Maths

[Samsonknight]

I have decided to do M1 and M2 as my applied units. So I am wondering if
that will give me an advantage over the student that does Statistics and M1
as part of their whole A-level. Reason being, from doing both S1/M1.
Mechanics seems to be harder then statistics. Also, I can imagine that the
content in the Mechanics could come in handy when dealing with programs that
require some knowledge of physics. Games programming for
example...Statistics seems to be handy for those who want to go into a
business related field. Banking, Economics etc.

Do Admission tutors look at the applied units students take as part of their
maths A-levels? Or is the overall grade what counts.

Thanks

[Stuart Williams]

Post by Samsonknight
I have decided to do M1 and M2 as my applied units. So I am wondering if
that will give me an advantage over the student that does Statistics and M1
as part of their whole A-level. Reason being, from doing both S1/M1.
Mechanics seems to be harder then statistics.

Wouldn't you be at a /dis/advantage, then? S1 is certainly easier than
M2: although there's quite a lot of content, it's all pretty low-level
stuff (Stem-and-leaf diagrams, for example). M2 is not as hard as M3, but
it's harder than M1.

Post by Samsonknight
Also, I can imagine that the
content in the Mechanics could come in handy when dealing with programs that
require some knowledge of physics. Games programming for
example...Statistics seems to be handy for those who want to go into a
business related field. Banking, Economics etc.
Do Admission tutors look at the applied units students take as part of their
maths A-levels? Or is the overall grade what counts.

Not being an AT, I can't be authoritative, but I would think very much
not: they've got quite enough data to process without going into the
details of which options you took. I imagine that all they get from UCAS
are the final A or AS level grades.

SW

[Matthew Huntbach]

Post by Stuart Williams

Post by Samsonknight
Do Admission tutors look at the applied units students take as part of
their maths A-levels? Or is the overall grade what counts.

Not being an AT, I can't be authoritative, but I would think very much
not: they've got quite enough data to process without going into the
details of which options you took. I imagine that all they get from UCAS
are the final A or AS level grades.

Yes, I'd just be grateful that someone *has* a Maths A-level without
bothering with the precise units. It's not the specific knowledge
from the Maths A-level that's required, rather it's the demonstration
of being able to deal with abstraction and formal systems which passing
A-level Maths shows. I used to think that the statistics modules of
Maths A-level would be the least useful, but recently I've had the
people who teach the 3rd year units saying they value it,
particularly the probability element, for things like information
retrieval and risk assessment.

Matthew Huntbach

[Samsonknight]

Post by Stuart Williams

Post by Samsonknight
I have decided to do M1 and M2 as my applied units. So I am wondering if
that will give me an advantage over the student that does Statistics and M1
as part of their whole A-level. Reason being, from doing both S1/M1.
Mechanics seems to be harder then statistics.

Wouldn't you be at a /dis/advantage, then? S1 is certainly easier than
M2: although there's quite a lot of content, it's all pretty low-level
stuff (Stem-and-leaf diagrams, for example). M2 is not as hard as M3, but
it's harder than M1.

Sure, my tutor and I did take that into consideration before I made my
final choice. However, the problem with statistics, is that it uses
very little of the material from the core course.
Therefore as I am doing the course at such a fast rate, I don't want
to be in a position where I am having to back track. With Statistics
this is more likely to happen then with Mechanics. As Mechanics
constantly reinforces the skills that you learn in the core course.

[Dr A. N. Walker]

In article <d0sp04$1mn$***@nwrdmz01.dmz.ncs.ea.ibs-infra.bt.com>,
Samsonknight <***@btinternet.com> wrote:
[...]

Post by Samsonknight
Do Admission tutors look at the applied units students take as part of their
maths A-levels? [...]

Can't speak for everyone, but *this* AT does not. Indeed,
the units are not "visible" on the results that we get from UCAS,
so it's only easy to tell if we can cross-relate with info on your
form. Our maths courses *have* to start from somewhere around AS
level anyway [intersection of all "standard" maths syllabuses]; we
then "sweep" through A-level Maths to a point well beyond Further
Maths in rather less than half of the first year. In that process,
we don't really care what maths you already know [within reason], as
we will be teaching you all that stuff anyway [properly, not in the
dumbed-down A-level way]. We care much more about how good you are
at maths.

[K. Edgcombe]

Post by Dr A. N. Walker
[...]

Post by Samsonknight
Do Admission tutors look at the applied units students take as part of their
maths A-levels? [...]

Can't speak for everyone, but *this* AT does not. Indeed,

Cambridge Colleges do generally ask people what modules they are taking, but in my
experience that's more for interest and so that we know what we can reasonably
ask about at an admissions interview. I think one or two of my colleagues
would be slightly anxious about a student who was not taking any mechanics
modules at all and was also not taking physics, because such a student might
find the first-year applied courses quite tough; but as Andy says it's
*much* more important how good they are at whatever maths they are doing.

Katy

[Stuart Williams]

In article <d148p9$e5q$***@oyez.ccc.nottingham.ac.uk>, ***@maths.nott.ac.uk
says...

as we will be teaching you all that stuff anyway [properly, not in the
dumbed-down A-level way].

It's nice to know one's efforts are appreciated....

Stuart Williams

[Dr A. N. Walker]

Post by Stuart Williams

as we will be teaching you all that stuff anyway [properly, not in the
dumbed-down A-level way].

It's nice to know one's efforts are appreciated....

You mean, you *haven't* been teaching your pupils that all
matrices are 2x2 [or, in *really* difficult cases, 3x3], that
vectors are 2-dimensional, that induction is "assuming what you want
to prove, and then using k=k+1", that all functions are given by
formula and are differentiable, etc., etc.? Good for you! But you
are in a small minority ....

My SO is planning a book about anarchic maths -- all the
places where (a) A-level/univ maths deviates from what maths is
really about, &/or (b) books gloss over the difficulties, &/or (c)
they gloss over the simplicities, &/or (d) opportunities for some
interesting maths are lost 'cos of dumbing down. I don't know
whether it will ever come to fruition; but if it does, it will be
required reading, in an ideal world, for all mathematicians.

[Stuart Williams]

In article <d14l4p$mdf$***@oyez.ccc.nottingham.ac.uk>, ***@maths.nott.ac.uk
says...

Post by Dr A. N. Walker

Post by Stuart Williams

as we will be teaching you all that stuff anyway [properly, not in the
dumbed-down A-level way].

It's nice to know one's efforts are appreciated....

You mean, you *haven't* been teaching your pupils that all
matrices are 2x2 [or, in *really* difficult cases, 3x3], that
vectors are 2-dimensional, that induction is "assuming what you want
to prove, and then using k=k+1", that all functions are given by
formula and are differentiable, etc., etc.? Good for you! But you
are in a small minority ....

Irony apart, yes, I do point out that e.g. mod x isn't differentiable at
x=0, and when induction was still part of A level (it's been dumped into
FM), I took pleasure in trying to convey its power (though I must admit
it was an approach they found hard to assimilate). Other areas where I
try to resist the general rush to substitute "how do the examiners want
me to do it" for "how do we justify doing it like this" include dividing
by zero, approaching a limit, and the idea of different kinds of
infinity. You'd be surprised (or perhaps you wouldn't) that the brighter
pupils get really wound up about these ideas: maybe I am part of a
minority - but is it so small?

Post by Dr A. N. Walker
My SO is planning a book about anarchic maths -- all the
places where (a) A-level/univ maths deviates from what maths is
really about, &/or (b) books gloss over the difficulties, &/or (c)
they gloss over the simplicities, &/or (d) opportunities for some
interesting maths are lost 'cos of dumbing down. I don't know
whether it will ever come to fruition; but if it does, it will be
required reading, in an ideal world, for all mathematicians

I believe you can flag up publishing opportunities to Amazon by
registering e.g. that you'd buy the complete Hill Street Blues if only
someone would offer it. Maybe if she...... (who am I kidding?).

SW

[Dr A. N. Walker]

Post by Stuart Williams
Irony apart, yes, I do point out that e.g. mod x isn't differentiable at
x=0, [...]

Do you also point out that, eg, f(x) = x^2 if x is rational,
= 0 otherwise, is differentiable *only* at x = 0? [:-)]

Post by Stuart Williams
You'd be surprised (or perhaps you wouldn't) that the brighter

Not at all surprised. There is, for example, enough maths
in the "structure" of the real line, within the capacity of a bright
A-level student, to keep them occupied for weeks. But *none* of it
penetrates into normal school maths -- we're effectively back with
Newton -- the real numbers "flow equably" along the x-axis, with the
rationals embedded like dense little plums in the middle.

Post by Stuart Williams
maybe I am part of a
minority - but is it so small?

Well, yes. With fewer qualified maths teachers than schools,
most maths teaching, and especially the really critical teaching in
primary and middle years, is being done by people who know diddly-
squat about mathematics, and all too often *hate* it. The private
sector and 6FCs are mostly better endowed, but the damage has been
done lower down. And the truly horrible GCSE/AS/A2 revision guides
just make matters worse, no matter how "useful" they are to weakish
students who just want the grade; they are anti-education for the
bright/interested students.

Worth bearing in mind too that the dragooned maths teachers
are not even the weaker physicists or engineers, who at least know
the importance of maths, even if they are not themselves very good
at it; for they can get good jobs in engineering.

[Samsonknight]

Post by Dr A. N. Walker

Post by Stuart Williams
maybe I am part of a
minority - but is it so small?

Well, yes. With fewer qualified maths teachers than schools,
most maths teaching, and especially the really critical teaching in
primary and middle years, is being done by people who know diddly-
squat about mathematics, and all too often *hate* it. The private

I don't see the logic of going into something that you *hate*. The pay in
the public sector is not exactly good. My tutor has said exactly what you
have said too, "teachers who teach mathematics at schools are often
underqualified", but what I don't understand is don't half of them have to
have a degree in mathematics as a requirement - in order to teach it in the
first place?

Post by Dr A. N. Walker
sector and 6FCs are mostly better endowed, but the damage has been
done lower down. And the truly horrible GCSE/AS/A2 revision guides
just make matters worse, no matter how "useful" they are to weakish
students who just want the grade; they are anti-education for the
bright/interested students.

I agree, it isn't fair. From my experience, many of the teachers I have had
just taught mathematics like how teachers would teach subjects such as
english. By encouraging students to learn a set list of formulae, rules and
then not really linking one topic to another, or making sure that all
students have a proper understanding of the theory. This made life so
difficult for us, because we were encouraged to treat mathematics in a
"robotic way" where when the questions got harder and did require an
understanding - we just couldnt do them. Our foundations wasn't there, and
life just got harder as things were added on.

[Dr A. N. Walker]

Post by Samsonknight
I don't see the logic of going into something that you *hate*.

It is perfectly possible to love teaching and hate some of
the things you have to teach. In primary education, it is normal
for teachers to be Jacks/Jills of all trades; they are assumed
to be able to teach English and geography and history and ... and
maths to the level needed for [eg] 10yos. Whether this works OK
for history is beyond my knowledge. For maths it certainly doesn't,
so that children are taught maths not as it really as but as some
reasonably-intelligent-but-otherwise-random person vaguely recalls
it from their attempts at O-level/GCSE.

Post by Samsonknight
[...], but what I don't understand is don't half of them have to
have a degree in mathematics as a requirement [...]

How to empty schools in one easy lesson .... Look, in the
70s, around 30% of our [maths] graduates went into teaching, often
lured by accelerated promotion. Then the computing boom and the
financial boom came along, and mathematicians started to earn Big
Money everywhere except teaching. Unsurprisingly, the numbers going
into teaching dropped, to around 2%. Following the Smith report,
they are somewhat back up, 6% according to our most recent confirmed
figures, perhaps even 10% now [I have written more references for
admission to teaching courses this year than for the previous decade];
but of course this is just as the '70s boom is retiring, so we are
still not keeping pace. Private schools and 6FCs offer the best
environment, so they can usually recruit. Other schools get the
dregs or nothing. You have 4C expecting to be taught maths. Your
job advert gets *no* response. Your choice -- you can teach them
no maths at all, or you can press-gang a botanist or a historian
into the job. Either way, you get the consequences [snipped] that
you describe.

[John Porcella]

Post by Dr A. N. Walker

Post by Samsonknight
[...], but what I don't understand is don't half of them have to
have a degree in mathematics as a requirement [...]

How to empty schools in one easy lesson .... Look, in the
70s, around 30% of our [maths] graduates went into teaching, often
lured by accelerated promotion. Then the computing boom and the
financial boom came along, and mathematicians started to earn Big
Money everywhere except teaching. Unsurprisingly, the numbers going
into teaching dropped, to around 2%.

Really? That is a surprise to me.

[John Porcella]

Post by Samsonknight

Post by Dr A. N. Walker

Post by Stuart Williams
maybe I am part of a
minority - but is it so small?

Well, yes. With fewer qualified maths teachers than schools,
most maths teaching, and especially the really critical teaching in
primary and middle years, is being done by people who know diddly-
squat about mathematics, and all too often *hate* it. The private

I don't see the logic of going into something that you *hate*. The pay in
the public sector is not exactly good. My tutor has said exactly what you
have said too, "teachers who teach mathematics at schools are often
underqualified", but what I don't understand is don't half of them have to
have a degree in mathematics as a requirement - in order to teach it in the
first place?

No, in the State sector you need a degree (in anything) and a teaching
qualification (e.g. PGCE). Once qualifed to teach, you can teach anything.

Post by Samsonknight

Post by Dr A. N. Walker
sector and 6FCs are mostly better endowed, but the damage has been
done lower down. And the truly horrible GCSE/AS/A2 revision guides
just make matters worse, no matter how "useful" they are to weakish
students who just want the grade; they are anti-education for the
bright/interested students.

I agree, it isn't fair. From my experience, many of the teachers I have had
just taught mathematics like how teachers would teach subjects such as
english. By encouraging students to learn a set list of formulae, rules and
then not really linking one topic to another, or making sure that all
students have a proper understanding of the theory. This made life so
difficult for us, because we were encouraged to treat mathematics in a
"robotic way" where when the questions got harder and did require an
understanding - we just couldnt do them. Our foundations wasn't there, and
life just got harder as things were added on.

If they only had five hours of contact time each week, then they have no
choice but to blast their way through the syllabus.

[Samsonknight]

Post by John Porcella

Post by Samsonknight

Post by Dr A. N. Walker

Post by Stuart Williams
maybe I am part of a
minority - but is it so small?

Well, yes. With fewer qualified maths teachers than schools,
most maths teaching, and especially the really critical teaching in
primary and middle years, is being done by people who know diddly-
squat about mathematics, and all too often *hate* it. The private

I don't see the logic of going into something that you *hate*. The pay in
the public sector is not exactly good. My tutor has said exactly what you
have said too, "teachers who teach mathematics at schools are often
underqualified", but what I don't understand is don't half of them have to
have a degree in mathematics as a requirement - in order to teach it in

the

Post by Samsonknight
first place?

No, in the State sector you need a degree (in anything) and a teaching
qualification (e.g. PGCE). Once qualifed to teach, you can teach anything.

Post by Samsonknight

Post by Dr A. N. Walker
sector and 6FCs are mostly better endowed, but the damage has been
done lower down. And the truly horrible GCSE/AS/A2 revision guides
just make matters worse, no matter how "useful" they are to weakish
students who just want the grade; they are anti-education for the
bright/interested students.

I agree, it isn't fair. From my experience, many of the teachers I have

had

Post by Samsonknight
just taught mathematics like how teachers would teach subjects such as
english. By encouraging students to learn a set list of formulae, rules

and

Post by Samsonknight
then not really linking one topic to another, or making sure that all
students have a proper understanding of the theory. This made life so
difficult for us, because we were encouraged to treat mathematics in a
"robotic way" where when the questions got harder and did require an
understanding - we just couldnt do them. Our foundations wasn't there, and
life just got harder as things were added on.

If they only had five hours of contact time each week, then they have no
choice but to blast their way through the syllabus.

The above still doesn't justify their poor teaching in my view. In respect
to the way math's was taught in my old school.

WE had a few good teachers but the standard procedure for many teachers at
my old school was: Spend 20 minutes learning the concepts behind the topic;
then learn the formulae in that topic and do some exercises, then move onto
another topic where the teacher makes absolutely no effort to link that
topic to x other topic. It also does not help when math's teachers patronize
you, because you asked an elementary question that they *assumed* that you
should know.

It's bad for your confidence in the subject. Which in turn can cause
problems, as the student ends up lacking creativity and flair in the subject
because he/she is too scared to try different approaches to a problem in
case they get the wrong answer - or he/she doesn't know what on earth they
are doing, due to shakey unresolved problems in their foundations..



Math's and I am sure you will agree is all about understanding, which is why
I think teachers should be much more understanding. However, it is ironic
that Mathematics in my old school (and I am sure in many other schools) was
the reverse of that, we had less understanding/patient teachers then in lets
say English, History or Science....

Post by John Porcella
--
MESSAGE ENDS.
John Porcella

[John Porcella]

Post by Samsonknight

Post by John Porcella
If they only had five hours of contact time each week, then they have no
choice but to blast their way through the syllabus.

The above still doesn't justify their poor teaching in my view.

I cannot agree with poor teaching, it serves nobody, that is for certain.

In respect

Post by Samsonknight
to the way math's was taught in my old school.
WE had a few good teachers but the standard procedure for many teachers at
my old school was: Spend 20 minutes learning the concepts behind the topic;
then learn the formulae in that topic and do some exercises, then move onto
another topic where the teacher makes absolutely no effort to link that
topic to x other topic. It also does not help when math's teachers patronize
you, because you asked an elementary question that they *assumed* that you
should know.

My own mathematics tutor was forever telling me that something that I asked
was "assumed knowledge" and my standard response was to tell him that
assumptions are dangerous and then he would teach me what I was thought to
know already.

Post by Samsonknight
It's bad for your confidence in the subject.

For many, I agree.

Which in turn can cause

Post by Samsonknight
problems, as the student ends up lacking creativity and flair in the subject
because he/she is too scared to try different approaches to a problem in
case they get the wrong answer - or he/she doesn't know what on earth they
are doing, due to shakey unresolved problems in their foundations..

Difficult to disagree.

Post by Samsonknight
Math's and I am sure you will agree is all about understanding,

For the level that we are doing it, it is about method and accuracy, which
display some understanding.

which is why

Post by Samsonknight
I think teachers should be much more understanding. However, it is ironic
that Mathematics in my old school (and I am sure in many other schools) was
the reverse of that, we had less understanding/patient teachers then in lets
say English, History or Science....

I wonder if that is because the mathematics syllabus at A level has been
harder than other subjects?

[Samsonknight]

Post by John Porcella

Post by Samsonknight

Post by John Porcella
If they only had five hours of contact time each week, then they have no
choice but to blast their way through the syllabus.

The above still doesn't justify their poor teaching in my view.

I cannot agree with poor teaching, it serves nobody, that is for certain.
In respect

Post by Samsonknight
to the way math's was taught in my old school.
WE had a few good teachers but the standard procedure for many teachers at
my old school was: Spend 20 minutes learning the concepts behind the

topic;

Post by Samsonknight
then learn the formulae in that topic and do some exercises, then move

onto

Post by Samsonknight
another topic where the teacher makes absolutely no effort to link that
topic to x other topic. It also does not help when math's teachers

patronize

Post by Samsonknight
you, because you asked an elementary question that they *assumed* that you
should know.

My own mathematics tutor was forever telling me that something that I asked
was "assumed knowledge" and my standard response was to tell him that
assumptions are dangerous and then he would teach me what I was thought to
know already.

I agree. Yes in theory we should know so and so, but if we don't then there
is no point moaning about it like some do. It would be a lot quicker and
much more beneficial as you said if the problem was reinforced right there
and then.

Post by John Porcella

Post by Samsonknight
It's bad for your confidence in the subject.

For many, I agree.
Which in turn can cause

Post by Samsonknight
problems, as the student ends up lacking creativity and flair in the

subject

Post by Samsonknight
because he/she is too scared to try different approaches to a problem in
case they get the wrong answer - or he/she doesn't know what on earth they
are doing, due to shakey unresolved problems in their foundations..

Difficult to disagree.

Post by Samsonknight
Math's and I am sure you will agree is all about understanding,

For the level that we are doing it, it is about method and accuracy, which
display some understanding.
which is why

Post by Samsonknight
I think teachers should be much more understanding. However, it is ironic
that Mathematics in my old school (and I am sure in many other schools)

was

Post by Samsonknight
the reverse of that, we had less understanding/patient teachers then in

lets

Post by Samsonknight
say English, History or Science....

I wonder if that is because the mathematics syllabus at A level has been
harder than other subjects?

Theres too much arrogance in the way mathematics is taught. I really don't
know why, but some teachers that teach mathematics expect us all to be
geniuses in the respect that we should *get* every mathematical concept
first time round. When in reality, only a handful are able to get
mathematical concepts first time round. But for the rest of us, it takes
time for things to *click*, and that is the most important part of AL
Mathematics. After this happens, everything else seems to falls into place.

I found Mechanics 1 harder then C3, only because with Mechanics everything
was new, whereas C3 built upon the theories in C1 and C2. Similarly I found
P1 (C1,and a tiny bit of C2) much harder then C3 & the latter part of C2,
due to the time it took to think of mathematics in a mathematics sort of
way.

In other subjects, the arrogance is less and the teachers are much more
sympathetic towards the student if he/she doesn't understand "something".
Primarily due to the lack of impatientness and the whole "assumption" balava
as stated above.

Post by John Porcella
--
MESSAGE ENDS.
John Porcella

[John Porcella]

Post by Samsonknight
I have decided to do M1 and M2 as my applied units. So I am wondering if
that will give me an advantage over the student that does Statistics and M1
as part of their whole A-level. Reason being, from doing both S1/M1.
Mechanics seems to be harder then statistics.

It is a personal thing. Some might prefer to stick to one type of applied
mathematics. Certainly by studying for M2, you will probably then find M1
easier. However, I suspect that M2 is slightly more advanced than M1, so M2
might be harder than S1. On the other hand, learning the first papers of
two different mathematics applications might be harder work.

Also, I can imagine that the

Post by Samsonknight
content in the Mechanics could come in handy when dealing with programs that
require some knowledge of physics. Games programming for
example...Statistics seems to be handy for those who want to go into a
business related field. Banking, Economics etc.

...and surely a lot of computer programming is business oriented?

Post by Samsonknight
Do Admission tutors look at the applied units students take as part of their
maths A-levels? Or is the overall grade what counts.

With the number of mathematics A levels in decline of late, I should not be
surprised if they are grateful for anyone with a good grade, whatever the
units taken.

[Samsonknight]

Post by John Porcella

Post by Samsonknight
I have decided to do M1 and M2 as my applied units. So I am wondering if
that will give me an advantage over the student that does Statistics and

M1

Post by Samsonknight
as part of their whole A-level. Reason being, from doing both S1/M1.
Mechanics seems to be harder then statistics.

It is a personal thing. Some might prefer to stick to one type of applied
mathematics. Certainly by studying for M2, you will probably then find M1
easier. However, I suspect that M2 is slightly more advanced than M1, so M2
might be harder than S1. On the other hand, learning the first papers of
two different mathematics applications might be harder work.

Yeah, exactly John you are spot on. I also find S1 boring personally. So it
may just be a better option of doing M2, as it not only reinforces earlier M
skills, but also reinforces the skills gained in Core. S1 is easier I agree,
but it's a risk as you've rightly said by:

"On the other hand, learning the first papers of two different mathematics
applications might be harder work."

I cannot afford to backtrack massively at this time of year by doing one
module then forgetting some aspects of the earlier modules I have learnt,
because that module doesn't reinforce anything from the other modules.

Post by John Porcella
Also, I can imagine that the

Post by Samsonknight
content in the Mechanics could come in handy when dealing with programs

that

Post by Samsonknight
require some knowledge of physics. Games programming for
example...Statistics seems to be handy for those who want to go into a
business related field. Banking, Economics etc.

...and surely a lot of computer programming is business oriented?

Yeah sure, which is why I can see why stats can prove useful. However I hope
to go into games programming after my degree, so I think it is better that I
have fundamental concepts such as kinematics,dynamics & statics of a
particle under my belt - as I have not done physics for years.

Post by John Porcella

Post by Samsonknight
Do Admission tutors look at the applied units students take as part of

their

Post by Samsonknight
maths A-levels? Or is the overall grade what counts.

With the number of mathematics A levels in decline of late, I should not be
surprised if they are grateful for anyone with a good grade, whatever the
units taken.

Yeah, as Matthew said. I feel it is a shame though that the applied modules
are not looked at. As I am very sure Mechanics is a lot more challenging
then Statistics.

Post by John Porcella
--
MESSAGE ENDS.
John Porcella