THERE are lies, damn lies and there are statistics. Never has that been so true. Misleading graphs, randomly quoted figures without context and probabilities misinterpreted or misunderstood have hit the headlines since the Covid crisis started.
Firstly, I need to own up to my special interest – I am a mathematics tutor going up to degree level. I was schooled in the 70s, gaining four top grade A-levels (three in maths – yes, I know I’m a geek!) Times change but, surely, maths doesn’t? Ah, but it does!
Unfortunately I’m now going to throw a few stats at you. In 1988 (the year GCSEs were introduced) the proportion of pupils getting grade A (the top grade) was 8 per cent. In 2019 for the equivalent of A or above it was 21 per cent (we’ll ignore the even bigger surge in this year’s results for obvious reasons). At A-level in the mid-80s, just under 10 per cent achieved an A (the top grade) whereas those getting A or A* now account for 28 per cent. At the end of the 70s nearly 15 per cent of pupils went to university while now (thanks to Mr Blair) the figure is about 50 per cent. In the early 90s (it is very difficult to get earlier data) 7 per cent of students gained a first-class degree. Nowadays 28 per cent obtain a first, and nearly 80 per cent at least an upper second.
I must stress that I’m not denigrating the performance and ability of the youth of today. Students can only take in what they are taught and sit the exams they are set, but unfortunately the standards have dropped, and the trend continues as each successive generation enters schools as teachers.
The main problem has been lack of lesson time. When I was doing my O-levels many years ago we had maths for three and a half to four hours a week. Everyone did seven O-levels with the top set also being entered for English literature and additional maths. At A-level we had 5 hours (at least) per A-level. However when my son was taking GCSEs ten years ago, schools were cramming in as many subjects as they could to boost their standing in the league tables, and he ended up with 14 passes. As the manipulation of league tables (with lesser schools shooting up the rankings by offering subjects such as hairdressing) came to light the government stopped counting the softer subjects, but the damage was done. At A-level it was similar. For years most students sat three A-levels, but in the 1990s sixth forms encouraged students to take four or possibly five even though universities wanted only three.
Now I’m going to scare you, especially if you have children at primary school. Did you realise that your child’s teacher may have scored only 16 per cent in his/her maths GCSE? Yes, I’m afraid so. Every time the GCSE changes over the years, the exam boards vastly overestimate the standard of the pupils as regards maths. This happened when A* was introduced and the boundary for grade C had to be lowered to 16 per cent, and it happened again at the start of the new GCSE with gradings 1-9 a few years ago. The mark for grade 4 at the Higher tier varied between 15 and 20 per cent amongst the exam boards. The qualification required to be a primary school teacher is level 4 in maths and English language. Now, I can’t speak for the English qualification, but I’m afraid there is no way I’d want a teacher who achieved level 4 in maths anywhere near a year 5 or 6 class! I knew of one secondary school where there was one teacher in the whole of the maths department with a mathematics degree and I know of students who have gone on to do maths degrees having achieved only a grade D at A-level.
Lastly I want to consider the effect of calculators. With the pace at which technology has moved you’d expect pupils to be experts at using calculators. No, generally they are appalling. This is despite the fact they are now allowed to use them in most of their GCSE (for one exam board it is allowable for all of it) and all of the A-level. This brings me back to the use of statistics. Since the 1990s there will have been students who have achieved an A* grade at A-level maths (including a module in statistics) who will never have met the normal distribution – a vitally important area of mathematics. The recent change in syllabus now means all students doing the traditional A-level will come across it but unfortunately the exam boards made a big mistake by allowing the use of advanced statistical functions on calculators. What I am now seeing is students (and I’m talking high level students) mindlessly pressing buttons (occasionally getting answers correct) without having the slightest understanding of how these distributions work. These same students will do extremely simple numerical calculations (I could shock you with examples) and basic algebra on these calculators when it should be faster for even an average student to do it without.
Returning to the issue of the mass of data and statistics thrown at us regarding the ‘pandemic’: are the government and their advisers clever? Are they being selective in choosing the data to release and how to manipulate the data to serve their own aims, playing on the mathematical ineptitude of the majority of the population? Or are they mathematically ignorant themselves (along with an appalling understanding of economics)? Perhaps it’s a combination of both. Matt Hancock did A-level maths in the late 1990s. Did he do that statistics module? If he did, perhaps he should resit it.