It seems there¡¯s slack maths all round. The government¡¯s poor sums over higher education tuition have left public accounts potentially many hundreds of millions of pounds adrift (¡°PAC minds the gap: MPs sound warning over fees reform¡±, 7 June, timeshighereducation.co.uk). The ?9,000 exception became the rule, and now the fear grows not just of funding gaps, but also of failing institutions and faltering demand. ?9,000 x 0 is, after all, not a lot of money.

After a surprisingly warm response to my previous column, which looked at errant averages in the recent tuition fees debate (¡°Average measurements¡±, 5 May), I am emboldened to push further on in the GCSE maths syllabus to the hot topic of the use and abuse of percentages.

One stock-in-trade of press and politician alike is the false application of percentages. I¡¯ll give a real example that we¡¯ve been dealing with at London Met recently.

After a long debate, we decided to reduce the number of courses offered at the university from 577 to 160. (Now, you might be asking why a university would ever have 577 distinct courses on its books, but that¡¯s a matter for another day.) My point is about how a simple statement about courses can be turned into a statement about people or about money.

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So, we effected this (577 - 160) divided by 577 x 100 = 72. per cent reduction in the number of courses. If you edit a newspaper, you might give it a sensational headline like ¡°Courses slashed by 70 per cent¡±. Fair enough. If you were being truly fair you could even point out that 80 per cent of students were actually studying on just 80 of these courses.

But can you now personalise it? One local MP obviously did the maths¡­72. per cent of (roughly) 13,500 is 9,756 student places¡­leading to a parliamentary statement and a headline, ¡°Over 10,000 places will go in university¡±. Not fair enough. That would be fair to conclude only if, for instance, the new portfolio of 160 revised courses had the same average per course enrolment as the entire original set of 577.

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You could go further, and now apply the percentage to money. Several clearly tried - mostly disastrously through confusing applicants with enrolled students - but you would come up with the sum of 9,756 x perhaps ?6,850 (London Met¡¯s average fee from 2012-13)¡­?66,828,600. And any newspaper could happily have written, ¡°Untold millions lost in course closures¡±!

A similar issue arises each year as the league tables roll out, and institutions scramble to show their best face.

The very same department, course or institution can have such different results between one league table and the next because of the different percentage weightings hidden away in the fine print. A department might be ranked in the middle of a table because of strong weightings on student-to-staff ratios or spending per student, but at the bottom of a table that emphasises student satisfaction, entry standards or research outputs.

While we have a ubiquity of percentages flying around, some percentages that we really do need at this time of change are absent or downplayed. Here are two questions that students should be asking:

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? What percentage of a ?9,000 tuition fee do I actually ¡°get¡±? I mean, after the compulsory spending on access activities, the bursary, the fee waiver and the accommodation voucher choices, and the family means-testing? Not to forget any last-minute discounting off the ticket price in the first place. As each university goes its merry way, the student is mightily confused.

? What percentage return do I receive after graduation for my investment in a degree? Lord Browne of Madingley frequently depicted graduate compared with non-graduate gains over a lifetime at ?100,000, if not ?150,000, on average. So your average lifetime return on fees investment might be 300 per cent or so. But what about not ¡°on average¡±? What about for you, as an arts student, male, 18, paying a fee of ?8,000 a year, and expecting to receive a 2:1? The need for clear information here is pressing, given the current campaign to promote the post-2012 system. We need more subject-specific, gender-specific and even institution-specific information.

¡°Differences by degree¡± (2010), a paper by Ian Walker of Lancaster University Management School and Yu Zhu of the University of Kent, concludes that ¡°a rise in tuition fees lowers returns by about 1-3 per cent¡±, and so little affects the quality of the investment. High quality - that is, large lifetime returns - is found for all degrees studied by women, but not for men. ¡°For men, we find very large returns for economics, management and law but not for other subjects - we even find small negative returns in arts, humanities and other social sciences.¡± Our students need the information to understand this.

With all the brouhaha about undergraduate tuition fees for domestic students, many have forgotten about the relativities with domestic postgraduate tuition fees. Tim Leunig has calculated a rough and ready ¡°typical¡± MSc/MA fee across English universities as ?4,266 (¡°Universities Challenged¡±, CentreForum, 2011). (I note that it does not include the more professional postgraduate fees, which are generally higher.) At the time of writing, that¡¯s just 49.21 per cent of THE¡¯s calculation of the average undergraduate fee across the sector - ?8,668. Do we really expect our hard-pressed undergraduates, and our international students, to subsidise their postgraduate colleagues? To this extent?

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