releases.)

The government's view:

The results show more young people both taking and succeeding in the traditional subjects. …

The 2005 AS and A level results show: … increasing numbers of students taking Mathematics, English and the Science…

So that's alright then - maths is up compared to last year. It's down, of course, relative to 2 years ago; and relative to 3 years ago; and 4 years ago, … in fact it's up by 0.2% compared to 1 year ago, but 40% down relative to 16 years ago. Hurray for New Labour's education progress!

(Previous discussion.)

There has been much coverage in the press about the state of A level maths. The report makes good reading, because there are few people better qualified than a group of maths professors for trashing government statistics. For some reason they didn't provide any graphs, so let's do some now.

That is their core figures — a 40% decline in 15 years. I couldn't find real figures online for before 2001; the Joint Council for Qualifications give figures for 2001 onward, which confirm a sharp decline in 2002. Here are the results for 2001-2004 for all UK, from the online results.

Table 3.1 of the government's own report on maths teaching also shows the same collapse in maths entries in 2002. It appears clear that the Curriculum 2000 reforms, which saw maths A levels, like other subjects, divided into an ASub part (roughly like an old AS level) and an A2 (which takes the subject up to A level standard), caused this collapse. The report notes that (section 3.23):

During 2000/01, serious difficulties with AS Mathematics were reported to the regulatory authorities. The overriding concern of teachers was that AS Mathematics appeared to be too difficult and was turning many students away from the subject. … The pass rate among the 17 year-old cohort was 71.8 per cent, very low compared to other mainstream subjects like English, history, …

Interestingly, pass rates improved, showing that at least in part students have been detered by the course being harder, not the exam. So the decline is due to students being scared off, not any essential difficulty, by my reading.

The government unhelpfully note that "In 2004 maths had the the highest entry rate of any GCSE and the third highest entry rate at A-level." — but the GCSE rate is to be expected since maths is taken by basically everyone, and maths as the 3rd most popular A level represents a sharp decline from being the most popular not many years ago (so the report says).

But with girls taking over at all levels of education, english and biology overtaking maths is no surprise, and is not a relevant benchmark. Importantly, it does not seem that the decline of maths is a gender thing: physics is more male dominated than maths, but has seen only stagnation and no serious decline; the proportion of A Level students, both male and female, taking maths is declining (from JCQ results figures).

Update: the graphs in this select committee report confirm the longer term decline — maths, now at 7%, was over 10% in 1992.

So it seems that, far from the problems being a temporory government recruiting mess, there is a real long-term decline in the number of maths students, and it is this that is causing the serious problems in teaching the subject. This article from the BBC, from 2000, looks disturbingly prescient now:

It claims that the biggest problem is a vicious circle of poor teaching leading to fewer people taking maths A-levels, thus creating an inadequate supply of mathematicians to become teachers.

The governments' own figures show that over 50% of all maths graduates each year need to be recruited each year to fill the allocated teacher training slots (2.65).

The most interesting feature, other than the decline in entrants, is the (resulting?) sharp rise in pass rate. To disentangle these, let's see the absolute numbers getting high grades (derived from the JCQ results figures):

So 2002 was a big blow, but there is a recovery after that. This may explain why this has not yet had much impact (except in 2002) on the number of maths undergraduates. But surely this recovery is in part the reaction to the perceived greater difficulty of the new exams — in other words the exams were made easier to maintain the pass rate? And, as the government report notes that the grade distribution for maths is out of line with other subjects; how long will the education authorities tolerate a large subject like maths giving nearly 40% A grades, while other subjects are averaging around 20%, and when the evidence is that maths is not achieving this through genuinely high standards, but is in fact in decline?