It just don’t add up

My old chemistry teacher, Geoffrey ‘Solomon’ Beaumont, used to say that everything worth knowing was difficult to understand, though he was quick to point out that the converse was not necessarily true.

So, you at the back, please pay attention!

After the statistics used to support the Memorandum of Understanding (MoU) between PCC and Pembrokeshire College on future ‘A’ level provision in the county come under attack (here, here and on that other website) Cabinet member for education David Lloyd emailed all councillors with a lengthy defence of the council’s calculations.

Cllr Lloyd begins:

“During the period following the Council decision to adopt the MOU, I am aware that there has been a lot of speculation in the press and social media that has queried the information that was provided to Council.

I thought it would be helpful to set out the background to some of the queries and challenges that have been raised and hence this briefing for you all.”

Being a charitable soul, I will pass over his use of the word “speculation” to describe my careful analysis of the information used to underpin this MoU, though, contrary to what Cllr Lloyd says, the following rather important table was not part of the “information that was provided to council.”

As can be seen, Fishguard and St Davids – neither of which will provide ‘A’ level classes in future – make a disproportionately large contribution to the final figure of 76%, which, as we shall see, is added to teaching costs to get an overall figure.

Indeed, if these two schools are excluded, the non-teaching costs come out at 66%.

My question was why these two schools had been included in a calculation regarding future ‘A’ level provision when sixth-formers from both schools were doing their ‘A’ levels at Pembrokeshire College.

Cllr Lloyd’s rather wordy explanation is as follows:

“All Pembrokeshire Schools were included in the calculation because all schools currently have sixth form provision. The calculation will change and the grant funding will decrease when full A Level provision from Dewi Sant and Bro Gwaun transfers to Pembrokeshire College. So whilst they have been included currently, the quantum of grant will reduce from this year. The calculation is to show how the current funding has been allocated so it is not erroneous to include YDS and YBG. The reduction in funding will reduce the overall amount available, and whilst the formula can be redesigned, the total amount of grant funding will continue to reduce as the number of Post 16 learners declines so however the grant is allocated, all schools will face reductions in their allocation.”

To call this twaddle would be an understatement because the calculation has nothing whatsoever with showing how “current funding has been allocated”.

Its purpose was to arrive at a figure for overheads that could be added onto the teaching costs in order to calculate the full cost of providing a teacher for an ‘A’ level course.

Indeed, later in his lengthy email, Cllr Lloyd explains the purpose thus:

“The figure of 76% for management costs is the aggregated figure of the individual schools at the current time. It is expressed clearly on the table as percentage of teacher costs. Everything that sits behind the calculation has been agreed and worked through with schools and their business managers. The overheads are calculated with a clear formula and a set of guidance to all schools. The figures were provided by schools not derived by the local authority.”

So, as I said previously, 76% is the figure to be added onto the salary costs to obtain the aggregate figure for the annual cost of providing an ‘A’ level course.

It was interesting to hear the chairman of the Schools and Learning scrutiny committee, Cllr John Davies, tell the most recent meeting of the committee that teachers’ salaries made up 85% of school budgets.

That leaves 15% for other costs, so it is something of a mystery why ‘A’ level classes should come out at five times that figure.

With regard to ‘A’ level teachers’ salaries Cllr Lloyd tells us:

“Questions related to teachers’ salary are clearly defined as being costed at upper pay spine (ups) 3 and those teachers who have teaching and learning responsibilities (TLR) where they manage aspects of the schools’ work. Each school provided individual costs and a consolidated costing model was derived from individual school responses. The responses relate to the full range of costs required to deliver subjects at A level.”

So you take a high-end teacher (£38,500 per annum) assume they have TLR responsibilities (£7,500) and add on pension and National Insurance costs (another twelve grand).

This gives a total of £58,000 to which is added the fanciful 76% overheads (£44,000) to give a grand total of £102,000 which is then divided by five to reflect the amount of time this hypothetical teacher will spend teaching an ‘A’ level course which is then in turn used as the basis for calculating how many students are required to make such a course viable.

One of the benefits of numbers is that they can be used to check whether your calculations are internally consistent.

For instance, 20% of the £58,000 teaching costs – which we must assume are uniform across all schools – is £11,600.

The teaching cost for Greenhill (Tenby) in the table above is £685,835 which divided by £11,600 gives 59 ‘A’ level teachers.

Split equally between upper and lower sixth forms (or whatever they’re called these days) gives 29.5 teachers per year group.

However there is a table on page 39 of the report to the extraordinary meeting where this MoU was agreed which shows that in 2016 Tenby only entered students in 19 subjects at ‘A’ level.

That comes to 38 teachers over the two years so there are some 20 phantom teachers lurking somewhere in these calculations.

Cllr Lloyd is also keen on telling us about sharing best practice between schools.

If he studies the table above he will notice that if all schools could match Tenby’s 49% for overheads it would represent a saving of some £750,000.

I have written to Cllr John Davies suggesting that the schools and learning scrutiny committee, of which he is chairman, might profitably examine these calculations on which the council’s decision to sign the MoU was based.

While I’m in mathematical mode I would point to another table presented to members at the extraordinary meeting:

This represents the calculation of the figure for the size of the sixth form at the new English medium school in Haverfordwest based on the number of year 11 (fifth formers) in the two existing schools who currently stay on to sit ‘A’ levels.

As can be seen, the “Combined” figure of 36% is derived by averaging the figures for STP (40%) and TM (32%).

I’m afraid that whoever devised this table is due a maths resit because averaging percentages from unequally-sized samples is methodologically flawed.