Re: Is logic taught to UK school children?

In article <44bfd9a1$0$22105$ed2619ec@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Damian R <theseus01@xxxxxxxxxxx> wrote:
I'm probably laying myself open to a severe verbal beating here.

Only if Ian gets himself into "grumpy old men" mode,
which is usually only when dealing with fools.

I can't speak for others, but I do my best to get students to see the
interconnectedness through the A level course. [... much snippage ...]

OK, but that makes you very unusual. It's a very patchy
thing. Good schools have the sort of ethos you describe, and
often have the maths dept well-equipped to teach Maths and FMaths
with "plenty" of decent graduates. Then there are the schools
where one or two good maths teachers are firefighting to cover
for the incompetents and the vacancies. Then there are the
schools where one or two incompetents are all there is, which
means that A-level maths "teaching" means "read page 73 of this
book, do exercises 1, 3 and 5, and try again until you get the
answer given in the back".

We were told some years back that there are fewer maths
graduates in teaching than there are secondary schools, and I
don't suppose the situation has improved. When the private
schools, grammar schools and SFCs hoover up four or more of
the maths graduates, guess what the rest of education is like.

They had to find the area of a triangle. So they all think of ^=absinc,
rather than actually looking at the diagram and realising just how easy the
question is. It's almost an attitude of having done much more complicated
stuff since then, and we surely can't need to perform any simple
calculations.

Right, tho' of course it needs a teacher able to tell them
how easy it is! I see it a lot eg in max/min, where it's almost
impossible to stop students from differentiatng first and thinking
second in situations where something is obviously a square and
so cannot go negative, or where the result is trivial from the
AM/GM inequality. Or in vectors, where the first resort is to
put things into x,y,z components and piggle with algebra/trig
instead of thinking about magnitudes and directions first.

Agreed entirely, though of course the corollary is that
univ courses have to start from somewhere around AS level.
Though of course there is a nationally agreed core for A level maths, laid
down by QCA, and contained within the 4 Core units in each A level maths
course. [...]

That *is* "around AS level"! Esp as one A-level unit/module
is around 3-4 days of univ work. But the situation is a lot better
than a decade or two back, when [IIRC] the guaranteed overlap between
boards and syllabuses was something around 7% of the pure maths [and
0% of applied/stats].

And the A level papers do try to make students think more, [...].

I agree, and I'm not one of the doom/gloom merchants saying
that A-level maths is stupidly easy. But there is still too much
"signposting", too much rote, and not enough encouragement [at
least, going by the "official" solutions and comments] of original
thought. "Improving, but could do better." [OTOH, if they *did*
do better, it would make the situation of students stuck in sink
schools/areas even worse.]

--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.
anw@xxxxxxxxxxxxxxxx
.

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