The best subject to take . . . probably
Monday afternoon, A-level further maths at Dame Alice Owen's School, Potters Bar, Hertfordshire. Dr Tony Asher is exploring a problem: "Four items are taken from a box of 12 and inspected. The box is rejected if more than one item is found to be faulty. If there are three faulty items, find the probability that the box is accepted."
The subsequent work takes the eight class members a double period of intense thought and calculation, led at times by Dr Asher from the front, using chalk and talk, at times breaking into consultation in pairs or working in the kind of solitary absorption in which non-mathematicians like to picture number-crunching boffins. But these are articulate, likeable teenagers who enjoy their subject.
What make maths so attractive? Charlotte Nolan, the only girl in the group, likes "it being new, new concepts. You can have new ways of looking at things." Ryan Jervis far prefers the subject to the arts, because "it's more logical and precise, there's no doubt either way, it's definite".
These highly able students do not seem put off maths by its perceived difficulty. Nor do they feel they suffered from a "GCSE gap" - between algebra-free GCSE tiers and A-levels. But they agreed that had they not done the old level 10 in key stage 4, or the extension paper for GCSE A* (which they all achieved), they might have been at a loss in the demanding A-level syllabus which is, as Ryan says, "all algebra, really". As to proof and the rigour of the subject, all seven boys pick on this "hard" aspect of the subject as the one they like. Charlotte is less sure: "There is scope for discussion, I think."
Maths teaching at Dame Alice Owen's is an invigorating mix of whole-class concept-explaining - "We do not approve of individualised learning schemes, " said Dr Asher - small group work and individual consolidation. It's also fun: there is a popular Year 7 maths club which does puzzles, curve stitching and solid-shape Christmas decorations; a school chess club, run last year by an upper sixth maths student, and regular entrants to the Hertfordshire Maths Master Class. The school was among the first to enter the UK Maths Challenges with large and successful numbers in each year and regularly goes on to enter the more difficult UK Maths Olympiad.
The school was a voluntary-aided comprehensive, but is now grant-maintained with 50 per cent of entries through selective examination. But its profile is well above the average, with 86.6 per cent gaining A*-C at GCSE in five subjects or more. Maths results last year included 17 A*s at GCSE and 11 As at A-level single subject, 12 at A-level double subject. Success breeds success; this year there are 40 taking maths (single subject) in Year 12.
The teaching style is fairly formal. Teachers are all well qualified and all new staff are offered an intellectually challenging A-level group to teach as well as lower-ability classes. Classes are streamed into bands and sets after Year 7, then mixed and set again in Year 10 for GCSE and the tier system.
Dr Asher, along with the authors of the London Mathematical Society report, is sceptical about the GCSE tier system and operates a policy of never letting pupils take A-level maths if they have only worked to the intermediate tier. He is even more sceptical about the key stage 3 tests, and the school sets its own key stage 3 papers.
There are "irritating little details" about the national curriculum for teachers at Dame Alice Owen's. Why must students memorise the formulae for area and circumference of a circle, but not those for rectangles and triangles? Why are the criteria for GCSE coursework so "rigid" and tied to the nuances between levels of achievement? And Dr Asher feels there is often injustice in the final marks.
Most of all, he, like many others, "is sick of change". Maths, after all, does not really change.
Sue Carr, taking a maths class with a low ability group in Year 9, agreed. They, too, are working through probability with dice and spinners and coins, with the odd shout of glee coming out at unusual results. They know the rule of a one in two chance, but the experiment will demonstrate how this general principle operates only over a large sample and space of time. Then the class moves to abstracting and generalising.
Jo shows the visitor out, and confesses to not having liked maths in Year 7, but says: "Now it's more fun - sometimes."