New maths and further maths A Levels

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The situation would of course get somewhat better but you are either overestimating the ability of the general cohort or underestimating STEP. People would get better on average but I highly doubt that much better, and either you would have the vast majority of people failing or absolutely laughable grade boundaries to ensure reasonable numbers pass.

I don't understand why people are so pessimistic about the hopes of this country becoming smarter. In China, it is often that the poorest students achieve the highest grades simply because they know what is expected of them.
Maybe if we set higher standards people would actually try harder to reach them. Maybe.

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Reply 81

username937760

Original post by arrow900

This is all well and good but the Chinese A Level Maths papers are still nowhere near as difficult as STEP. One difference that should be noted is that they have a much larger emphasis on Geometry in China, and I don't believe teach integration until university.

(See here: http://www.thestudentroom.co.uk/showthread.php?t=2719561 )

Reply 82

SmashTimeFool

I can see STEP being used as entry requirement for every uni soon since A-level Maths are getting easier and easier :tongue:

Reply 83

arrow900

Original post by DJMayes

Yes but then this at least encourages participation in Olympiad type maths questions which enhances ones problem solving ability. The same can't be said about the informal approach taken to Calculus at A level, where all we are required to do is familiarize ourselves with integration and differentiation as Algorithms and nothing more.

Tbh I don't understand the need to even cover calculus at A level, as every maths based courses at University teaches Analysis which basically starts from scratch.

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Reply 84

username937760

Original post by arrow900

I don't think that's the important point - the important point is that it is infeasible to suggest making A Level Maths exams the same difficulty as STEP when the Maths exams taken by the best countries in the world at Maths are still noticeably easier than STEP. STEP is, and likely always will be, the extension exam for entry into the top universities.

Reply 85

arrow900

Original post by DJMayes

You may be right, but we'll never know what this countries limitations are if we don't try.

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Reply 86

Mr M

Study Forum Helper

Original post by DJMayes

I was teaching a Year 12 who is about to go into Year 13 yesterday and he needed to differentiate x with respect to x. After staring at it for 30 seconds he said "I should know this" followed by "Is it 0?" and "Oh I know. x squared?".

Reply 87

Mr M

Study Forum Helper

Original post by arrow900

Tbh I don't understand the need to even cover calculus at A level, as every maths based courses at University teaches Analysis which basically starts from scratch.

The majority of users of calculus never study analysis.

Reply 88

Stickman

Original post by arrow900

Tbh I don't understand the need to even cover calculus at A level, as every maths based courses at University teaches Analysis which basically starts from scratch.

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If you don't cover calculus at a level for engineering related courses at unis like Oxbridge/Imperial , then you'll struggle my friend.

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Reply 89

davros

Original post by arrow900

Tbh I don't understand the need to even cover calculus at A level, as every maths based courses at University teaches Analysis which basically starts from scratch.

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The same reason we don't teach people how the internal combustion engine works before they're allowed to drive, or why we don't get primary school kids to learn the philosophical basis of integers as set cardinality before asking them to add up. Starting something "from scratch" doesn't necessarily make you better at it and can occupy an enormous amount of time that would be better spent elsewhere. Maths is a facilitating subject for a lot of people - it's important that they know the techniques of calculus, but the foundations are unimportant.

I'm all for increasing rigour and raising standards - and I broadly like the new draft proposals - but I think you've got to start earlier than A level to build people's confidence. We should be asking why A level students on TSR can't add two fractions together confidently before wondering why we can't raise our game at A level.

Original post by Mr M

You should be careful - someone might see this as a reflection on your teaching ability :biggrin:

Reply 90

Dalek1099

Original post by Mr M

New maths and further maths A Levels are being introduced for first teaching from September 2016.

Click to read the new content for maths and further maths.

These should be read in conjunction with the report from ALCAB.

Decision maths is dead. Exams are longer and less structured. There is no module choice in A Level. There is little choice in FM. Coursework is gone.

This is not necessarily the case "There is potentially a place in further mathematics for a serious strand of mathematics based on discrete mathematics and this could be considered as an additional strand alongside mechanics and statistics. However, this will require scrutiny to ensure that it will be perceived as a valuable part of further mathematics." so it looks like decision mathematics may well form part of further mathematics.Can anyone else find out where it says AFM is dead? if it is it is a real shame and shows how bad the Department of Education has become because all universities for Maths and mathematically related courses want their students to study as much mathematics as possible and I feel that Additional Further Maths gives the very best maths students a chance to stand out and enrich their mathematical study making them more prepared for their university course.

Reply 91

DFranklin

Original post by Dalek1099

Can anyone else find out where it says AFM is dead? if it is it is a real shame and shows how bad the Department of Education has become because all universities for Maths and mathematically related courses want their students to study as much mathematics as possibleComments I've heard from (generally top) universities usually bemoan the *depth* of student knowledge, not the breadth of it. (For students doing M+FM, at any rate. M by itself doesn't really cover enough by itself IMHO).

Reply 92

Claree

Original post by arrow900

I can see why calculus should be taught at A level. A level maths isn't just intended for people going on to do maths degrees but also e.g. science and engineering degrees, where it is use of calculus/familiarisation with the "algorithms", not formal analysis, that is needed most. :smile:

To a future engineer, basic calculus at A level would probably be far more useful than solving Olympiad-style number theory problems. :tongue:

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Reply 93

Dalek1099

Original post by DFranklin

Comments I've heard from (generally top) universities usually bemoan the *depth* of student knowledge, not the breadth of it. (For students doing M+FM, at any rate. M by itself doesn't really cover enough by itself IMHO).

Additional Further Maths requires a deeper understanding of Mathematics as you do all of the hardest modules like M4-M5 which are seriously probably like Mechanics modulesv at university from what I have heard and they require you to be superb at pure and mechanics all at once.

Reply 94

the bear

Original post by loperdoper

Decision is going, I am crying forever.

No, I understand why people would see it as the least maths of the maths, so to speak. However, I'm always a fan of more choice so it's a shame to see that there's no longer a third route for students who may not be as strong in science-related maths and not enjoy statistics, and it could make them want to drop it?

But alas, what do I know.

ermm no, in my humble opinion that honour goes to SAMPLING TECHNIQUES which have triumphantly reappeared :mob:

Reply 95

the bear

Original post by Arithmeticae

I think it's about standardizing the normal distribution in terms of stretches and translations etc.

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not sure why that would help you understand Normal Distribution tho' :confused:

Reply 96

username937760

Original post by Mr M

I have unfortunately seen many similar things occur in classes when I was doing A Level; and often from students who on paper sound decent at the subject (B grade and above)!

Original post by Dalek1099

Not really - M4 has little bearing on university mechanics over perhaps introducing basic concepts such as greater consideration of energy and calculus in kinematics, at least as far as Edexcel goes. M5 has a bit more overlap with content; variable mass is much the same at university but although moments of inertia are common threads in both, at university they were part of a much larger consideration of systems of particles and were approached quite differently.

University mechanics feels quite different to A Level from my experience (only a first year Cambridge course, which is worth bearing in mind) as it has more emphasis on derivation (You can be asked to prove conservation of energy for objects moving under forces such as gravity, for example, or to derive Kepler's laws or the orbital equation). I think the difficulty of questions ramps up considerably as well. Even in the first year there is a lot of completely new content (Electromagnetism, Orbits, Special Relativity to name a few) and significantly more in later years.

Reply 97

Dalek1099

Original post by DJMayes

I have unfortunately seen many similar things occur in classes when I was doing A Level; and often from students who on paper sound decent at the subject (B grade and above)!

Not really - M4 has little bearing on university mechanics over perhaps introducing basic concepts such as greater consideration of energy and calculus in kinematics, at least as far as Edexcel goes. M5 has a bit more overlap with content; variable mass is much the same at university but although moments of inertia are common threads in both, at university they were part of a much larger consideration of systems of particles and were approached quite differently.

University mechanics feels quite different to A Level from my experience (only a first year Cambridge course, which is worth bearing in mind) as it has more emphasis on derivation (You can be asked to prove conservation of energy for objects moving under forces such as gravity, for example, or to derive Kepler's laws or the orbital equation). I think the difficulty of questions ramps up considerably as well. Even in the first year there is a lot of completely new content (Electromagnetism, Orbits, Special Relativity to name a few) and significantly more in later years.

I don't think I really expected M1-M5 to cover first year Mechanics at Cambridge I think I meant just an average universities courses.
How much do you think Additional Further Maths helped towards your Cambridge Maths Degree and to STEP?

Reply 98

username937760

Original post by Dalek1099

It helped me more than perhaps others because my school did not teach FP3, or M3 and above. The added statistics was largely useless for both thus far, but the added Mechanics was very useful (As I think having only done M1 + M2 is not a lot of Mechanics experience, or sufficient to attempt the majority of questions in STEP III Mechanics). However by the time it gets to M5 it is only giving you access to another Mechanics question each year if you are lucky. I suppose the added Mechanics experience was also useful for Tripos but the paper with Mechanics did transpire to be my worst by a good margin.

I don't so much bemoan the loss of AFM for its applicability - I'm not sure you can find a more niche subject, and the majority of the important content will be covered again in much greater depth, I believe. I simply felt that for mathematicians it was a more interesting fourth choice than any other subject and (given that chances are it would have to be self taught) a good way of demonstrating interest in the subject for university applications.

Reply 99

atsruser

Original post by Dalek1099

I don't think I really expected M1-M5 to cover first year Mechanics at Cambridge I think I meant just an average universities courses.

An "average" 1st year university course in mechanics will cover far more, and far more quickly, than M1-M5 at A level. Typically you're going to see some combination of:

1. A fully 3D vector-based approach
2. Frequent use of different coord systems and transformations between them
3. 3D rotations; Euler angles etc
4. Philosophical underpinnings; e.g. concept of inertia; galilean transformations
5. Rotating frames; "fictitious" forces; Coriolis force
6. Rotational mechanics; MI, torque etc
7. Forced and damped oscillations from a DE point of view.
8. Variable mass systems
9. Conservative forces; path integrals; energy conservation, div, curl and all that.
10. Motion under gravity; central forces; orbits
11. Small oscillations and approximations; stability
12. Lagrangian formalism and its applications
13. General treatment of the two-body problem
14. Intro to special relativity; Lorentz transformation; relativistic energy; 4-vectors etc

et al.

This is somewhat off-topic though.