Re: Is logic taught to UK school children?

On Thu, 20 Jul 2006 14:56:55 UTC, anw@xxxxxxxxxxxxxxxx (Dr A. N.
Walker) wrote:

: In article <cCUlhtvFIYkV-pn2-xG1BRoxSLf8w@localhost>,
: Ian Johnston <ian.groups@xxxxxxxxxxxxxx> wrote:
: >: So what standards should we be applying to the thousands of
: >: sixth-formers who are doing maths "for fun"?
: >What exactly do you mean by "standards" here? Are you saying that
: >someone doing maths-for-fun should be able to get a grade A with lower
: >grades than someone going on to do maths at university?
:
: No. It was a question! Manifestly, we should be trying
: to ensure that "grade A" [and, lest we forget through our elitism,
: grades BCDEFUNCLETOMCOBLEYANDALL as well] means, as far as we are
: able, the same standard for every A-level subject, so that UCAS
: tariff points [or any other "use" of grades] are equally earned.

Absolutely. Is there any way of doing that apart from norm
referencing, perhaps taking into account hours studied as well?

: >I'm all in favour of widening the subject - in fact, of widening all
: >subjects. Chemistry-for-historians should be as different from
: >chemistry-for-medics as maths-for-classicists should be different from
: >maths-for-engineers.
:
: That's actually a different proposition. In some ways, it
: would be Nice to have three different maths A-levels: real maths,
: maths for physicists and engineers, and maths for people who just
: want to do some more in the sixth form.

Well, the fist two already exist: further maths and just-maths. So all
that's needed is a "Maths in Society" course for the last lot.

: Equally good" was meant to be the 16yo's own perception,
: or that of the teachers. IOW, people should not be opting out of
: maths and into history because they have been told that it's much
: easier to get a good grade in history.

Isn't maths still the single biggest A-level, by a long way? I am
pretty sure it was the last time I looked ...

: >I think we are. No good engineering course in the UK will take less
: >than A in Maths these days, many of them can't cope. A in Maths and B
: >in Further Maths is a minimum for anyone wanting to make a go of an
: >MEng.
:
: Umm. Well, you seem to have a very elitist view of what a
: "good engineering course in the UK" is, then.

MEng.

: None of the eng'g courses here ask for A in maths; some
: don't even ask for B. And whatever the "ask", in practice I see
: a *lot* of eng'g students with C or worse

Oh. My. God.

: (a) Most eng'g depts, in general, are finding it harder to
: recruit good students, as other subjects become flavour of the month.
: The good students are still out there, and getting AAA, but fewer
: are doing eng'g.

Yes. And sensible too, since most university engineering courses are
so hopelessly stuck in the past that no sane student would take them.
Not that that's entirely the universities' fault - unltil recently the
IMechE insisted on a minimum nunber of technical drawings done on
paper, and would not accept anything done with CAD ... depsite the
fact that the "drawing board" has been a dust covered curio in the
corner of the design office for a couple of decades now.

: (b) Some eng'g depts are finding it harder to recruit good
: students, as other depts produce better web sites, open days, or
: rankings.

Doesn't that apply to all subjects? I know some engineering
departments which do jolly good open days.

: (c) Even if you can still recruit enough AAA students, if
: you are affected by (a,b), then your proportion of borderline AAA
: to clear AAA students will increase, and your students will be less
: good.

That is, I think, the core effect I see.

: (d) And, of course, not that this applies to anyone here,
: oh no, but if your department is one of those that has inflicted
: the same test on incoming students for the past half-century and
: has not noticed the changes to A-level syllabus and style, does not
: believe in IT, calculators, formula sheets, and is amazed to find
: that some students are coming in with history or French at A-level,
: then it's not at all surprising that you *have* noticed that your
: students aren't as good as they used to be. Discuss ....

Definitely a problem in some institutions, though luckily not the ones
I mainly deal with. In my personal defence, I've been telling students
to get and use Maple for twenty years now.

: >I reckon they are every bit as bright as they ever were, as a cohort
: >but that a) they are being badly taught for easy exams
:
: *Some* teaching is indeed awful, esp in maths. Not at all
: surprising when so many maths teachers lack even basic competence

A friend of mine was employed as a supply teacher in a school in
Wolverhampton. She was given charge of the A-level maths class for a
couple of months. Her degree is in three-dimensional design and she
has failed maths GCSE several times (which is why she is not a
teacher). Oh, for more litigious pupils and parents ...

: I'm unconvinced that maths exams, in general, are "easy".

I think the problem is the modules - breaking down stuff into tiny
chunks which can be retaken.

Basically, there are two roles for an A level (or a higher, or a
degree)

1) To establish that someone knows a certain amount of stuff to a
certain level. This is the minor purpose.

2) To establish that someone is capable of learning a certain amount
of stuff in a certain amount of time. This is the major purpose.

With the commndable diversity of syllabi these days it's pointless to
expect everyone to come to university knowing a fixed package of stuff
called "A-level maths". However, it is reasonable to expect that
students who have taken an A-level in two years have the ability to
learn at a certain rate - and I don't think A-level gives that
information any more.

: There's
: no point setting an exam only for good students! Getting the B's
: right is more important than ensuring that only A*** students can
: get near to 100%.

Maybe it's time to end the daftly huge range of As and make A - E 10%
bands. Or just give marks?

: >I've been trying to persuade the very bight daughter of a colleague
: >that she ought to apply for Maths and Philosophy, because she finds
: >the wackier bits of A-level intriguing - she came to me the other week
: >to ask how on earth one could take e to an imaginary power in first
: >place, let alone get a real as a result, and she was truly fascinated
: >by the idea.
:
: Yep. Of course, she's lucky to have you to turn to; one
: wonders how many equally bright children went to their teachers
: with similar questions and were told "don't know, go away and stop
: trying to be clever, we need to do quadratics".

Why do you think she asked me?

: It's appalling
: when that happens to sixth-formers. It's a crime against education
: when similar things happen, as they do, at primary school, when a
: child who wants to know about infinity, or negative numbers, or a
: whole host of "difficult" questions, is fobbed off or told off by
: an innumerate teacher, and thereby turned against maths for life.

Couldn't agree more. The brightest mathematician I ever met was a ten
year old boy who knew that the square root of -1 was i. "So what's the
square root of i?" we asked him. "You can't do it" he replied ...
looked puzzled, pause of ten seconds ... "Erm, I don't know what you'd
call it, but it would be here (sketches two axes and points to exp (i
pi/4)) on the complex plane."

His local primary school, in Oxford, had refused to take him because
they said they couldn't possibly cope with his needs, and the next one
along said "Well we can take him, but you do realise that he'll be
terribly bullied if he comes here, don't you?". No private school
would touch him, so he ended up being home educated.

: I would like to think that that's the fault of the school or
: the particular teacher(s) at least as much as of A-level. In the
: last three weeks, we've had our Open Days and a Sutton Trust session,
: and it was a joy to see so many 17yos bubbling over with enthusiasm
: for maths. Not for A-level, which is just a hurdle they know they've
: got to clear, but for seeing and investigating maths problems, and
: applying logic and imagination to them.

I have great fun running Motivate videoconferences each year, for a
rather younger ae group, and the enthusiam and imagination you
describe is very clear there too.

Ian
.