IMHO the problems in the UK go back to the choices of course material when the switch to all comprehensive schools was made. Those who supported switching to all comprehensive won the argument by saying that the more academic students would have a positive effect on the less academic and not vice-versa. Well I would have agreed with that *except* before the switch to comprehensive in general the Grammar school syllabus (in nearly all subjects) was more advanced than the Secondary Modern syllabus and what did they do ? They switched all over to the lesser syllabus thus completely negating any advantage created by the switch to comprehensive. IMHO the answer is proper streaming in *all* subjects and at least 2 different syllabuses in each subject depending on the ability/aptitude of the student in that subject, in fact preferably more than 2. When I was at Grammar School (30+ years ago) we were streamed into 5 sets (each of around 32 pupils) for maths and even then sets 1 to 4 did the "O" level syllabus (with calculus) but set 5 did the lesser CSE (no calculus). In a Comprehensive situation for the lower sets math study should in fact concentrate on everyday maths e.g. the maths required to maintain good family finances etc. and nothing much more than this - I say this as it should be remembered that in the Grammar school system as I described even set 5 at the Grammar school were apparently part of the top 45% of the population academically speaking. On 12 Mar 2011, at 11:43, Adam P. Goucher wrote:
Another issue with the mathematics curriculum in the United Kingdom is the lack of Euclidean geometry. Throughout the entire GCSE and A-level syllabus (equivalent to 'high school'), there is nothing beyond Pythagoras' theorem, basic trigonometry, and Thales' theorem. The triangle centres are never even suggested to students (except the centroid as the 'centre of mass' during Mechanics modules), and there is no mention of Ceva's theorem.
Discrete maths are taught in the A-level syllabus, but only in the most laborious way possible. The majority of the course involves weighted graphs and optimisation, followed by a bombardment of algorithms capable of dissuading all but the most tenacious of students.
Rather than devising algorithms (i.e. programming), the emphasis is on mechanically following algorithms without any insight as to why the algorithms work. The course (entitled 'decision maths') reduces people to mindless automata.
Believe it or not, the Decision Maths course even involves *solving the Travelling Salesman Problem* -- how torturous is that?! It could be replaced with something much more enjoyable, such as Fourier transforms.
In my opinion, concepts such as binary and Turing machines should be taught in school, mainly as preparation for informatics/computer science.
What are your views on this?
Sincerely,
Adam P. Goucher
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