Think spreadsheets are tricky? Bamboozled by equations? Sam Ellis has an old-fashioned technique for calculating pupil-teacher ratios which just might help.

Nomograms: they're not what you think...

Spreadsheets and equations about school finance are not everyone’s idea of fun. I suspect many members would probably regard root canal treatment as a preferable option to listening to me and ASCL Deputy General Secretary Malcolm Trobe go on about finance as we tend to at various events.

But finance, or the diminishing amount of it, is clearly a hot topic and it is difficult to avoid the ubiquitous spreadsheet in managing the school in its widest financial sense.

In the feedback Malcolm and I have received over the past year on strategic financial management courses and at regional conferences there was one comment to the effect of: “Oh no! Not another spreadsheet!” This set me thinking back to the times when we managed without them.

I did my first school budget in April 1990. The LA, or LEA as it was, required a handwritten return and even supplied a set of bound paper grids so you could do it the hard way with a pencil and the calculator between the ears. I set up a spreadsheet on a BBC microcomputer called Supercalc 5. Having a dog and barking myself has never been one of my strong points.

But what about the idea of not using a spreadsheet at all? After a little thought I realised there was a way of not only losing the spreadsheet but also bypassing the maths, at least as far as the end user was concerned.

Arcane mathematics

Before the electronic calculator the most common day-to-day calculation aids were probably log tables and slide rules. As someone brought up using a slide rule I remembered a bit of arcane Victorian mathematics used mostly in engineering circles to enable workers who had no mathematical understanding to do complex calculations rapidly and repeatedly. It was called a nomogram.

I decided to design a nomogram for school finances. I ended up designing two which were shown to members at a national conference seminar, then made available on the ASCL website. There is also an article with them to support any insomniac members who feel the need to design their own customised version.

The nomograms are a series of parallel scales. By using a straight edge and pivoting around a point on one of the scales as a reference anyone can investigate the pupil-teacher ratio (PTR) a school can afford for different combinations of revenue funding per pupil, average teacher cost and proportion of revenue budget available for spending on teachers.

Once a value of PTR has been decided the other nomogram allows the corresponding pairs of values for teacher contact ratio and average class size in the curriculum to be investigated. There is a subsidiary scale which connects the PTR to the number of full-time equivalent (FTE) teachers employed for a given roll.

Limited accuracy

There are several disadvantages to a nomogram. Its accuracy is limited to how well you can read the scales; some scales run down rather than up, which can easily lead to pilot error on the part of the user; and, above all, the scales are fixed, so if your values fall outside the range of the nomogram it is not much use.

On the positive side, a nomogram for every group member does make discussion about the key strategic financial issues very simple and accessible to all. It is actually very easy to chase “What if?” trails on a nomogram as all one needs to do is slide a ruler around on a sheet of paper to cover any possibility within the scale range.

I worked out my prototype using pencil, paper and a set of log tables. I then tried using Excel to plot the nomogram but ran into difficulty when the software decided to scale things for me. My solution was to rely on Pippa at ASCL headquarters who plotted my scale calculations and produced the pdf file that can be downloaded by members at www.ascl.org.uk/fundingresources

In essence for a given level of funding it tells you how many teaching staff you can afford to employ and for a given teacher contact ratio, what sort of curriculum you can offer.

If you download a copy from the ASCL website remember to print it with page scaling option set to none and the printer set to print A4 with no borders. If the nomogram is distorted by scaling it will give false answers.

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