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Maths graduates can't do STEP?

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I think this is fundamentally where we disagree. I don't believe most degree courses make you do stuff that's similar or as hard as STEP. They may water it down by handing out model answers to Qs, and then repeating those Qs in the exam; but then that's not really STEP is it. Infact, it seems like most degree courses don't even cover material that relevant to STEP (nor as difficult).

Well, given I've seen exam questions from loads of universities (they are often used as examples in textbooks), I'd disagree.

Note, as usual, I'm arguing from experience, you're talking from "belief".

Based on your final post, it doesn't sound like you'd find STEP much easier now than 20 years ago, even with practise. And bare in mind you're a quick learner and very sharp; a lot of people just don't improve.

Again, I just don't understand your logic.

It's 20 years since I studied mathematics; I have a good grasp of the material, but I am rusty enough that, for example, I always have to check whether to divide or multiply by du/dx when doing integration by substitution. And yet I'm better at STEP now than when I basically spent most of a year doing little but prepare for my S-level (STEP equivalent) exams.

To me, this is a clear indication that mathematical experience/knowledge can make up for a lot of exam sharpness.

It's also worth noting that "low-S, 1" to "118+, 110+" is actually a pretty substantial improvement.

That you conclude the exact opposite, is, um, interesting.

For what it's worth, back when I was studying at Cambridge, when I had both the knowledge and the exam sharpness, I don't have much doubt I could have got a perfect 120/120 in STEP II/STEP III. I think quite a few people could have done the same.

Infact, I remember a post of yours where you say some people just never get to grips with STEP and don't improve, even after 6 months. I'm 100% sure these peope went on to do Maths degrees and get 1sts/2.1s.

Some of them probably did. Quite a lot of them won't. And quite a lot of those that do will be able to deal with STEP by the end of their degree.

3 years of full time directed study is quite different from 6 months working on your own while still studying for other A-levels.

I guess now this argument will turn to me being obsessed about STEP.

You do seem to make an incredible number of posts about it. (Although I also have a lot of STEP posts, most of mine are actually to do with helping people with STEP).

Reply 21

DFranklin

Original post by Physics Enemy

Because after your degree, MSc, job etc and helping out students on STEP, you're perhaps a little better and more experienced in spotting how to do the Qs, than when you were 18. The mechanics of doing it, as you said, is the easier part.If the mechanics is the easy part, why have you repeatedly complained that STEP is a speed test and you'd have been fine if you'd had more time?

We're on different pages. I'm not talking about exam sharpness, I'm talking about ability and intuition. My point is, you can learn as much material as you want and be 'exam sharp', but if you don't have 'it', then nothing will save you. What you're talking about is the converse; you have 'it', but lost sharpness by not doing much Maths, yet you do fine.

Except you're the one saying that 'it' is some mysterious non-fungible thing that can't be taught, and yet my STEP ability improved a *lot* due to doing a degree.

This supports my entire talent/'it'/ability lines of argument. The knowledge in your degree(s) can't be a factor, because STEP is based on pre-uni knowledge.

This isn't true; there are lots of STEP questions that are basically "here's something from university maths, here are some hints on how to do it, see how you get on".

In addition, you need to consider the converse: there's lots of university topics that include "oh, by the way, you now need to solve this integral that's 3 times harder than anything you saw at A-level", or "now find the solutions to this complicated differential equation".

By analogy: The GCSE exam is obviously based on pre-A-level knowledge. But it would be very surprising to find someone who got 'B' in the GCSE, went on to get an 'A' at A-level, and hadn't improved to an 'A*' in the GCSE (excluding the geometry stuff you only do at GCSE, perhaps).

Perhaps, but taking someone who can't do STEP pre-uni after months and months of toil, into someone with great intuition who can do STEP after their degree, is comparatively a huge improvement. I am of the belief that one's natural ability will cap their grades assuming they put the work in.

Sure, the question is, where is the cap? If pushed, I might concede that a lot of people doing a maths degree these days can't do STEP (I find it shocking, and I don't honestly believe your "evidence", because I've seen you talk a lot of nonsense you can't back up, but still).

However, I can assure you that 20 years ago, most graduates from a decent university could do STEP. (That might not be true of teachers, but most neither have a maths degree, nor have done university mathematics for many years). I don't believe natural ability has changed so much in 20 years, so I don't see that as being the limiting factor here.

What would you tell prospective athletes or snooker players; if you're failing, just put more effort in and you'll get there?

If someone is in full-time training for a football career, and after 3 years they can't beat local amateurs, I'd say they've made a poor choice of career. (And the person who said, "yeah, turn pro" has given them bad advice).

Your whole position seems based on STEP being some amazing level of maths that only a very few elite can do. But there are actually a lot of people getting these grades every year.

You're trying to tell us a degree can change the way someone's brain works and thus they'll spot how to do tricky STEP Qs. I don't agree.

I know you don't agree. I mean, how could studying Laplace Transforms at university possibly help you to do last year's question (or possibly the year before) on Laplace Transforms? That's an extreme case, but there are lots of less extreme examples.

Simon also says Cambridge Maths papers are 'different', but of a similar standard to STEP. This also supports my/our view that most Maths grads won't be able to do STEP, by virtue that their uni papers are (much) easier than Cam ones.

This is one of those statements that's "possibly true, but misleading".

For example, when I did Part II, one of the toughest courses was reckoned to be DAG (Differential Analysis and Geometry). But if you were to look at the worked solutions, you could probably do about 4 of them in the time of one STEP III question. The point being that the difficulty was in the concepts and the abstraction, not the 'manipulation of symbols on paper' that STEP tends to emphasize.

The examiners usually trade things off; the more difficult the concepts, the "easier" the questions. In some of the more 'mechanical' topics, the examiners have set questions where the algebra involved makes STEP questions look straightforward.

Since the better mathmos tend to avoid these topics (because they take longer in the exam), you tend to get bias towards "I pick the topics I understand really well that don't have loads of manipulation, and they're no harder than STEP".

Yet some students get SS on STEP doing just that, whilst others do 4 year degrees and still don't have a clue. So what does that tell you? Talent!

No one is denying talent. But at the same time an 'S' in STEP I or STEP II is really not that much of an achievement for someone with years of maths study at university level.

Reply 22

IrrationalNumber

Original post by DFranklin

If so, I'm not going to pretend I think that first from Warwick is worth very much (*).

(*) To elaborate: it's probably possible to concentrate on a very narrow section of courses so that although your degree was a decent standard, you still aren't happy with STEP. I wouldn't say that's a worthless degree, but I do think it's misguided - it's one thing to specialise, but you should still have a reasonable general standard. If you read Littlewood's Miscellany, he talks a fair bit about applied maths, despite the fact that he was a number theory specialist.

I feel the need to stick up for Warwick's degree. There are a decent number of students who will work hard to understand difficult concepts and practice working with them and get a first. Those people will surely be capable of doing STEP. The people who get a first from Warwick who are unable to do step are likely to be the ones who tried to take a large number of modules from other departments. They may not be able to do STEP, but they can understand economics or have a decent knowledge of various programming languages and concepts in computer science. I don't think that's a bad thing. Instead of wasting their time trying to understand maths that isn't coming easily to them, they have learnt stuff from other degrees (and have a working knowledge of analysis and algebra). Seems worthwhile to me, and it deserves recognition.

In any case, I feel like Warwick's exams are far harder than any STEP exam.

Reply 23

DFranklin

Original post by IrrationalNumber

I largely agree, although I think if you go too far down that route you may have a worthwhile degree, but it probably shouldn't be directly compared with a maths degree.

At the end of the day, a certain amount of common sense is helpful in these discussions - otherwise all the caveats and reservations double the length of everything posted.

In any case, I feel like Warwick's exams are far harder than any STEP exam.

As I said earlier, "harder" is actually quite a vague term. But to back you up, I seem to recall some Warwick mechanics questions being posted that were clearly harder than anything you'd likely see on STEP.

(edited 13 years ago)

Reply 24

DFranklin

I'm not wasting any more time with this. The fact that you keep posting analogies that are off by 3 orders of magnitude illustrates just how skewed your own understanding is.

Reply 25

Simplicity

Original post by Physics Enemy

Do you believe there are uni maths professors who can't do IMO? What about Maths teachers who can't do STEP? What about students better/brighter than their teacher? What about young whizzes on here vs generic Masters students?

My old F Maths teacher has decades of Maths experience, more than you in numbers terms. He's taught Further Maths for years and years, done a 4 year engineering degree (back when it was 'hard'). He can't do STEP. The other F Maths teacher struggled to help me with the Ox Physics Maths test back when I was fumbling through some past papers before interviews.

What's their excuse? Are they worse than Maths grads? How could that be, they're further along in the system ... (!)

I think I understand your problem.

Mathematics=/= the crap you are doing now.

In engineering degree you don't do proofs, you don't do axioms and set theory or the gay stuff that justifies calculus e.t.c. You do Mathematical methods in a engineering degree. So to suggest that a engineering graduate is more experienced than DFranklyn at Mathematics is very stupid. Also, F Maths isn't Maths experience,

What ever you think is Maths or what Maths grads do is stupid. It certainly isn't STEP or IMO. Also, are you seriously suggesting that F Maths teacher are further along in the system, what the hell you mean by that?

Now not to insult Maths teacher, I'm sure they enjoy children hating you for forcing them to learn it. But, to become a Maths teacher you don't need to know Uni Maths, you don't even need to get a first or pass STEP. You just need some teacher training. I could teach F Maths, however I have no teaching experience so that would be the big problem not the Maths . If a person was good at Maths, they wouldn't become a Maths teacher as they could earn more money.

P.S. Can't imagine a worse job than teaching Maths.

(edited 13 years ago)

Reply 26

Square

(edited 13 years ago)

Reply 27

DFranklin

Original post by Square

in my experience, STEP is a weird type of exam.

It takes some very basic maths and asks 'difficult' questions on it. The only way to even attempt STEP seems to be to prepare solely by doing similar type STEP questions and studying the limited syllabus in great depth, apart from the odd few smart people who walk in and get S,S.Actually, I don't really agree. Although university maths isn't directly relevant, you do so much more in 3 full time years that even if 1% of stuff is relevant, it adds up to quite a lot.

For example, taking this years 2010 STEP I paper (chosen simply as the most obvious one to look at):

Q1: This is very much A-level, but you'll see not dissimilar equations if you end up grinding out Mobius transform questions by hand, for example.

Q2: Again, really an A-level question, but you do similar sketches when analysing convergence in Numerical Methods questions.

Q3: Really, this is pure A-level. But, the bit most people on here struggled with was the handling the if-and-only-if side of things, and that should be straightforward when you have years of formal proofs under your belt.

Q4: The manipulation needed in these integrals is very similar to what you do with hyperbolic functions. Also, the mucking about with denominators of 1/sqrt(x+1) - 1/sqrt(x) etc. is similar to proofs you do in analysis for derivatives for sqrt(x) etc.

Q5: During a degree, you'll see explicit demonstrations of how to find these sums. Probably several times.

Q6: The question is about a standard method of solving differential equations that you're taught at university.

Q7: By university vector calculus standards, this is an easy question.

Q8: This should be trivial to anyone who's done any Number Theory at university.

Q9: Depends on what you do at Uni. I'll count this as a "no real help from Uni" question.

Q10: Straightforward if you've done vector calculus.

Q11: Again, I'll count is as "no real help from Uni", although uni mechanics questions are usually around this difficulty.

Q12: First part of the question is bookwork from Uni. Rest is easy by university probability standards.

Q13: I'll count as a "no real help from Uni".

So, of 13 questions, there are 4 or 5 where a uni grad should be thinking "Yeah, I've been shown how to do problems like this" (explicitly, Q5, Q6, Q8 Q10 and Q12)", and another 3 or 4 where they should have a significant advantage from university knowledge (Q1, Q3, Q4, Q7).

Yeah, it's not quite as simple as that in practice, but conversely, university doesn't need to teach you how to do *all* the questions. If you get 3 cheap questions from uni knowledge, you only need roughly a "STEP grade 3" type of performance on the rest of the exam to get an S.

Reply 28

DFranklin

Original post by Physics Enemy

Yes shown, not done it themselves. So unless they've seen it in model answers/lectures (in other words, copying the lecturers work), they're screwed if they aren't good enough. If the STEP examiners knew uni people would sit STEP one year, they would avoid Qs that are gifts to uni students, and just have ones that focus on A-Level knowledge.

"Unless...", "If...".

I thought we were discussing the STEP exams as they actually are, not some fantasy version in your head.

You're the one who keeps saying "University material isn't relevant to STEP", so why you're now saying the examiners would need to avoid questions that are gifts to uni students I don't know.

Furthermore, a 'STEP Grade 3'performance when faced with the unfamiliar Qs, would indicate their true ability. It says they're of that calibre.

Well, that's a different question. Is someone who gets a 1 in STEP with only A-level experience more talented than someone who can only do so with 3 years of university experience. Almost certainly. But they both get the same STEP grade, nonetheless. Since this is a point that I've been arguing and you've been denying, I fail to see why you think this helps your case.

I was expecting some sort of 'these Qs are easy for uni students, they're now smarter and have better skills, they should have the intuition to spot how to solve them, irregardless of knowledge' type of response.

Well, the fact you were expecting that knowledge doesn't matter says a lot about your understanding.

Although you should note that they do have better skills - a university graduate will be far more confident about proof techniques, they'll know number theory, they will be far more practised with vectors, etc. As to intuition, as many famous mathematicians have said, a large part of what people think of as intuition is recognizing a problem as similar to something you've seen before.

(edited 13 years ago)

Reply 29

Dirac Delta Function

having just looked at STEP 2010, I have to agree with DFranklin. It's looking a hell of a lot easier than when I first saw a step paper as an A level student, and Im not even a maths grad.

Reply 30

Slumpy

Original post by Physics Enemy

And infact, it's not even always the case that STEP examiners give full marks for stuff done the wrong way.

I'm not sure I believe that.

Reply 31

Chwirkytheappleboy

Despite having a first class degree in maths and physics, I'm pretty sure I'd fail if I took STEP now. I'm also crap at proving stuff. You can quite easily get through a maths degree by rote memorisation of exam questions... Only the intelligent people actually understand what's going on, the rest of us just bumble on through wondering what it is that we're writing down

Reply 32

DFranklin

Original post by Physics Enemy

Well it depends on the paper, the year etc. And what modules a certain person took in their degree, and where they did they degree too. The argument you're drawing up is grads may well be able to do STEP (I) if they've seen it before. In other words, had the answers handed to them by someone else. That's pretty much cheating. This is just so ridiculous that it's obvious there's no point discussing this further.

Reply 33

Schoolio93

STEP is a nightmare. Out of the around 400 offer holders only 250 meet the conditions - reason: didn't meet the STEP criteria. It's really frustrating, but that lets Cambridge distinguish between students that are extremely bright and students that are extremely^10000 bright.

Reply 34

Slumpy

Original post by Physics Enemy

You overrate degrees and underrate STEP, this is obvious. People are flunking STEP badly and getting 90% in their degree. To me this paints a clear picture. Your Kings' anecdotes seem out of date to me. Infact, I'm going to check my post history and find those Imperial Maths papers. :smile:

I didn't find STEP too hard, but uni maths is much much harder. They're basically different, and comparing them is fairly fruitless. Despite this I must agree with DFranklin that someone who's just finished a maths degree will do better at STEP than when they'd just left school.

Edit:

Original post by Schoolio93

Not even 250 meet the conditions, it's something like 140-170 meet them, and most of the rest narrowly miss STEP(as I recall).

(edited 13 years ago)

Reply 35

Noble.

Original post by Physics Enemy

That's not the argument and nobody would suggest otherwise. You should read more closely.

No offence intended, but how it is you always manage to get into arguments wherever you go on the maths forum? :tongue:

Reply 36

DFranklin

As far as STEP numbers go, about 300/1000 get a 1 or better in STEP II, about 300/700 get a 1 or better in STEP III.
Only about 150/1000 get a 1 or better in STEP I; of course many taking STEP I don't need to get a 1.

About 12000 people take further maths. So roughly 3% of them get at least a 1 in STEP III, probably around 5% get a 1 in either STEP II or STEP III.

Rare, but a heck of a lot more common than some of the analogies being punted around (being signed for Man United!).

(edited 13 years ago)

Reply 37

Mark13

Original post by DFranklin

About 12000 people take further maths. So roughly 3% of them get at least a 1 in STEP III, probably around 5% get a 1 in either STEP II or STEP III.

I expect the actual figures are actually lower than this; not everyone taking STEP is an A level further maths candidate.

Reply 38

DFranklin

Original post by Mark13

I expect the actual figures are actually lower than this; not everyone taking STEP is an A level further maths candidate.

I think something over 90% of them will have A-level FM; they may have taken it the year before, but if you're looking at number of 1/S grades I suspect it doesn't make much odds in terms of calculating "what proportion of people doing FM get a 1 in STEP".